Embryo editing.page

---
title: Embryo editing for intelligence
description: A cost-benefit analysis of CRISPR-based editing for intelligence with 2015-2016 state-of-the-art
tags: decision theory, biology, psychology, statistics, transhumanism
created: 22 Jan 2016
status: in progress
confidence: likely
importance: 10
...


# Embryo editing

One approach not discussed in Shulman & Bostrom is embryo editing, which has compelling advantages over selection:

1. Embryo selection must be done collectively for any meaningful gains, so one must score all viable embryos; while editing can potentially be done singly, editing only the embryo being implanted, and no more if that embryo yields a birth.
2. Further, a failed implantation is a disaster for embryo selection, since it means one must settle for a possibly much lower scoring embryo with little or no gain while still having paid upfront for selection; on the other hand, the edit gains will be largely uniform across all embryos and so the loss of the first embryo is unfortunate (since it means another set of edits and an implantation will be necessary) but not a major setback.
3. Embryo selection suffers from the curse of thin tails and being unable to start from a higher mean (except as part of a multi-generational scheme): one takes 2 steps back for every 3 steps forward, so for larger gains, one must brute-force them with a steeply escalating number of embryos.
4. Embryo selection is constrained by the broad-sense heritability, and the number of available embryos.

    - No matter how many GWASes are done on whole-genomes or fancy algorithms are applied, embryo selection will never surpass the upper bound set by a broad-sense heritability 0.8; while the effects of editing has no known upper bound either in terms of existing population variation, as there appear to be thousands of variants inclusive of all genetic changes, and evolutionarily novel changes could theoretically be made as well^[Although it is hard to imagine any parent authorizing the creation of never-before-seen mutations in their child, regardless of how compelling a neurobiological mechanistic case is made for it. In comparison, switching SNPs is knowably safe because they all exist in the human population at high frequencies and can be observed to correlate or not with health problems. Animal experiments can help but inherently are unrepresentative of effects in humans, so the first child will still be subject to an unknown and probably large risk.] (a bacteria or a chimpanzee is, after all, not simply a small human who refuses to talk).
    - Editing is also largely independent of the number of embryos, since each embryo can be edited about as much as any other, and as long as one has enough embryos to expect a birth, more embryos make no difference.
5. Editing scales linearly and smoothly by going to the root of the problem, rather than difficulty increasing exponentially in gain - an example:

    as calculated above, the Rietveld et al 2013 polygenic score can yield a gain no greater than 2.58 IQ points with 1-in-10 selection, and in practice, we can hardly expect more than 0.14-0.56 IQ points in practice due to fewer than 10 embryos usually being viable etc.
    But with editing, we can do better: the same study reported 3 SNP hits (rs9320913, rs11584700, rs4851266) each predicting +1 month of schooling, the largest effects translating to ~0.5IQ points (the education proxy makes the exact value a little tricky but we can cross-check with other GWASes which regressed directly on fluid intelligence, like Davies et al 2015's whose largest hit, rs10457441, does indeed have a reported beta of -0.0324SD or -0.486) with fairly even balanced frequencies around 50% as well.^[Indeed, most of the reported hits have balanced frequencies. I haven't seen anyone specifically mention why this is so. My best guess is that it's the same reason we expect to see SNPs with the largest effects detected first: it's due to [statistical power](!Wikipedia). Imbalanced reduces power since the smaller group has larger standard errors; hence, if there are two SNPs with the same effect, but one has a frequency of 10% (with 90% of people having the bad variant) and another has an even 50-50 split, the second will be detected earlier by GWASes. This seems more sensible than expecting some force like [balancing selection](!Wikipedia) to be operating on most IQ-related SNPs.]
    So one can see immediately that if an embryo is sequenced & found to have the bad variant on any of those SNPs, a *single* edit has the same gain as the entire embryo selection process!
    Unlike embryo selection, there is no inherent reason an editing process must stop at one edit - and with two edits, one doesn't even need to sequence in the first place, as the frequency means that the expected value of editing the SNP is 0.25 points and so two *blind* edits would have the same gain!
    Continuing, the gains can stack; taking the 15 top hits from Davies et al 2015's [Supplementary Table S3](http://www.nature.com/mp/journal/v20/n2/extref/mp2014188x3.xlsx), 15 edits would yield 6.35 points and yes, combined with the next 15 after that would yield ~14 points, blowing past the SNP embryo selection upper bounds.
    While on average any embryo would not need half of those edits, that just means that an editing procedure will go down another entry down the list and edit that instead (given a budget of 15 edits, one might wind up editing, say #30). Since the estimated effects do not decline too fast and frequencies are high, this is similar to if we skipped every other edit and so the gains are still substantial:

    ~~~{.R}
    davies2015 <- data.frame(Beta=c(-0.0324, 0.0321, -0.0446, -0.032, 0.0329, 0.0315, 0.0312, 0.0312, -0.0311, -0.0315, -0.0314, 0.0305,
     0.0309, 0.0306, 0.0305, 0.0293, -0.0292, -0.0292, -0.0292, 0.0292, -0.0292, 0.0292, -0.0291, -0.0293, -0.0293, 0.0292, -0.0296,
     -0.0293, -0.0291, 0.0296, -0.0313, -0.047, -0.0295, 0.0295, -0.0292, -0.028, -0.0287, -0.029, 0.0289, 0.0302, -0.0289, 0.0289,
     -0.0281, -0.028, 0.028, -0.028, 0.0281, -0.028, 0.0281, 0.028, 0.028, 0.028, -0.029, 0.029, 0.028, -0.0279, -0.029, 0.0279,
     -0.0289, -0.027, 0.0289, -0.0282, -0.0286, -0.0278, -0.0279, 0.0289, -0.0288, 0.0278, 0.0314, -0.0324, -0.0288, 0.0278, 0.0287,
     0.0278, 0.0277, -0.0287, -0.0268, -0.0287, -0.0287, -0.0272, -0.0277, 0.0277, -0.0286, -0.0276, -0.0267, 0.0276, -0.0277, 0.0284,
     0.0277, -0.0276, 0.0337, 0.0276, 0.0286, -0.0279, 0.0282, 0.0275, -0.0269, -0.0277),
                  Frequency=c(0.4797, 0.5199, 0.2931, 0.4803, 0.5256, 0.4858, 0.484, 0.4858, 0.4791, 0.4802, 0.4805, 0.487, 0.528,
                  0.5018, 0.5196, 0.5191, 0.481, 0.481, 0.4807, 0.5191, 0.4808, 0.5221, 0.4924, 0.3898, 0.3897, 0.5196, 0.3901,
                  0.3897, 0.4755, 0.4861, 0.6679, 0.1534, 0.3653, 0.6351, 0.6266, 0.4772, 0.3747, 0.3714, 0.6292, 0.6885, 0.668,
                  0.3319, 0.3703, 0.3696, 0.6307, 0.3695, 0.6255, 0.3695, 0.3559, 0.6306, 0.6305, 0.6309, 0.316, 0.684, 0.631,
                  0.3692, 0.3143, 0.631, 0.316, 0.4493, 0.6856, 0.6491, 0.6681, 0.3694, 0.3686, 0.6845, 0.3155, 0.6314, 0.2421,
                  0.7459, 0.3142, 0.3606, 0.6859, 0.6315, 0.6305, 0.3157, 0.5364, 0.3144, 0.3141, 0.5876, 0.3686, 0.6314, 0.3227,
                  0.3695, 0.5359, 0.6305, 0.3728, 0.3318, 0.3551, 0.3695, 0.2244, 0.6304, 0.6856, 0.6482, 0.6304, 0.6304, 0.4498, 0.6469))
    davies2015$Beta <- abs(davies2015$Beta)
    sum(head(davies2015$Beta,n=30))*15
    # [1] 13.851
    editSample <- function(editBudget) { head(Filter(function(x){rbinom(1, 1, prob=davies2015$Frequency)}, davies2015$Beta), n=editBudget) }
    mean(replicate(1000, sum(editSample(30) * 15)))
    # [1] 13.534914
    ~~~
6. Editing can be done on low-frequency or rare variants, whose effects are known but will not be available in the embryos in most selection instances.

    For example, [George Church lists 10 rare mutations of large effect](http://www.ipscell.com/2015/03/georgechurchinterview/ "A conversation with George Church on Genomics & Germline Human Genetic Modification") that may be worth editing into people:

    > 1. [LRP5](!Wikipedia)              G171V/+        Extra-strong bones^[For [astronauts](!Wikipedia "Spaceflight osteopenia"), or simply preventing [age-related falling](!Wikipedia "Falls in older adults"), a major cause of morbidity & increased mortality in the elderly.]
    > 2. [MSTN](!Wikipedia)             -/-                  Lean muscles
    > 3. [SCN9A](!Wikipedia)           -/-                   Insensitivity to pain
    > 4. [ABCC11](!Wikipedia)        -/-                    Low Odor production
    > 5. [CCR5](!Wikipedia), [FUT2](!Wikipedia) -/-                    Virus resistance
    > 6. [PCSK9](!Wikipedia)           -/-                   Low coronary disease
    > 7. [APP](!Wikipedia "Amyloid precursor protein")                A673T/+         Low Alzheimer's
    > 8. [GHR](!Wikipedia "Growth hormone receptor"), GH       -/-                    Low cancer
    > 9. [SLC30A8](!Wikipedia)       -/+                   Low T2 Diabetes
    > 10. [IFIH1](!Wikipedia)              E627X/+         Low T1 Diabetes

    To which I would add: sleep duration, quality, morningness-eveningness, and resistance to sleep deprivation ([Kuna et al 2012](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3413799/ "Heritability of Performance Deficit Accumulation During Acute Sleep Deprivation in Twins")) are, like most traits, heritable. The extreme case is that of "short-sleepers", the ~1% of the population who normally sleep 3-6h; they often mention a parent who was also a short-sleeper, short sleep starting in childhood, that 'over' sleeping [is](https://www.reddit.com/r/science/comments/3kj669/science_ama_series_im_yinghui_fu_i_study_the/cuy7fjh) [unpleasant](!Wikipedia "Sleep inertia") & they do not fall asleep faster & don't sleep excessively more on weekends (indicating they are not merely chronically sleep-deprived), and are anecdotally described as [highly energetic](http://nymag.com/scienceofus/2015/02/what-its-like-to-need-hardly-any-sleep.html "What It's Like to Need Hardly Any Sleep 'I get three or four hours sleep a night, and I never get tired.'") [multi-taskers,](http://www.wsj.com/articles/SB10001424052748703712504576242701752957910 "The Sleepless Elite: Why Some People Can Run on Little Sleep and Get So Much Done") [thin,](http://www.bbc.com/future/story/20150706-the-woman-who-barely-sleeps "The people who need very little sleep: Is it true that some people need only a few hours of sleep? Helen Thomson talks to a woman whose genes might hint at how we all could survive on less shuteye") [with positive attitudes & high pain thresholds](http://www.npr.org/2011/04/16/135450214/eight-is-too-much-for-short-sleepers "Eight Is Too Much For 'Short Sleepers'") ([Monk et al 2001](http://onlinelibrary.wiley.com/doi/10.1046/j.1365-2869.2001.00254.x/full "A sleep diary and questionnaire study of naturally short sleepers")) without any known health effects or downsides in humans[^sleep-side-effects] or [mice](https://www.reddit.com/r/science/comments/3kj669/science_ama_series_im_yinghui_fu_i_study_the/cuy8cts) (aside from, presumably, greater caloric expenditure).

    Some instances of short-sleepers [are due to](http://www.newyorker.com/science/maria-konnikova/a-gene-makes-you-need-less-sleep "A Gene That Makes You Need Less Sleep?") [DEC2](!Wikipedia "BHLHE41"), with a variant found in short-sleepers vs controls (6.25h vs 8.37h, -127m) and the effect confirmed by knockout-mice ([He et al 2010](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2884988/ "The Transcriptional Repressor DEC2 Regulates Sleep Length in Mammals")); another short-sleep variant was identified in a discordant twin pair with an effect of -64m ([Pellegrino et al 2014](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4096202/ "A Novel BHLHE41 Variant is Associated with Short Sleep and Resistance to Sleep Deprivation in Humans")). DEC2/BHLHE41 SNPs are also rare (for example, 3 such SNPs have frequencies of [0.08%](http://www.ncbi.nlm.nih.gov/projects/SNP/snp_ref.cgi?searchType=adhoc_search&type=rs&rs=rs4963956), [3%](http://www.ncbi.nlm.nih.gov/projects/SNP/snp_ref.cgi?searchType=adhoc_search&type=rs&rs=rs1480037), & [5%](http://www.ncbi.nlm.nih.gov/projects/SNP/snp_ref.cgi?searchType=adhoc_search&type=rs&rs=rs4963955)). Hence, selection would be almost entirely ineffective, but editing is easy.

    As far as costs and benefits go, we can observe that being able to stay awake an additional 127 minutes a day is equivalent to being able to live an additional 7 years, 191 minutes to 11 years; to negate that, any side-effect would have to be tantamount to lifelong smoking of tobacco.

[^sleep-side-effects]: This may seem contrary to the many reported correlations of morbidity & mortality with shiftwork/less self-reported sleep, or less resistance to infection, but those results are always driven by the general population suffering from insomnia, stress, disease, etc, and not by the tiny minority of short-sleepers. The short-sleepers themselves do not report greater vulnerability to infection or early mortality, and I don't believe any of the bad results focus on short-sleepers.

The largest disadvantage of editing, and the largest advantage of embryo selection, is that selection relies on proven, well-understood known-priced PGD technology already in use for other purposes; while the former hasn't existed and has been science fiction, not fact.

## Genome synthesis

The cost of CRISPR editing will scale roughly as the number of edits: 100 edits will cost 10x 10 edits. It may also scale superlinearly if each edit makes the next edit more difficult.
This poses challenges to profitable editing since the marginal gain of each edit will keep decreasing as the SNPs with largest effect sizes are edited first - it's hard to see how 500 or 1000 edits would be profitable.
Similar to the daunting cost of iterated embryo selection, where the IES is done only once or a few times and then gametes are distributed en masse to prospective parents to amortize per-child costs to small amounts, one could imagine doing the same thing for a heavily CRISPR-edited embryo.

But at some point, doing many edits raises the question of why you are bothering with the wild type genome? Couldn't you just create a *whole* [human genome](!Wikipedia) from scratch incorporating every possible edit?
Synthesize a whole genome's DNA and incorporate all edits one wishes; in the design phase, take the GWASes for a wide variety of traits and set each SNP, no matter how weakly estimated, to the positive direction; in copying in the data of regions with rare variants, they are probably harmful and can be erased with the modal human base-pairs at those positions, for systematic health benefits across most diseases; or to imitate iterative embryo selection, which exploits the tagging power of SNPs to pull in the beneficial rare variants, copy over the haplotypes for beneficial SNPs which might be tagging a rare variant.
Between the erasing of mutation load and exploiting all common variants simultaneously, the results could be a staggering phenotype.

DNA synthesis, synthesizing a strand of DNA [base-pair](!Wikipedia) by base-pair, has long been done, but generally limited to a few hundred BPs, which is much less than the 23 human chromosomes' collective ~3.3 billion BP.
Past work in synthesizing genomes has included Craig Venter's minimal bacterium in 2008 with 582,970 BP; http://www.nature.com/news/2008/080124/full/news.2008.522.html
1.1 million BP in 2010 http://www.nature.com/news/2010/100520/full/news.2010.253.html
483,000 BP and 531,000 BP in 2016 http://www.nature.com/news/minimal-cell-raises-stakes-in-race-to-harness-synthetic-life-1.19633
(spending somewhere ~$40m on these projects)
272,871 in 2014 (1 yeast chromosome; 90k BP costing \$50k at the time) and plans for synthesizing the whole yeast genome in 5 years http://www.nature.com/news/first-synthetic-yeast-chromosome-revealed-1.14941
http://science.sciencemag.org/content/290/5498/1972
http://science.sciencemag.org/content/329/5987/52
http://science.sciencemag.org/content/342/6156/357
http://science.sciencemag.org/content/333/6040/348
2,750,000 BP in 2016 for _E. coli_ http://www.nature.com/news/radically-rewritten-bacterial-genome-unveiled-1.20451 "Design, synthesis, and testing toward a 57-codon genome", Ostrov et al 2016 http://science.sciencemag.org/content/353/6301/819

https://www.quora.com/How-many-base-pairs-of-DNA-can-I-synthesize-for-1-dollar

The biggest chromosome is #1, with 8.1% of the base-pairs or 249,250,621; the smallest is #21, 1.6%, or 48,129,895.
DNA synthesis prices drop each year in an exponential decline (if not remotely as fast as the DNA sequencing cost curve), and so 2016 synthesizing costs have reached <$0.3; let's say \$0.25/BP.

Chromosome Length in base-pairs Fraction Synthesis cost at \$0.25/BP
---------- -------------------- -------- ---------------------------
1           249,250,621         0.081    \$62,312,655
2           243,199,373         0.079    \$60,799,843
3           198,022,430         0.064    \$49,505,608
4           191,154,276         0.062    \$47,788,569
5           180,915,260         0.058    \$45,228,815
6           171,115,067         0.055    \$42,778,767
7           159,138,663         0.051    \$39,784,666
8           146,364,022         0.047    \$36,591,006
9           141,213,431         0.046    \$35,303,358
10          135,534,747         0.044    \$33,883,687
11          135,006,516         0.044    \$33,751,629
12          133,851,895         0.043    \$33,462,974
13          115,169,878         0.037    \$28,792,470
14          107,349,540         0.035    \$26,837,385
15          102,531,392         0.033    \$25,632,848
16          90,354,753          0.029    \$22,588,688
17          81,195,210          0.026    \$20,298,802
18          78,077,248          0.025    \$19,519,312
19          59,128,983          0.019    \$14,782,246
20          63,025,520          0.020    \$15,756,380
21          48,129,895          0.016    \$12,032,474
22          51,304,566          0.017    \$12,826,142
X           155,270,560         0.050    \$38,817,640
Y           59,373,566          0.019    \$14,843,392
total       3,095,693,981       1.000    \$773,923,495

So the synthesis of one genome in 2016, assuming no economies of scale or further improvement, would come in at ~\$773m.
This is a staggering but finite and even feasible amount: the original [Human Genome Project](!Wikipedia) cost ~\$3b, and other large science projects like the LHC, Manhattan Project, ITER, Apollo Program, ISS, [the National Children's Study](http://undark.org/article/the-death-of-a-study-national-childrens-study/) etc have cost many times what 1 human genome would.

https://en.wikipedia.org/wiki/Human_Genome_Project_-_Write
http://www.nature.com/news/plan-to-synthesize-human-genome-triggers-mixed-response-1.20028
http://science.sciencemag.org/content/early/2016/06/01/science.aaf6850.full
http://science.sciencemag.org/content/sci/suppl/2016/06/01/science.aaf6850.DC1/Boeke.SM.pdf
http://www.nytimes.com/2016/06/03/science/human-genome-project-write-synthetic-dna.html
http://diyhpl.us/wiki/transcripts/2017-01-26-george-church/

Church is optimistic: maybe even \$100k/genome by 2037 http://www.wired.co.uk/article/human-genome-synthesise-dna "Humans 2.0: these geneticists want to create an artificial genome by synthesising our DNA; Scientists intend to have fully synthesised the genome in a living cell - which would make the material functional - within ten years, at a projected cost of $1 billion"
> But these are the "byproducts" of HGP-Write, in Hessel's view: the project's true purpose is to create the impetus for technological advances that will lead to these long-term benefits. "Since all these [synthesis] technologies are exponentially improving, we should keep pushing that improvement rather than just turning the crank blindly and expensively," Church says. In 20 years, this could cut the cost of synthesising a human genome to $100,000, compared to the $12 billion estimated a decade ago.

The benefit of this investment would be to bypass the death by a thousand cuts of CRISPR editing and create a genome with an arbitrary number of edits on an arbitrary number of traits for the fixed upfront cost.
Unlike multiple selection, one would not need to trade off multiple traits against each other (except for pleiotropy); unlike editing, one would not be limited to making only edits with a marginal expected value exceeding the cost of 1 edit.
Doing individual genome syntheses will be out of the question for a long time to come, so genome synthesis is like IES in amortizing its cost over prospective parents.

The ["2013 Assisted Reproductive Technology National Summary Report"](http://www.cdc.gov/art/pdf/2013-report/art_2013_national_summary_report.pdf) says ~10% of IVF cycles use donor eggs, and a total of 67996 infants, implying >6.7k infants conceived with donor eggs, embryos, or sperm (sperm is not covered by that report) and were only half or less related to their parents.
What immediate 1-year return over 6.7k infants would justify spending \$773m? Considering just the low estimate of IQ at \$3270/point and no other traits, that would translate to (773m/6.7k) / 3270 = 35 IQ points or at an average IQ gain of 0.1 points, the equivalent of 350 causal edits. This is doable.
If we allow amortization at a high discount rate of 5% and reuse the genome indefinitely for each year's crop of 6.7k infants, then we need at least X IQ points where
((x*3270*6700) / log(1.05)) - 773000000 >= 0
x >= 1.73
or at ~0.1 points per edit, 18 edits.
We could also synthesize only 1 chromosome and pay much less upfront (but at the cost of a lower upper bound, as GCTA heritability/length regressions and GWAS polygenic score results indicates that intelligence and many other complex traits are spread very evenly over the genome, so each chromosome will harbor variants proportional to its length).

The causal edit problem remains but at 12% causal rates, 18 causal edits can easily be made with 150 edits of SNP candidates, which is less than already available.
So at first glance, whole genome synthesis can be profitable with optimization of only one trait using existing GWAS hits, and will be extremely profitable if dozens of traits are optimized and mutation load minimized.

How much profitable? ...see embryo selection calculations... At 70 SDs and 12% causal, then the profit would be 70*15*3270*0.12*6700 - 773000000 = $1,987,534,000 the first year or NPV of $55,806,723,536. TODO: only half-relatedness

TODO:
- model DNA synthesis cost curve; when can we expect a whole human genome to be synthesizable with a single lab's resources, like $1m/$5m/$10m? when does synthesis begin to look better than IES?
eyeballing http://science.sciencemag.org/content/sci/suppl/2016/06/01/science.aaf6850.DC1/Boeke.SM.pdf , 0.01/$ or 100$ in 1990, 3/$ or 0.3$ in 2015?
R> synthesis <- data.frame(Year=c(1990,2015), Cost=c(100, 0.33))
R> summary(l <- lm(log(Cost) ~ Year, data=synthesis))
R> prettyNum(big.mark=",", round(exp(predict(l, data.frame(Year=c(2016:2040), Cost=NA))) * 3095693981))
            1             2             3             4             5             6             7             8             9            10            11            12            13
"812,853,950" "646,774,781" "514,628,265" "409,481,413" "325,817,758" "259,247,936" "206,279,403" "164,133,195" "130,598,137" "103,914,832"  "82,683,356"  "65,789,813"  "52,347,894"
           14            15            16            17            18            19            20            21            22            23            24            25
 "41,652,375"  "33,142,123"  "26,370,653"  "20,982,703"  "16,695,599"  "13,284,419"  "10,570,198"   "8,410,536"   "6,692,128"   "5,324,818"   "4,236,872"   "3,371,211"

"Large-scale de novo DNA synthesis: technologies and applications", Kosuri & Church 2014 http://arep.med.harvard.edu/pdf/Kosuri_Church_2014.pdf

## CRISPR

The past 5 years have seen major breakthroughs in cheap, reliable, general-purpose genetic engineering & editing using [CRISPR](!Wikipedia), since the [2012 demonstration that it could edit cells](http://science.sciencemag.org/content/337/6096/816.long "'A Programmable Dual-RNA-Guided DNA Endonuclease in Adaptive Bacterial Immunity', Jinek et al 2012"), including human ones ([Jinek et al 2013](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3557905/ "RNA-programmed genome editing in human cells")).^[Interestingly, this was not even the first application of CRISPR. That would appear to be [DuPont in 2007](http://www.the-scientist.com/?articles.view/articleNo/41676/title/There-s-CRISPR-in-Your-Yogurt/ "There's CRISPR in Your Yogurt: We've all been eating food enhanced by the genome-editing tool for years"), which began improved breeding of virus-resistant dairy cultures by introducing troublesome viral infections, and selecting for further use only those bacteria with changed CRISPR-related genomes, indicating they had acquired resistance to the virus.] Commentary in 2012 and 2013 regarded prospects for embryo editing as highly remote^[[November 2013](http://www.independent.co.uk/news/science/crispr-gene-therapy-scientists-call-for-more-public-debate-around-breakthrough-technique-8927606.html "CRISPR gene therapy: Scientists call for more public debate around breakthrough technique"): "'But it is far too early to contemplate using these methods to alter the human germline'...Professor Dagan Wells, an IVF researcher at Oxford University, said that although there is still a long way to go before CRISPR could even be considered for use on IVF embryos"] Even as late as July 2014, coverage was highly circumspect, with [vague musing](http://www.nytimes.com/2014/07/17/science/a-call-to-fight-malaria-one-mosquito-at-a-time-by-altering-dna.html "A Call to Fight Malaria One Mosquito at a Time by Altering DNA") that "Some experiments also hint that doctors may someday be able to use it to treat genetic disorders"; successful editing of zebrafish ([Hwang et al 2013](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3686313/ "Efficient In Vivo Genome Editing Using RNA-Guided Nucleases")), monkey, and human embryos was already being demonstrated in the lab, and human trials would begin 2-3 years later.
(Surprisingly, Shulman & Bostrom do *not* mention CRISPR, but that gives an idea of how shockingly fast CRISPR went from strange to news to standard, and how low expectations for genetic engineering were pre-2015 after decades of agonizingly slow progress & high-profile failures & deaths, such that the default assumption was that direct cheap safe genetic engineering of embryos would not be feasible for decades and certainly not the foreseeable future.)

The CRISPR/Cas system exploits a bacterial anti-viral immune system in which snippets of virus DNA are stored and an enzyme system detects the presence in the bacterial genome of fresh viral DNA and then edits it, breaking it, and presumably stopping the infection in its latent phase. This requires the CRISPR enzymes to be highly precise (lest it attack legitimate DNA, damaging or killing itself), repeatable (it's a poor immune system that can only fight off one infection ever), and programmable by short RNA sequences (because viruses constantly mutate).

This turns out to be usable in animal and human cells to delete/knock-out genes: create an RNA sequence matching a particular gene, inject the RNA sequence along with the key enzymes into a cell, and it will find the gene in question inside the nucleus and snip it; this can be augmented to edit rather than delete by providing another DNA template which the snip-repair mechanisms will unwittingly copy from.
Compared to the major earlier approaches using [zinc finger nuclease](!Wikipedia) & [TALENs](!Wikipedia "Transcription activator-like effector nuclease"), CRISPR is far faster and easier and cheaper to use, with large (at least halving) decreases in time & money cited, and use of it has exploded in research labs, drawing comparisons to the invention of PCR and Nobel Prize predictions.
It has been used to edit at least 36 creatures as of June 2015^[[_Nature_](http://www.nature.com/news/crispr-the-disruptor-1.17673): "Jennifer Doudna, a CRISPR pioneer at the University of California, Berkeley, is keeping a list of CRISPR-altered creatures. So far, she has three dozen entries, including disease-causing parasites called trypanosomes and yeasts used to make biofuels."
As of May 2017, somewhere around 20 human trials (most in vivo) were [reportedly underway](https://www.newscientist.com/article/2133095-boom-in-human-gene-editing-as-20-crispr-trials-gear-up/ "Boom in human gene editing as 20 CRISPR trials gear up: A pioneering CRISPR trial in China will be the first to try editing the genomes of cells inside the body, in an effort to eliminate cancer-causing HPV virus").
Note that BGI's [commercially-sold micropigs](http://www.nature.com/news/gene-edited-micropigs-to-be-sold-as-pets-at-chinese-institute-1.18448 "Gene-edited 'micropigs' to be sold as pets at Chinese institute: The pigs are endearing but scientists warn that they may be a distraction from more serious research"), BGI's myostatin/muscly pigs, and muscly sheep & cattle ([Proudfoot et al 2015](http://link.springer.com/article/10.1007%2Fs11248-014-9832-x "Genome edited sheep and cattle")), were done using TALENs, not CRISPR; but reportedly, BGI is [redoing the muscly pigs with CRISPR](http://www.nature.com/news/super-muscly-pigs-created-by-small-genetic-tweak-1.17874 "Super-muscly pigs created by small genetic tweak: Researchers hope the genetically engineered animals will speed past regulators")], including:

- rhesus monkey embryos ([Midic et al 2017](/docs/genetics/2017-midic.pdf "Quantitative assessment of timing, efficiency, specificity, and genetic mosaicism of CRISPR/Cas9 mediated gene editing of hemoglobin beta gene in rhesus monkey embryos"))
- sheep
- muscly beagles ([Zou et al 2015](http://intl-jmcb.oxfordjournals.org/content/7/6/580.full "Generation of gene-target dogs using CRISPR/Cas9 system"))
- muscly ([Ni et al 2014](http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0106718 "Efficient gene knockout in goats using CRISPR/Cas9 system")) & hairy goats ([Wang et al 2015](http://www.nature.com/articles/srep13878 "Generation of gene-modified goats targeting MSTN and FGF5 via zygote injection of CRISPR/Cas9 system"))
- human embryos, curing [β-thalassaemia](!Wikipedia "Beta thalassemia") ([Liang et al 2015](http://link.springer.com/article/10.1007/s13238-015-0153-5%20/fulltext.html  "CRISPR/Cas9-mediated gene editing in human tripronuclear zygotes")^[[_Nature_](http://www.nature.com/news/embryo-editing-sparks-epic-debate-1.17421 "Embryo editing sparks epic debate: In wake of paper describing genetic modification of human embryos, scientists disagree about ethics") comments on the Liang work: "A Chinese source familiar with developments in the field said that at least four groups in China are pursuing gene editing in human embryos."])
- curing retinitis pigmentosa in mice cells ([Bakondi et al 2016](http://www.nature.com/mt/journal/vaop/ncurrent/full/mt2015220a.html "In Vivo CRISPR/Cas9 Gene Editing Corrects Retinal Dystrophy in the S334ter-3 Rat Model of Autosomal Dominant Retinitis Pigmentosa")) & live mice ([Zhu et al 2017](http://www.nature.com/cr/journal/vaop/ncurrent/full/cr201757a.html "Gene and mutation independent therapy via CRISPR-Cas9 mediated cellular reprogramming in rod photoreceptors")) and human cells, ([Bassuk et al 2016](http://www.nature.com/articles/srep19969 "Precision Medicine: Genetic Repair of Retinitis Pigmentosa in Patient-Derived Stem Cells")); prelude to [planned 2017 trials on Leber congenital amaurosis in live humans](http://www.popsci.com/biotech-company-will-use-crispr-on-people-in-next-two-years) and Duchenne muscular dystrophy ([Long et al 2014](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4398027/ "Prevention of muscular dystrophy in mice by CRISPR/Cas9-mediated editing of germline DNA"))
- cure rats or mice of [tyrosinemia](!Wikipedia) ([Yin et al 2015](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4157757/ "Genome editing with Cas9 in adult mice corrects a disease mutation and phenotype"), [Yin et al 2016](/docs/genetics/2016-yin.pdf "Therapeutic genome editing by combined viral and non-viral delivery of CRISPR system components in vivo")), cataracts ([Wu et al 2013](http://www.sciencedirect.com/science/article/pii/S1934590913004621 "Correction of a Genetic Disease in Mouse via Use of CRISPR-Cas9")), [hemophilia](http://www.uphs.upenn.edu/news/News_Releases/2016/11/wilson/ "Penn Scientists Use CRISPR for First Time to Correct Clotting in Newborn and Adult Mice: Findings Presented at ASH Meeting Offer Clues about Use of Gene Editing for Disease-Causing Mutations"), & HIV ([Yin et al 2017](/docs/genetics/2017-yin.pdf "In Vivo Excision of HIV-1 Provirus by saCas9 and Multiplex Single-Guide RNAs in Animal Models"))
- cure human cells of cystic fibrosis ([Schwank et al 2013](/docs/genetics/2013-schwank.pdf "Functional repair of CFTR by CRISPR/Cas9 in intestinal stem cell organoids of cystic fibrosis patients")) and HIV ([Ebina et al 2013](http://www.nature.com/articles/srep02510 "Harnessing the CRISPR/Cas9 system to disrupt latent HIV-1 provirus"), [Kaminski et al 2016](http://www.nature.com/articles/srep22555 "Elimination of HIV-1 Genomes from Human T-lymphoid Cells by CRISPR/Cas9 Gene Editing"))
- cut out up to 62 copies of a gene from a pig ([Yang et al 2016](http://arep.med.harvard.edu/pdf/Yang_Science_2015.pdf "Genome-wide inactivation of porcine endogenous retroviruses (PERVs)"); other multiple-edit capabilities have been demonstrated; eg in bacteria ([Citorik et al 2014](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4237163/ "Sequence-specific antimicrobials using efficiently delivered RNA-guided nucleases")), mice ([Wang et al 2013](http://www.sciencedirect.com/science/article/pii/S0092867413004674 "One-Step Generation of Mice Carrying Mutations in Multiple Genes by CRISPR/Cas-Mediated Genome Engineering")), rats ([Li et al 2013](http://www.sunbiotech.com.cn/UserFiles/UploadFile/File/20131018045031_18_0.pdf "Simultaneous generation and germline transmission of multiple  gene mutations in rat using  CRISPR-Cas systems")), goats ([Wang et al 2015](http://www.nature.com/articles/srep13878 "Generation of gene-modified goats targeting MSTN and FGF5 via zygote injection of CRISPR/Cas9 system")), up to 14 in elephant cells^[[Callaway 2015](http://www.nature.com/news/mammoth-genomes-provide-recipe-for-creating-arctic-elephants-1.17462 "Mammoth genomes provide recipe for creating Arctic elephants: Catalogue of genetic differences between woolly mammoths and elephants reveals how ice-age giants braved the cold"): "Similar work is already being carried out in the lab of George Church, a geneticist at Harvard Medical School in Boston. Using a technology known as CRISPR/Cas9 that allows genes to be easily edited, his team claims to have engineered elephant cells that contain the mammoth version of 14 genes potentially involved in cold tolerance - although the team has not yet tested how this affects the elephant cells. Church plans to do these experiments in "organoids" created from elephant iPS cells."], and human cells ([Sakuma et al 2014](http://www.nature.com/articles/srep05400 "Multiplex genome engineering in human cells using all-in-one CRISPR/Cas9 vector system"), [Mali et al 2013](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3712628/ "RNA-guided human genome engineering via Cas9")))
- create [gene drives](!Wikipedia) in yeast ([DiCarlo et al 2015](http://biorxiv.org/content/biorxiv/early/2015/03/19/013896.full.pdf "RNA-guided gene drives can efficiently and reversibly bias inheritance in wild yeast")), fruit flies ([Gantz & Bier 2015](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4687737/ "The mutagenic chain reaction: A method for converting heterozygous to homozygous mutations")), & mosquitoes ([Gantz et al 2015](http://www.pnas.org/content/112/49/E6736.full "Highly efficient Cas9-mediated gene drive for population modification of the malaria vector mosquito Anopheles stephensi"). [Hammond et al 2015](http://www.nature.com/nbt/journal/v34/n1/full/nbt.3439.html "A CRISPR-Cas9 gene drive system targeting female reproduction in the malaria mosquito vector Anopheles gambiae"))
- insert [woolly mammoth genes into elephant cells](http://www.popsci.com/woolly-mammoth-dna-brought-life-elephant-cells "Woolly Mammoth DNA Successfully Spliced Into Elephant Cells But don't expect mammoth clones anytime soon")
- virus-resistant pigs ([Whitworth et al 2016](/docs/genetics/2016-whitworth.pdf "Gene-edited pigs are protected from porcine reproductive and respiratory syndrome virus"))
- sterile farmed catfish^[Reardon 2016: "To address such concerns, fish geneticist Rex Dunham of Auburn University in Alabama has been using CRISPR to inactivate genes for three reproductive hormones - in this case, in catfish, the most intensively farmed fish in the United States. The changes should leave the fish sterile, so any fish that might escape from a farm, whether genetically modified or not, would stand little chance of polluting natural stocks. "If we're able to achieve 100% sterility, there is no way that they can make a genetic impact," Dunham says. Administering hormones would allow the fish to reproduce for breeding purposes. And Dunham says that similar methods could be used in other fish species."]
- cattle with no female offspring which need to be culled^[Reardon 2016: "CRISPR could also reduce the need for farmers to cull animals, an expensive and arguably inhumane practice. Biotechnologist Alison van Eenennaam at the University of California, Davis, is using the technique to ensure that beef cattle produce only male or male-like offspring, because females produce less meat and are often culled. She copies a Y-chromosome gene that is important for male sexual development onto the X chromosome in sperm. Offspring produced with the sperm would be either normal, XY males, or XX females with male traits such as more muscle."] and vice-versa, chickens without male offspring^[Reardon 2016: "In the egg industry, male chicks from elite egg-laying chicken breeds have no use, and farmers generally cull them within a day of hatching. Tizard and his colleagues are adding a gene for green fluorescent protein to the chickens' sex chromosomes so that male embryos will glow under ultraviolet light. Egg producers could remove the male eggs before they hatch and potentially use them for vaccine production."]
- cattle without horns that need to be painfully cut off^[Reardon 2016: "Molecular geneticist Scott Fahrenkrug, founder of Recombinetics in Saint Paul, Minnesota, is using gene-editing techniques to transfer the gene that eliminates horns into elite breeds [12](http://www.pnas.org/content/110/41/16526.full "'Efficient nonmeiotic allele introgression in livestock using custom endonucleases', Tan et al 2013"). The company has produced only two polled calves so far - both male - which are being raised at the University of California, Davis, until they are old enough to breed."]
- [tuberculosis](!Wikipedia "Mycobacterium bovis")-resistant cows ([Gao et al 2017](http://genomebiology.biomedcentral.com/articles/10.1186/s13059-016-1144-4 "Single Cas9 nickase induced generation of NRAMP1 knockin cattle with reduced off-target effects"))
- edited ferrets ([Kou et al 2015](http://www.nature.com/cr/journal/v25/n12/full/cr2015130a.html "CRISPR/Cas9-mediated genome engineering of the ferret")); ferrets may be used for flu experiments^[Reardon 2016: "But until the arrival of CRISPR, virologists lacked the tools to easily alter ferret genes. Xiaoqun Wang and his colleagues at the Chinese Academy of Sciences in Beijing have used CRISPR to tweak genes involved in ferret brain development14, and they are now using it to modify the animals' susceptibility to the flu virus. He says that he will make the model available to infectious-disease researchers."]
- autistic-like macaque monkeys ([Liu et al 2016](/docs/genetics/2016-liu-2.pdf "Autism-like behaviours and germline transmission in transgenic monkeys overexpressing MeCP2"))
- [mushrooms resistant to spoiling](http://www.nature.com/news/gene-edited-crispr-mushroom-escapes-us-regulation-1.19754 "Gene-edited CRISPR mushroom escapes US regulation: A fungus engineered with the CRISPR-Cas9 technique can be cultivated and sold without further oversight")
- planned: make allergen-free eggs^[from ["Welcome to the CRISPR zoo: Birds and bees are just the beginning for a burgeoning technology", Reardon 2016](http://www.nature.com/news/welcome-to-the-crispr-zoo-1.19537): "The group expects to hatch its first generation of chicks with gene modifications later this year as a proof of concept. Doran realizes that it could be some time before regulators would approve gene-edited eggs, and he hopes that his daughter will have grown out of her allergy by then. "If not, I've got someone ready and waiting to try the first egg," he says."], disease/parasite-resistant bees^[Reardon 2016: "Gillis has been studying the genomes of 'hygienic' bees, which obsessively clean their hives and remove sick and infested bee larvae. Their colonies are less likely to succumb to mites, fungi and other pathogens than are those of other strains, and Gillis thinks that if he can identify genes associated with the behaviour, he might be able to edit them in other breeds to bolster hive health. But the trait could be difficult to engineer. No hygiene-associated genes have been definitively identified, and the roots of the behaviour may prove complex, says BartJan Fernhout, chairman of Arista Bee Research in Boxmeer, the Netherlands, which studies mite resistance. Moreover, if genes are identified, he says, conventional breeding may be sufficient to confer resistance to new populations, and that might be preferable given the widespread opposition to genetic engineering."], cattle resistant to sleeping sickness^[Reardon 2016: "Other researchers are making cattle that are resistant to the trypanosome parasites that are responsible for sleeping sickness."], [koi](!Wikipedia) carp of different sizes & color patterns^[Reardon 2016: "BGI is also using CRISPR to alter the size, colour and patterns of koi carp. Koi breeding is an ancient tradition in China, and Jian Wang, director of gene-editing platforms at BGI, says that even good breeders will usually produce only a few of the most beautifully coloured and proportioned, 'champion quality' fish out of millions of eggs. CRISPR, she says, will let them precisely control the fish's patterns, and could also be used to make the fish more suitable for home aquariums rather than the large pools where they are usually kept. Wang says that the company will begin selling koi in 2017 or 2018 and plans to eventually add other types of pet fish to its repertoire."]
- [mildew-resistant wine grapes](http://www.pbs.org/wgbh/nova/next/nature/crispr-grapes/ "Editing Out Pesticides")

(I am convinced some of these were done primarily for the lulz.)

It has appeared to be a very effective and promising genome editing tool in mammalian cells
Cho et al., 2013 "Targeted genome engineering in human cells with the Cas9 RNA-guided end" http://www.bmskorea.co.kr/bms_email/email2013/13-0802/paper.pdf human cells
Cong et al., 2013 "Multiplex genome engineering using CRISPR/Cas systems" http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3795411/ mouse and human cells
Jinek et al., 2012 "A programmable dual-RNA-guided DNA endonuclease in adaptive bacterial immunity"
zebrafish somatic cells at the organismal level Hwang et al 2013"Efficient genome editing in zebrafish using a CRISPR-Cas system" http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3686313/
genomic editing in cultured mammalian cells
[Mali et al 2013](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3712628/ "RNA-guided human genome engineering via Cas9")
pluripotent stem cells, but also in zebrafish embryos with efficiencies that are comparable to those obtained using ZFNs and TALENs (Hwang et al., 2013).

Jenko et al 2016, "Potential of promotion of alleles by genome editing to improve quantitative traits in livestock breeding programs" https://gsejournal.biomedcentral.com/articles/10.1186/s12711-015-0135-3

Estimating the profit from CRISPR edits is, in some ways, less straightforward than from embryo selection:

1. taking the highest _n_ reported betas/coefficients from a GWAS OLS regressions implies that they will be systematically biased upwards due to the winner's curse and statistical-significance filtering, thereby exaggerating the potential benefit from each SNP
2. the causal tagging problem: GWAS estimates correlating SNPs with phenotype traits, while valid for prediction (and hence selection), are not necessarily *causal* (such that an edit at that SNP will have the estimated effect), and the probability of being non-causal
3. each CRISPR edit has a chance of not making the correct edit, and making wrong edits; an edit may not work in an embryo (the specificity, false negative), and there is a chance of an 'off-target' mutation (false positive). A non-edit is a waste of money, while an off-target mutation could be fatal.
4. CRISPR has advanced at such a rapid rate that numbers on cost, specificity, & off-target mutation rate are generally either not available, or are arguably out of date before they were published^[For example, Liang et al 2015's reported off-target mutation numbers in human embryos was greeted with a comment from George Church that ["the researchers did not use the most up-to-date CRISPR/Cas9 methods and that many of the researchers' problems could have been avoided or lessened if they had."](http://www.nature.com/news/embryo-editing-sparks-epic-debate-1.17421 "Embryo editing sparks epic debate: In wake of paper describing genetic modification of human embryos, scientists disagree about ethics")]

The winner's curse can be dealt with several ways; [the supplementary of Rietveld et al 2014](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4183313/bin/pnas.1404623111.sapp.pdf) discusses 4 methods ("inverting the conditional expectation of the OLS estimator, maximum likelihood estimation (MLE), Bayesian estimation, and empirical-Bayes estimation").
The best one for our purposes would be a Bayesian approach, yielding posterior distributions of effect sizes.
Unfortunately, the raw data for GWAS studies like Rietveld et al 2013 is not available; but for our purposes, we can, like in the Rietveld et al 2014 supplement, simply simulate a dataset and work with that to get posteriors to find the SNPs with unbiased largest posterior means.

The causal tagging problem is more difficult. The background for the causal tagging problem is that genes are recombined randomly at conception, but they are not recombined at the individual gene level; rather, genes tend to live in 'blocks' of contiguous genes called [haplotypes](!Wikipedia), leading to [linkage disequilibrium](!Wikipedia) (LD). Not every possible variant in a haplotype is detected by a SNP array chip, so if you have genes A/B/C/D, it may be the case that a variant of A will increase intelligence but your SNP array chip only detects variants of D; when you do a GWAS, you then discover D predicts increased intelligence. (And if your SNP array chip tags B or C, you may get hits on those as well!)
This is not a problem for embryo selection, because if you can only see D's variants, and you see that an embryo has the 'good' D variant, and you pick that embryo, it will indeed grow up as you hoped because that D variant pulled the true causal A variant along for the ride. Indeed, for selection or prediction, the causal tagging problem can be seen as a *good* thing: your GWASes can pick up effects from parts of the genome you didn't even pay to sequence - "buy one, get one free". (The downside can be underestimation due to imperfect proxies.)
But this is a problem for embryo editing because if a CRISPR enzyme goes in and carefully edits D while leaving everything untouched, A by definition remains the same and there will be no benefits.
A SNP being non-causal is not a serious problem for embryo editing if we know which SNPs are non-causal; as illustrated above, the distribution of effects is smooth enough that discarding a top SNP for the next best alternative costs little. But it is a serious problem if we don't know which ones are non-causal, because then we waste precious edits (imagine a budget of 30 edits and a non-causal rate of 50%; if we are ignorant which are non-causal, we effectively get only 15 edits, but if we know which to drop, then it's almost as good as if all were causal).
Causality can be established in a few ways; for example, a hit can be reused in a mutant laboratory animal breed to see if it also predicts there (This is behind some striking breakthroughs like [Sekar et al 2016](/docs/genetics/2016-sekar.pdf "Schizophrenia risk from complex variation of complement component 4")'s proof that neural pruning is a cause of schizophrenia), either using existing strains or creating a fresh modification (using, say, CRISPR). This has not been done for the top intelligence hits and given the expense & difficulty of animal experimentation, we can't expect it anytime soon. <!-- TODO: later on, estimate VoI for individual SNP confirmations -->
One can also try to use prior information to boost the posterior probability of an effect: if a gene has already been linked to the nervous system by previous studies exploring mutations or gene expression data etc, or other aspects of the physical structure point towards that SNP like being closest to a gene, then that is evidence for the association being causal. Intelligence hits are enriched for nervous system connections, but this method is inherently weak.
A better method is fine-mapping or whole-genome sequencing: when all the variants in a haplotype are sequenced, then the true causal variant will tend to perform subtly better and one can single it out of the whole SNP set using various statistical criteria (eg [Farh et al 2015](http://www.nature.com/nature/journal/v518/n7539/full/nature13835.html "Genetic and epigenetic fine mapping of causal autoimmune disease variants") using their algorithm on autoimmune disorder estimate 5.5% of their 4.9k SNPs are causal). Useful, but whole-genomes are still expensive enough that they are not created nearly as much as SNPs and there do not seem to be many comparisons to ground-truths or meta-analyses.
Another approach is similar to the lab animal approach: human groups differ genetically, and their haplotypes & LD patterns can differ greatly; if D looks associated with intelligence in one group, but is not associated in a genetically distant group with different haplotypes, that strongly suggests that in the first group, D was indeed just proxying for another variant. We can also expect that variants with high frequencies will not be population-specific but be ancient & shared causal variants.
Some of the intelligence hits have replicated in European-American samples, as expected but not helpfully; more importantly, in African-American ([Domingue et al 2015](http://ero.sagepub.com/content/1/3/2332858415599972?full "Polygenic Influence on Educational Attainment")) and East Asian samples ([Zhu et al 2015](/docs/genetics/2015-zhu.pdf "Educational attainment-related loci identified by GWAS are associated with select personality traits and mathematics and language abilities")), and the top SNPs have some predictive power of mean IQs across ethnic groups ([Piffer 2015](http://emilkirkegaard.dk/en/wp-content/uploads/PifferIntelligence2015.pdf "A review of intelligence GWAS hits: Their relationship to country IQ and the issue of spatial autocorrelation")).
More generally, while GWASes usually are paranoid about ancestry, using as homogeneous a sample as possible and controlling away any detectable differences in ancestry, GWASes can use cross-ethnic and differing ancestries in ["admixture mapping"](http://emilkirkegaard.dk/en/wp-content/uploads/Admixture-Mapping-comes-of-age-2010-winkler.pdf "'Admixture Mapping Comes of Age', Winkler et al 2010") to home in on causal variants, but this hasn't been done for intelligence.
We can note that some GWASes have compared how hits replicate across populations (eg [Carlson et al 2010](http://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.1001661 "Generalization and Dilution of Association Results from European GWAS in Populations of Non-European Ancestry: The PAGE Study"),  [Waters et al 2010](http://journals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.1001078 "Consistent Association of Type 2 Diabetes Risk Variants Found in Europeans in Diverse Racial and Ethnic Groups"), [Torgerson et al 2011](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3445408/ "Meta-analysis of Genome-wide Association Studies of Asthma In Ethnically Diverse North American Populations"), [Zuo et al 2011](http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0026726 "A Novel, Functional and Replicable Risk Gene Region for Alcohol Dependence Identified by Genome-Wide Association Study"), [Chang et al 2011](http://circgenetics.ahajournals.org/content/early/2011/08/10/CIRCGENETICS.111.959577.full.pdf "Race / Ethnic Variation in the Association of Lipid-Related Genetic Variants with Blood  Lipids in the Adult U.S. Population"), [Nyholt et al 2012](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3527416/ "Genome-wide association meta-analysis identifies new endometriosis risk loci"), [Fesinmeyer et al 2013](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3482415/ "Genetic risk factors for body mass index and obesity in an ethnically diverse population: results from the Population Architecture using Genomics and Epidemiology (PAGE) Study")/[Gong et al 2013](http://www.sciencedirect.com/science/article/pii/S000292971300387X "Fine-mapping and Identification of BMI Loci in African Americans"), [Taylor et al 2013](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3694490/ "A Meta-Analysis Identifies New Loci Associated with Body Mass index in Individuals of African Ancestry"), [Xing et al 2014](http://iovs.arvojournals.org/article.aspx?articleid=2265959 "Transethnic Replication of Association of CTG18.1 Repeat Expansion of TCF4 Gene With Fuchs' Corneal Dystrophy in Chinese Implies Common Causal Variant"), [DIAGRAM Consortium et al 2014](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3969612/ "Genome-wide trans-ancestry meta-analysis provides insight into the genetic architecture of type 2 diabetes susceptibility"), [Yin et al 2015](http://www.nature.com/ncomms/2015/150423/ncomms7916/full/ncomms7916.html "Genome-wide meta-analysis identifies multiple novel associations and ethnic heterogeneity of psoriasis susceptibility"), [Locke et al 2015](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4382211/ "Genetic studies of body mass index yield new insights for obesity biology"), [He et al 2015](/docs/genetics/2015-he.pdf "Meta-analysis of genome-wide association studies of adult height in East Asians identifies 17 novel loci")); despite interpretative difficulties such as statistical power, hits often replicate from European-descent samples to distant ethnicities, and the example of the schizophrenia GWASes ([Candia et al 2013](http://www.sciencedirect.com/science/article/pii/S000292971300325X "Additive Genetic Variation in Schizophrenia Risk Is Shared by Populations of African and European Descent"), [Ripke et al 2014](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4112379/ "Biological Insights From 108 Schizophrenia-Associated Genetic Loci")) also offers hope in showing a strong correlation of 0.66/0.61 between African & European schizophrenia SNP-based [GCTA](!Wikipedia)s.
(It also seems to me that there is a trend with the complex highly polygenic traits having better cross-ethnic replicability than in simpler diseases.)

23. Ntzani et al 2012, "Consistency of genome-wide associations across major ancestral groups" /docs/genetics/2012-ntzani.pdf
24. Marigorta & Navarro 2013 "High Trans-ethnic Replicability of GWAS Results Implies Common Causal Variants" http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3681663/

"Genetic effects influencing risk for major depressive disorder in China and Europe", Bigdeli et al 2017 https://www.nature.com/tp/journal/v7/n3/full/tp2016292a.html

"Father Absence and Accelerated Reproductive Development ", Gaydosh et al 2017 http://biorxiv.org/content/biorxiv/early/2017/04/04/123711.full.pdf

[http://biorxiv.org/content/early/2016/02/23/036657 "Transethnic genetic correlation estimates from summary statistics"], Brown et al 2016

"Consistent Association of Type 2 Diabetes Risk Variants Found in Europeans in Diverse Racial and Ethnic Groups", Waters et al 2010 http://journals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.1001078
Martin et al 2016, "Human demographic history impacts genetic risk prediction across diverse populations" http://biorxiv.org/content/early/2016/11/24/070797 http://www.cell.com/ajhg/fulltext/S0002-9297(17)30107-6
Ware et al 2017, "Heterogeneity in polygenic scores for common human traits" http://biorxiv.org/content/early/2017/02/05/106062 Figure 3 - the height/education/etc polygenic scores roughly 5x as predictive in white Americans as African-Americans, ~0.05 R^2 vs ~0.01 R^2, and since African-Americans average about 25% white anyway, that's consistent with 10% or less...
"Using Genetic Distance to Infer the Accuracy of Genomic Prediction", Scutari et al 2016 http://journals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.1006288

["Trans-ethnic genome-wide association studies: advantages and challenges of mapping in diverse populations"](https://genomemedicine.biomedcentral.com/articles/10.1186/s13073-014-0091-5), Li & Keating 2014

"Genetic contributors to variation in alcohol consumption vary by race/ethnicity in a large multi-ethnic genome-wide association study", Jorgenson et al 2017 /docs/genetics/correlation/2017-jorgenson.pdf

"High-Resolution Genetic Maps Identify Multiple Type 2 Diabetes Loci at Regulatory Hotspots in African Americans and Europeans", Lau et al 2017 /docs/genetics/2017-lau.pdf

"The genomic landscape of African populations in health and disease", Rotimi et al 2017 /docs/genetics/2017-rotimi.pdf

MDDWG PGC 2017, ["Genome-wide association analyses identify 44 risk variants and refine the genetic architecture of major depression"](http://www.biorxiv.org/content/early/2017/07/24/167577):

- European/Chinese depression: r_g=0.31
- European/Chinese schizophrenia: r_g=0.34
- European/Chinese bipolar disorder: r_g=0.45

Given the practice of embryo editing, the causal tagging problem can gradually solve itself: as edits are made, forcibly breaking the potential confounds, the causal nature of an SNP becomes clear. But how to allocate edits across the top SNPs to determine each's causal nature as efficiently as possible without spending too many edits investigating?
A naive answer might be something along the lines of a power analysis: in a two-group _t_-test trying to detect a difference of ~0.03 SD for each variant (the rough size of the top few variants), with variance reduced by the known polygenic score, and desired power is the standard 80%; it follows that one would need to randomize a total sample of _n_=34842 to reject the null hypothesis of 0 effect[^t-test-editing]. Setting up a [factorial experiment](!Wikipedia) & randomizing several variants simultaneously may allow inferences on them as well, but clearly this is going to be a tough row to hoe.
This is unduly pessimistic, since we neither need nor desire 80% power, nor are we comparing to a null hypothesis, as our goal is more modest: since only a certain number of edits will be doable for any embryo, say 30, we merely want to accumulate enough evidence about the top 30 variants to either demote it to #31 (and so we no longer spend any edits on it) or confirm it belongs in the top 30 and we should always be editing it.
This is immediately recognizable as [reinforcement learning](!Wikipedia): the [multi-armed bandit (MAB) problem](!Wikipedia "Multi-armed bandit") (each possible edit being an independent arm which can pulled or not); or more precisely, since early childhood (5yo) IQ scores are relatively poorly correlated with adult scores ([_r_=0.55](http://infoproc.blogspot.com/2011/08/predictive-power-of-early-childhood-iq.html)) and many embryos may be edited before data on the first edits starts coming in, a multi-armed bandit with multiple plays and delayed feedback. (There is no way immediately upon birth to receive meaningful feedback about the effect of an edit, although there might be ways to get feedback faster, such as using short-sleeper gene edits to enhance education.)
[Thompson sampling](!Wikipedia) is a randomized Bayesian approach which is simple and theoretically optimal, with excellent performance in practice as well; an [extension to multiple plays](http://arxiv.org/abs/1506.00779 "'Optimal Regret Analysis of Thompson Sampling in Stochastic Multi-armed Bandit Problem with Multiple Plays', Komiyama et al 2015") is also optimal.
Dealing with the delayed feedback is known to be difficult and multiple-play Thompson sampling may not be optimal, but in simulations it [performs better with delayed feedback than other standard MABs](http://www.research.rutgers.edu/~lihong/pub/Chapelle12Empirical.pdf "'An Empirical Evaluation of Thompson Sampling', Chapelle & Li 2011").
We can consider a simulation of the scenario in which every time-step is a day and 1 or more embryos must be edited that day; a noisy measure of IQ is then made available `9*31+5*365=2104` days later, which is fed into a GWAS [mixture model](!Wikipedia) in which the GWAS correlation for each SNP is considered as drawn with an unknown probability from a causal distribution and from a nuisance distribution, so with additional data, the effect estimates of the SNPs are refined, the probability of being drawn from the causal distribution is refined, and the overall mixture probability is likewise refined, similar to the ["Bayes B" paradigm from the "Bayesian alphabet" of genomic prediction methods in animal breeding](http://www.annualreviews.org/eprint/AEMMACidWrxGtS8eBFrT/full/10.1146/annurev-animal-022114-110733 "'One Hundred Years of Statistical Developments in Animal Breeding', Giancola & Rosa 2015").
(So for the first 2104 time-steps, a Thompson sample would be performed to yield a new set of edits, then each subsequent time-step a datapoint would mature, the posteriors updated, and another set of edits created.) The relevant question is how much regret will fall and how many causal SNPs become the top picks after how many edits & days: hopefully high performance & low regret will be achieved within a few years after the initial 5-year delay.
<!-- best-arm Thompson sampling:
https://arxiv.org/pdf/0802.2655.pdf "Pure exploration in multi-armed bandits problems", Bubeck et al 2009
https://hal.inria.fr/file/index/docid/654404/filename/COLT10.pdf "Best Arm Identification in Multi-Armed Bandits", Audibert et al 2010
https://papers.nips.cc/paper/4478-multi-bandit-best-arm-identification.pdf "Multi-Bandit Best Arm Identification", Gabillon et al 2011
https://www.escholar.manchester.ac.uk/api/datastream?publicationPid=uk-ac-man-scw:227658&datastreamId=FULL-TEXT.PDF "Decision Making Using Thompson Sampling", Mellor 2014
http://nowak.ece.wisc.edu/bestArmSurvey.pdf "Best-arm Identification Algorithms for Multi-Armed Bandits in the Fixed Confidence Setting", Jamieson & Nowak 2014
http://arxiv.org/pdf/1407.4443v1.pdf "On the Complexity of Best Arm Identification in Multi-Armed Bandit Models", Kaufmann et al 2014
https://arxiv.org/abs/1602.08448 "Simple Bayesian algorithms for best arm identification", Russo 2016

in general "Learning the Distribution With Largest Mean: Two Bandit Frameworks", Kaufmann & Garivier 2017 https://hal.archives-ouvertes.fr/hal-01449822/document
-->

a more concrete example: imagine we have a budget of 60 edits (based on the multiplex pig editing), a causal probability of 10%, an exponential distribution (rate 70.87) over 500000 candidate alleles of which we consider the top 1000, each of which has a frequency of 50% and we sequence before editing to avoid wasting edits.
What is our best case and worst-case IQ increase?
In the worst case, the top 60 are all non-causal, so our improvement is 0 IQ points; in the best case where all hits are causal, half of the hits are discarded after sequencing, and then the remaining top 60 get us ~6.1 IQ points; the intermediate case of 10% causal gets us to ~0.61 IQ points, and so our regret is 5.49 IQ points per embryo.
Unsurprisingly, a 10% causal rate is horribly inefficient.
In the 10% case, if we can infer the true causal SNPs, we only need to start with ~600 SNPs to saturate our editing budget on average, or ~900 to have <1% chance of winding up with <60 causal SNPs, so 1000 SNPs seems like a good starting point.
(Of course, we also want a larger window so as our edit budget increases with future income growth & technological improvement, we can smoothly incorporate the additional SNPs.)
So what order of samples do we need here to reduce our regret of 5.49 to something more reasonable like <0.25 IQ points?

~~~{.R}
SNPs <- 500000
SNPlimit <- 1000
rate <- 70.87
editBudget <- 60
frequency <- 0.5
mean(replicate(1000, {
    hits <- sort(rexp(SNPs, rate=rate), decreasing=TRUE)[1:SNPlimit]
    sum(sample(hits, length(hits) * 0.5)[1:editBudget])
    }))
~~~

http://jmlr.csail.mit.edu/proceedings/papers/v31/agrawal13a.pdf
Regret of Thompson sampling with Gaussian priors & likelihood is O(sqrt(N * T * ln(N))), where N = number of different arms/actions and T = current timestep
hence, if we have 1000 actions and we sample 1 time, our expected total regret is on the order of sqrt(1000 * 1 * ln(1000)) = 83; with 100 samples, our expected total regret has increased by two orders to 831 but we are only incurring an additional expected regret of ~4 or 5% of the first timestep's regret
diff(sapply((1:10000, function(t) { sqrt(1000 * t * log(1000)) } )))

Thompson sampling also achieves the lower bound in multiple-play but the asymptotic is more complex, and does not take into account the long delay & noise in measuring IQ.
TS empirically performs well but hard to know what sort of sample size is required. But at least we can say that the asymptotics don't imply dozens of thousands of embryos.




[^t-test-editing]: Power calculation using the Rietveld et al 2013 polygenic score:

    ~~~{.R}
    power.t.test(delta=0.03, sd=(1-0.025^2), power=0.80)

         Two-sample t test power calculation

                  n = 17421.11975
              delta = 0.03
                 sd = 0.999375
          sig.level = 0.05
              power = 0.8
        alternative = two.sided

    NOTE: n is number in *each* group
    17421 * 2
    # [1] 34842
    ~~~

problem: what's the probability of non-causal tagging due to LD? probably low since they work cross-ethnically don't they? on the other hand: http://emilkirkegaard.dk/en/?p=5415
"If the GWAS SNPs owe their predictive power to being actual causal variants, then LD is irrelevant and they should predict the relevant outcome in any racial group. If however they owe wholly or partly their predictive power to just being statistically related to causal variants, they should be relatively worse predictors in racial groups that are most distantly related. One can investigate this by comparing the predictive power of GWAS betas derived from one population on another population. Since there are by now 1000s of GWAS, meta-analyses have in fact made such comparisons, mostly for disease traits. Two reviews found substantial cross-validity for the Eurasian population (Europeans and East Asians), and less for Africans (usually African Americans) (23,24). The first review only relied on SNPs with p<α and found weaker results. This is expected because using only these is a threshold effect, as discussed earlier.

The second review (from 2013; 299 included GWAS) found much stronger results, probably because it included more SNPs and because they also adjusted for statistical power. Doing so, they found that: ~100% of SNPs replicate in other European samples when accounting for statistical power, ~80% in East Asian samples but only ~10% in the African American sample (not adjusted for statistical power, which was ~60% on average). There were fairly few GWAS for AAs however, so some caution is needed in interpreting the number. Still, this throws some doubt on the usefulness of GWAS results from Europeans or Asians used on African samples (or reversely)."
and http://emilkirkegaard.dk/en/?p=6415

"Identifying Causal Variants at Loci with Multiple Signals of Association", Hormozdiari et al 2014 http://genetics.org/content/198/2/497.full
"Where is the causal variant? On the advantage of the family design over the case-control design in genetic association studies", Dandine-Roulland & Perdry 2015 http://www.nature.com/ejhg/journal/v23/n10/abs/ejhg2014284a.html
worst-case, ~10% of SNPs are causal?


-----------------------

https://www.addgene.org/crispr/reference/
http://www.genome.gov/sequencingcosts/
https://crispr.bme.gatech.edu/
http://crispr.mit.edu/
low, near zero mutation rates:
"High-fidelity CRISPR-Cas9 nucleases with no detectable genome-wide off-target effects" Kleinstiver et al 2016, /docs/genetics/2016-kleinstiver.pdf ; "Rationally engineered Cas9 nucleases with improved specificity", Slaymaker et al 2016 /docs/genetics/2016-slaymaker.pdf
Church, April 2016: "Indeed, the latest versions of gene-editing enzymes have zero detectable off-target activities." http://www.wsj.com/articles/should-heritable-gene-editing-be-used-on-humans-1460340173
Church, June 2016 "Church: In practice, when we introduced our first CRISPR in 2013,19 it was about 5% off target. In other words, CRISPR would edit five treated cells out of 100 in the wrong place in the genome. Now, we can get down to about one error per 6 trillion cells...Fahy: Just how efficient is CRISPR at editing targeted genes? Church: Without any particular tricks, you can get anywhere up to, on the high end, into the range of 50% to 80% or more of targeted genes actually getting edited in the intended way. Fahy: Why not 100%? Church: We don't really know, but over time, we're getting closer and closer to 100%, and I suspect that someday we will get to 100%. Fahy: Can you get a higher percentage of successful gene edits by dosing with CRISPR more than once? Church: Yes, but there are limits." http://www.lifeextension.com/Lpages/2016/CRISPR/index
"A person familiar with the research says 'many tens' of human IVF embryos were created for the experiment using the donated sperm of men carrying inherited disease mutations. Embryos at this stages are tiny clumps of cells invisible to the naked eye. 'It is proof of principle that it can work. They significantly reduced mosaicism. I don't think it's the start of clinical trials yet, but it does take it further than anyone has before', said a scientist familiar with the project. Mitalipov's group appears to have overcome earlier difficulties by 'getting in early' and injecting CRISPR into the eggs at the same time they were fertilized with sperm." https://www.technologyreview.com/s/608350/first-human-embryos-edited-in-us/
cost of the top variants?
want to edit all variants such that:
sequencing-based edit: posterior mean * value of IQ point > cost of 1 edit
for blind edits: probability of the bad variant * posterior mean * value of IQ point > cost of 1 edit

how to simulate posterior probabilities?
https://cran.r-project.org/web/packages/BGLR/BGLR.pdf https://cran.r-project.org/web/packages/BGLR/vignettes/BGLR-extdoc.pdf looks useful but won't handle the mixture modeling

previous: Liang et al 2015 "CRISPR/Cas9-mediated gene editing in human tripronuclear zygotes" http://link.springer.com/article/10.1007/s13238-015-0153-5%20/fulltext.html http://www.nature.com/news/chinese-scientists-genetically-modify-human-embryos-1.17378
Kang et al 2016, "Introducing precise genetic modifications into human 3PN embryos by CRISPR/Cas-mediated genome editing" /docs/genetics/2016-kang.pdf http://www.nature.com/news/second-chinese-team-reports-gene-editing-in-human-embryos-1.19718
Komor et al 2016, "Programmable editing of a target base in genomic DNA without double-stranded DNA cleavage" https://ase.tufts.edu/chemistry/kumar/jc/pdf/Liu_2016.pdf
http://www.nature.com/news/chinese-scientists-to-pioneer-first-human-crispr-trial-1.20302
"CRISPR/Cas9-mediated gene editing in human zygotes using Cas9 protein" Tang et al 2017 /docs/genetics/2017-tang.pdf : no observed off-target mutations; efficiency of 20%, 50%, and 100%
"Correction of a pathogenic gene mutation in human embryos", Ma et al 2017 https://www.nature.com/nature/journal/vaop/ncurrent/full/nature23305.html no observed off-targets, 27.9% efficiency

legal in USA (no legislation but some interesting regulatory wrinkles: see [ch7 of _Human Genome Editing: Science, Ethics, and Governance_](https://www.nap.edu/read/24623/chapter/7#100) 2017 ), legal in China (only 'unenforceable guidelines') as of 2014, according to "International regulatory landscape and integration of corrective genome editing into in vitro fertilization", Araki & Ishii 2014 http://rbej.biomedcentral.com/articles/10.1186/1477-7827-12-108
as of 2015 too according to http://www.nature.com/news/where-in-the-world-could-the-first-crispr-baby-be-born-1.18542
illegal in the UK but they have given permission to modify human embryos for research http://www.popsci.com/scientists-get-government-approval-to-edit-human-embryos? http://www.nytimes.com/2016/02/02/health/crispr-gene-editing-human-embryos-kathy-niakan-britain.html
legal in Japan for research, but maybe not application? http://mainichi.jp/english/articles/20160423/p2g/00m/0dm/002000c
legal in Sweden for editing, which has been done as of September 2016 by Fredrik Lanner http://www.npr.org/sections/health-shots/2016/09/22/494591738/breaking-taboo-swedish-scientist-seeks-to-edit-dna-of-healthy-human-embryos

Also, what about mosaicism? When the CRISPR RNA is injected into an even single-celled zygote, it may already have created some of the DNA for a split and so the edit covers only a fraction of the cells of the future full-grown organism.
"Additionally, editing may happen after first embryonic division, due to persistence of Cas9:gRNA complexes, also causing mosaicism. We (unpublished results) and others (Yang et al. 2013a; Ma et al. 2014; Yen et al. 2014) have observed mosaic animals carrying three or more alleles. A recent study reported surprisingly high percentage of mosaic mice (up to 80%) generated by CRISPR targeting of the tyrosinase gene (Tyr) (Yen et al. 2014). We have observed a varying frequency of mosaicism, 11-35%, depending on the gene/locus (our unpublished data)... The pronuclear microinjection of gRNA and Cas9, in a manner essentially identical to what is used for generating transgenic mice, can be easily adapted by most transgenic facilities. Facilities equipped with a Piezo-electric micromanipulator can opt for cytoplasmic injections as reported (Wang et al. 2013; Yang et al. 2013a). Horii et al. (2014) performed an extensive comparison study suggesting that cytoplasmic injection of a gRNA and Cas9 mRNA mixture as the best delivery method. Although the overall editing efficiency in born pups yielded by pronuclear vs. cytoplasmic RNA injection seems to be comparable (Table 1), the latter method generated two- to fourfold more live born pups. Injection of plasmid DNA carrying Cas9 and gRNA to the pronucleus was the least efficient method in terms of survival and targeting efficiency (Mashiko et al. 2013; Horii et al. 2014). Injection into pronuclei seems to be more damaging to embryos than injection of the same volume or concentration of editing reagents to the cytoplasm. It has been shown that cytoplasmic injection of Cas9 mRNA at concentrations up to 200 ng/μl is not toxic to embryos (Wang et al. 2013) and efficient editing was achieved at concentrations as low as 1.5 ng/μl (Ran et al. 2013a). In our hands, injecting Cas9 mRNA at 50-150 ng/μl and gRNA at 50-75 ng/μl first into the pronucleus and also into the cytoplasm as the needle is being withdrawn, yields good survival of embryos and efficient editing by NHEJ in live born pups (our unpublished observations)." http://genetics.org/content/199/1/1.full

dnorm((150-100)/15) * 320000000
[1] 493,529.2788
dnorm((170-100)/15) * 320000000
[1] 2382.734679

if you're curious how I calculated that, '(10*1000 + 10 * 98 * 500) > 500000 ~> [1] FALSE` `sum(sort((rexp(10000)/1)/18, decreasing=TRUE)[1:98] * 0.5) ~> [1] 15.07656556'


hm. there are ~50k IVF babies each year in the USA. my quick CRISPR sketch suggested that for a few mill you could get up to 150-170. `dnorm((150-100)/15) * 320000000 ~>
                  [1] 493,529.2788; dnorm((170-100)/15) * 320000000 ~> [1] 2382.734679`. so depending on how many IVFers used it, you could boost the total genius population by anywhere
                  from 1/10th to 9x

but if only 10% causal rate and so only 100 effective edits from 1000, and a net gain of 15 IQ points (1SD) then increases:
IVF <- (dnorm((115-100)/15) * 50000); genpop <- (dnorm((150-100)/15) * 320000000); (IVF+genpop)/genpop
[1] 1.024514323
IVF <- (dnorm((115-100)/15) * 50000); genpop <- (dnorm((170-100)/15) * 320000000); (IVF+genpop)/genpop
[1] 6.077584313
an increase of 1.02x (150) and 6x (170) respectively

"To confirm these GUIDE-seq findings, we used targeted amplicon sequencing to more directly measure the frequencies of indel mutations induced by wild-type SpCas9 and SpCas9-HF1. For these experiments, we transfected human cells only with sgRNA- and Cas9encoding plasmids (without the GUIDE-seq tag). We used next-generation sequencing to examine the on-target sites and 36 of the 40 off-target sites that had been identified for six sgRNAs with wild-type SpCas9 in our GUIDE-seq experiments (four of the 40 sites could not be specifically amplified from genomic DNA). These deep sequencing experiments showed that: (1) wild-type SpCas9 and SpCas9-HF1 induced comparable frequencies of indels at each of the six sgRNA on-target sites, indicating that the nucleases and sgRNAs were functional in all experimental replicates (Fig. 3a, b); (2) as expected, wild-type SpCas9 showed statistically significant evidence of indel mutations at 35 of the 36 off-target sites (Fig. 3b) at frequencies that correlated well with GUIDE-seq read counts for these same sites (Fig. 3c); and (3) the frequencies of indels induced by SpCas9-HF1 at 34 of the 36 off-target sites were statistically indistinguishable from the background level of indels observed in samples from control transfections (Fig. 3b). For the two off-target sites that appeared to have statistically significant mutation frequencies with SpCas9-HF1 relative to the negative control, the mean frequencies of indels were 0.049% and 0.037%, levels at which it is difficult to determine whether these are due to sequencing or PCR error or are bona fide nuclease-induced indels. Based on these results, we conclude that SpCas9-HF1 can completely or nearly completely reduce off-target mutations that occur across a range of different frequencies with wild-type SpCas9 to levels generally undetectable by GUIDE-seq and targeted deep sequencing."

So no detected off-target mutations down to the level of lab error rate detectability. Amazing. So you can do a CRISPR on a cell with a >75% chance of making the edit to a desired gene correctly, and a <0.05% chance of a mistaken (potentially harmless) edit/mutation on a similar gene. With an error rate that low, you could do hundreds of CRISPR edits to a set of embryos with a low net risk of error... The median number of eggs extracted from a woman during IVF in America is ~9; assume the worst case of 0.05% risk of off-target mutation and that one scraps any embryo found to have any mutation at all even if it looks harmless; then the probability of making 1000 edits without an off-target mutation could be (1-(0.05/100)) ^ 1000 = 60%, so you're left with 5.4 good embryos, which is a decent yield. Making an edit of the top 1000 betas from the Rietveld 2013 polygenic score and figuring that it's weakened by maybe 25% due to particular cells not getting particular edits and that is... a very large number.

When I was doing my dysgenics analysis, I found that the Rietveld betas could be reasonably approximated by `rexp`, and we can anchor it by assuming the biggest effect is 0.5 IQ points, so we divide by 18, in which case we might estimate the top 750 edits at a cumulative value of `sum(sort((rexp(10000)/1)/18, decreasing=TRUE)[1:750] * 0.5) ~> [1] 73.97740467`. (Caveats: assumes knowledge of true betas, needs to be weakened for actual posterior probabilities, etc etc.)

How much did that <74 IQ points cost? Well, I hear that TALENS in bulk costs \$500 so you could ballpark marginal costs of particular CRISPR edits at that much too (and hopefully much less), and whole-genomes still cost \$1k, and you need to do 1000 edits on each embryo and whole-genomes at the end to check for off-target mutations, so you could ballpark a full suite of edits to 10 embryos at ~\$5m: `10*1000 + 10 * 1000 * 500 ~> [1] 5010000`. Of them 40% will have an off-target mutation, so you get 6 embryos to implant at a success rate of ~20% each which gives you about even odds for a healthy live birth, so you need to double the \$5m.

CRISPR: \$30? vs \$5k for TALENs http://www.nature.com/news/crispr-the-disruptor-1.17673
"Zayner says the kits will contain everything a budding scientist needs to carry out CRISPR experiments on yeast or bacteria. For US$130, you can have a crack at re-engineering bacteria so that it can survive on a food it normally wouldn't be able to handle, or for $160, you can get your eukaryote on and edit the ADE2 gene of yeast to give it a red pigment." https://www.indiegogo.com/projects/diy-crispr-kits-learn-modern-science-by-doing#/
https://www.thermofisher.com/us/en/home/life-science/genome-editing/geneart-crispr/crispr-cas9-based-genome-editing.html
http://www.sigmaaldrich.com/technical-documents/articles/biology/crispr-cas9-genome-editing.html
http://www.genscript.com/CRISPR-genome-edited-mammalian-cell-lines.html
http://ipscore.hsci.harvard.edu/genome-editing-services
http://www.blueheronbio.com/Services/CRISPR-Cas9.aspx
http://www.addgene.org/crispr/
'Jennifer Doudna, one of the co-discoverers of CRISPR, told MIT Tech Review's Antonio Regalado just how easy it was to work with the tool: "Any scientist with molecular biology skills and knowledge of how to work with [embryos] is going to be able to do this." Harvard geneticist George Church, whose lab is doing some of the premier research on CRISPR, says: "You could conceivably set up a CRISPR lab for $2000."' http://www.businessinsider.com/how-to-genetically-modify-human-embryos-2015-4
"Democratizing genetic engineering: This one should keep you up at night. CRISPR is so accessible-you can order the components online for $60-that it is putting the power of genetic engineering into the hands of many more scientists. But the next wave of users could be at-home hobbyists. This year, developers of a do-it-yourself genetic engineering kit began offering it for $700, less than the price of some computers. The trend might lead to an explosion of innovation-or to dangerous, uncontrolled experiments by newbies. Watch out, world. " https://www.technologyreview.com/s/543941/everything-you-need-to-know-about-crispr-gene-editings-monster-year/
"Individual plasmids can be ordered at $65 per plasmid, and will be shipped as bacterial stabs" https://www.addgene.org/crispr/yamamoto/multiplex-crispr-kit/
"At least since 1953, when James Watson and Francis Crick characterized the helical structure of DNA, the central project of biology has been the effort to understand how the shifting arrangement of four compounds-adenine, guanine, cytosine, and thymine-determines the ways in which humans differ from each other and from everything else alive. CRISPR is not the first system to help scientists pursue that goal, but it is the first that anyone with basic skills and a few hundred dollars' worth of equipment can use. "CRISPR is the Model T of genetics," Hank Greely told me when I visited him recently, at Stanford Law School, where he is a professor and the director of the Center for Law and the Biosciences. "The Model T wasn't the first car, but it changed the way we drive, work, and live. CRISPR has made a difficult process cheap and reliable. It's incredibly precise. But an important part of the history of molecular biology is the history of editing genes."..."In the past, this would have taken the field a decade, and would have required a consortium," Platt said. "With CRISPR, it took me four months to do it by myself." In September, Zhang published a report, in the journal Cell, describing yet another CRISPR protein, called Cpf1, that is smaller and easier to program than Cas9." http://www.newyorker.com/magazine/2015/11/16/the-gene-hackers?mbid=rss

2017 7% http://predictionbook.com/predictions/177110
2018 30% http://predictionbook.com/predictions/177114
2019 55% http://predictionbook.com/predictions/177115
by 2020, 75% http://predictionbook.com/predictions/177111

Whither embryo editing? The problem with IVF is that it is expensive, painful, and requires patience & planning. Even with large gains from editing, can we expect more than the current 1% or so of parents to ever be willing to conceive via IVF for those gains? If not, then the benefits may take generations to mix into the general population as offspring reproduce normally with unedited people and people happen to need to use IVF for regular fertility reasons. A solution is suggested by the adult CRISPR trials: make the germline edits in advance. In females, it seems like it might be hard to reach all the eggs which could potentially result in conception, but in males, sperm turnover is constant https://en.wikipedia.org/wiki/Spermatogenesis and sperm are replenished by stem cells in https://en.wikipedia.org/wiki/Seminiferous_tubule
already demonstrated CRISPR edits to spermatogonia and subsequent inheritance by offspring: "Targeted Germline Modifications in Rats Using CRISPR/Cas9 and Spermatogonial Stem Cells", Chapman et al 2014 http://www.sciencedirect.com/science/article/pii/S2211124715001989
"Genome Editing in Mouse Spermatogonial Stem Cell Lines Using TALENS and Double-Nicking CRISPR/Cas9", Sato et al 2015 http://www.sciencedirect.com/science/article/pii/S221367111500154X
extraction, modification, and re-transplanting is likely also a no-fly, but the edits demonstrate that CRISPR will not interfere with reproduction, and so better delivery methods can be developed
editing via two intravenous injections of a virus (carrying the editing template) and lipid-encapsulated Cas9-enzyme into the mice' tail vein: [Yin et al 2016](/docs/genetics/2016-yin.pdf "Therapeutic genome editing by combined viral and non-viral delivery of CRISPR system components in vivo"), yielding 6% of cells edited in the liver

https://en.wikipedia.org/wiki/Status_quo_bias
"The Reversal Test: Eliminating Status Quo Bias in Applied Ethics", Bostrom & Ord 2006 https://ethicslab.georgetown.edu/phil553/wordpress/wp-content/uploads/2015/01/Ord-and-Bostrom-Eliminating-Status-Quo-Bias-in-Applied-Ethics-.pdf
A [mutation load review](/docs/genetics/2015-henn.pdf "'Estimating the mutation load in human genomes', Henn et al 2015")  leads me to some hard figures from [Simons et al 2014](/docs/genetics/2014-simons.pdf "The deleterious mutation load is insensitive to recent population history") ([supplement](/docs/genetics/2014-simons-supplementary.pdf)) using data from [Fu et al 2012](/docs/genetics/2012-fu.pdf "Analysis of 6,515 exomes reveals the recent origin of most human protein-coding variants")/[Fu et al 2013](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3676746/ "Analysis of 6,515 exomes reveals a recent origin of most human protein-coding variants"); particularly relevant is figure 3, the number of single-nucleotide variants per person over the European-American sample, split by estimates of harm from least to most likely: `21345 + 15231 + 5338 + 1682 + 1969 = 45565`.
The supplementary tables gives a count of all observed SNVs by category, which sum to `300209 + 8355 + 220391 + 7001 + 351265 + 10293 = 897514`, so the average frequency must be `45565/897514=0.05`, and then the binomial SD will be `sqrt(897514*0.05*(1-0.05))=206.47`.
https://en.wikipedia.org/wiki/Paternal_age_effect
http://biorxiv.org/content/biorxiv/early/2016/03/08/042788.full.pdf "Older fathers' children have lower evolutionary fitness across four  centuries and in four populations"
"Rate of de novo mutations and the importance of father's age to disease risk" http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3548427/
"Novel variation and de novo mutation rates in population-wide de novo assembled Danish trios" http://www.nature.com/ncomms/2015/150119/ncomms6969/full/ncomms6969.html
http://www.genetics.org/content/202/3/869
"Thus, keeping in mind that some mutations in repetitive DNA likely go undetected owing to mapping difficulties in genome-sequencing projects, with a diploid genome size of ~6 billion bases, an average newborn contains ~100 de novo mutations....Numerous studies with model organisms indicate that such effects have a broad distribution (Lynch et al. 1999; Halligan and Keightley 2009)-most mutations have minor effects, very few have lethal consequences, and even fewer are beneficial. In all organisms, the majority of mutations with effects on fitness reduce viability/fecundity by something on the order of 1% per mutation (Lynch et al. 1999; Yampolsky et al. 2005; Eyre-Walker and Keightley 2007), and this class is thought to constitute 1-10% of all human mutations, the remainder being essentially neutral (Lindblad-Toh et al. 2011; Keightley 2012; Rands et al. 2014). Taking the lower end of the latter range suggests that the recurrent load of mutations imposed on the human population drags fitness down by 1% per generation, more so if the fraction of deleterious mutations exceeds 0.01 or if the environment is mutagenic, and less so if the average fitness effect of a mutation were to be <1%"

["Genome Graphs and the Evolution of Genome Inference"](http://biorxiv.org/content/biorxiv/early/2017/03/14/101816.full.pdf), Paten et al 2017:

> From short-read based assays, it is estimated that the average diploid human has between 4.1 and 5 million point mutations, either single nucleotide variants (SNVs), multi-nucleotide variants (MNVs), or short indels, which is only around 1 point variant every 1450 to 1200 bases of haploid sequence (Auton et al. 2015). Such an average human would also have about 20 million bases-about 0.3% of the genome-affected by around 2,100-2,500 larger structural variants (Auton et al. 2015). It should be noted that both these estimates are likely somewhat conservative as some regions of the genome are not accurately surveyed by the short read technology used. Indeed, long read sequencing demonstrates an excess of structural variation not found by earlier short read technology (Chaisson et al. 2015; Seo et al. 2016).
>
> - Auton et al 2015, ["A global reference for human genetic variation"](http://www.nature.com/nature/journal/v526/n7571/full/nature15393.html)
> - Chaisson et al 2015, ["Resolving the complexity of the human genome using single-molecule sequencing"](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4317254/)
> - Seo et al 2016, ["De novo assembly and phasing of a Korean human genome"](http://www.nature.com/nature/journal/v538/n7624/full/nature20098.html)

http://gnxp.nofe.me/2017/04/15/genetic-variation-in-human-populations-and-individuals/

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3155974/
"Genetic costs of domestication and improvement" Moyers et al 2017 http://biorxiv.org/content/early/2017/03/29/122093

"The demographic history and mutational load of African hunter-gatherers and farmers", Lopez et al 2017 http://biorxiv.org/content/early/2017/04/26/131219

SNPs have two relevant properties: a frequency of being zero, and an effect size

Benyamin polygenic score distribution: looks either exponential or log-normal and a Cullen & Frey graph indicates it is closes to exponential & log-normal distributions.

~~~{.R}
library(fitdistrplus)
with(benyamin[benyamin$EFFECT_A1>0,], descdist(abs(EFFECT_A1)/15, discrete=FALSE))
fit.exp <- with(benyamin[benyamin$EFFECT_A1>0,], fitdist(abs(EFFECT_A1)/15, "exp")); fit.exp
# Fitting of the distribution ' exp ' by maximum likelihood
# Parameters:
#        estimate  Std. Error
# rate 1063.15695 1.281452665
fit.ln <- with(benyamin[benyamin$EFFECT_A1>0,], fitdist(abs(EFFECT_A1)/15, "lnorm")); fit.ln
# Fitting of the distribution ' lnorm ' by maximum likelihood
# Parameters:
#             estimate      Std. Error
# meanlog -7.402017853 0.0013198365617
# sdlog    1.095050030 0.0009332618808
~~~

Plotting residuals & diagnostics, the log-normal performs much worse due to overestimating the number of near-zero effects (the Q-Q plot is particularly bad), so we'll use the exponential for effect sizes

As proportions, the frequencies are probably close to either uniform or beta distributions; in this case, they are very nearly uniformly distributed 0-1:

~~~{.R}
R> fitdist(benyamin$FREQ_A1, "beta", method="mme")
Fitting of the distribution ' beta ' by matching moments
Parameters:
          estimate
shape1 1.065412339
shape2 1.126576711
~~~

Set up: 50k SNPs, true effect sizes are exponentially distributed with exponential(rate=1063.15695), frequencies distributed beta(1.065412339, 1.126576711)
can't do full simulation of 500k SNPs with 100k datapoints, not enough RAM given inefficient R format for booleans: (100000 * 100000 * 48 bytes) / 1000000000 ; 4.8e+11 bytes or 480GB
can JAGS even handle that much data?

~~~{.R}
SNPs <- 500000
SNPlimit <- 50000
N <- 10000
genes <- data.frame(Effects = sort(rexp(SNPs, rate=1063.15695), decreasing=TRUE)[1:SNPlimit], Frequencies = rbeta(SNPlimit, shape1=1.065412339, shape2=1.126576711))
person <- function() { rbinom(SNPlimit, 1, prob=genes$Frequencies) }
test <- as.data.frame(t(replicate(N, person())))
format(object.size(test), units="GB")
# [1] "1.9 Gb"
test$Polygenic.score <- sapply(1:nrow(test), function(i) { sum(ifelse(test[i,], genes$Effects, 0)) })
test$IQ <- 100 + 15 * rnorm(N, mean=scale(test$Polygenic.score), sd=sqrt(1-0.33))

library(BGLR)
b <- BGLR(test$IQ, ETA=list(list(X=test[,1:SNPlimit], model="BL", lambda=202, shape=1.1, rate=2.8e-06)), R2=0.33)
gc()
~~~

BGLR problem: I can't scale it to n=100k/SNP=500k, BGLR RAM consumption maxes out at n=10k/SNP=50k.
This wouldn't be a problem for the Thompson sampling, but I need to use JAGS anyway for that.
So BGLR can't give me posteriors for Rietveld et al 2013 or Benyamin 2014 data.

can do Bayesian GWAS from public summary statistics using RSS "Bayesian large-scale multiple regression with summary statistics from genome-wide association studies" http://biorxiv.org/content/biorxiv/early/2016/03/04/042457.full.pdf Matlab library https://github.com/stephenslab/rss
installation: https://github.com/stephenslab/rss/wiki/RSS-via-MCMC
RSS example 1 https://github.com/stephenslab/rss/wiki/Example-1 code: https://github.com/stephenslab/rss/blob/master/examples/example1.m data https://uchicago.app.box.com/example1
doesn't run under Octave at the moment although I got it close: https://github.com/stephenslab/rss/issues/1
what are my alternatives? RSS is the best looking Bayesian one so far. I can try pirating Matlab, or apparently the Machine Learning Coursera gives one a temporary 120-day subscription

~~~{.R}
groundTruth <- function(alleles, causal, genotype) {
    score <- rnorm(1, mean=100, sd=15)
    for (i in 1:length(genotype)) {
      if(causal[i] && genotype[i]) { print(alleles[i]); score <- score + alleles[i]; } }
      return(score);}

alleles <- sort(rexp(10000, rate=70), decreasing=TRUE)[1:10]
causal <- c(TRUE, rep(FALSE, 8), TRUE)

df <- data.frame()
for(i in 1:50) {
 genotype <- rbinom(n=10,1,prob=0.50)
 IQ <- groundTruth(alleles, causal, genotype)
 df <- rbind(df, c(IQ, genotype))
 }
names(df) <- c("IQ", "A", "B", "C", "D", "E", "F", "G", "H", "I", "J")
library(reshape2)
df2 <- melt(df, "IQ")

model1 <- function() {
  for (i in 1:N) {
   for (j in 1:K) {
     b[j] ~ dexp(70)
     y[i] ~ dnorm(100, 0.06) + b[j]
    }
    }
    }
data1 <- list(N=nrow(df2), K=10, y=df2$IQ, b=1:length(unique(df2$variable)))
jags(data=data1, parameters.to.save="b", model.file=model1)




# eg groundTruth(c(TRUE, FALSE, TRUE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE))
simulate <- function(a, c) {
   }

library(runjags)
model1 <- "model {
  for (i in 1:N) {
   y[i] ~ dnorm(mu[i], tau[i])
   mu[i] <- muOfClust[ clust[i] ]
   clust[i] ~ dcat(pi[])
  }

  for (i in 1:K) {
    pi[i] <- 0.05
    muOfClust[i] ~ dexp(70)
    tau[i] ~ dgamma(1.0E-3, 1.0E-3)
  }
 }"
j1 <- autorun.jags(model1, monitor=c("theta"), data = list(N=nrow(oldData2), y=oldData2$Yes, n=oldData2$N, switch=c(0.5, 0.5), clust=c(1,NA))); j1
# ...      Lower95  Median Upper95    Mean       SD Mode      MCerr MC%ofSD SSeff    AC.10   psrf
# theta[1] 0.70582 0.75651 0.97263 0.77926  0.07178   --   0.001442       2  2478  0.12978 1.0011
# theta[2] 0.72446 0.75078 0.77814 0.75054 0.013646   -- 0.00009649     0.7 20000 0.009458      1
~~~

https://github.com/jeromyanglim/JAGS_by_Example/blob/master/03-multilevel/varying-intercept-long/varying-intercept-long.rmd
http://doingbayesiandataanalysis.blogspot.com/2012/06/mixture-of-normal-distributions.html
http://www.stats.ox.ac.uk/~bardenet/Material/mixture_with_jags_only_mu.html

---

"Genome-wide association study identifies 74 [162] loci associated with educational attainment", Okbay et al 2016 https://www.dropbox.com/s/my9719yd8s5hplf/2016-okbay-2.pdf
supplementary info: http://www.nature.com/nature/journal/vaop/ncurrent/extref/nature17671-s1.pdf http://www.nature.com/nature/journal/vaop/ncurrent/extref/nature17671-s2.xlsx http://www.thessgac.org/#!data/kuzq8 http://ssgac.org/documents/FAQ_74_loci_educational_attainment.pdf

> Educational attainment is strongly influenced by social and other environmental factors, but genetic factors are estimated to account for at least 20% of the variation across individuals1. Here we report the results of a genome-wide association study (GWAS) for educational attainment that extends our earlier discovery sample1, 2 of 101,069 individuals to 293,723 individuals, and a replication study in an independent sample of 111,349 individuals from the UK Biobank. We identify 74 [162 total] genome-wide significant loci associated with the number of years of schooling completed. Single-nucleotide polymorphisms associated with educational attainment are disproportionately found in genomic regions regulating gene expression in the fetal brain. Candidate genes are preferentially expressed in neural tissue, especially during the prenatal period, and enriched for biological pathways involved in neural development. Our findings demonstrate that, even for a behavioural phenotype that is mostly environmentally determined, a well-powered GWAS identifies replicable associated genetic variants that suggest biologically relevant pathways. Because educational attainment is measured in large numbers of individuals, it will continue to be useful as a proxy phenotype in efforts to characterize the genetic influences of related phenotypes, including cognition and neuropsychiatric diseases.
>
> Using procedures identical to those described in SI Section 1.6, we conducted a meta-analysis of the EduYears phenotype, combining the results from our discovery cohorts (N = 293,723) and the results from the UKB replication cohort (N = 111,349). Expanding the overall sample size to N = 405,072 increases the number of approximately independent genome-wide significant loci from 74 to 162.
>
> ...This background suffices to motivate the biological questions that arise in the interpretation of GWAS results and the means by which these questions might be tentatively addressed. For starters, since a GWAS locus typically contains many other SNPs in LD with the defining lead SNP and with each other, it is natural to ask: which of these SNPs is the actual causal site responsible for the downstream phenotypic variation? Many SNPs in the genome appear to be biologically inert-neither encoding differences in protein composition nor affecting gene regulation-and a lead GWAS SNP may fall into this category and nonetheless show the strongest association signal as a result of statistical noise or happenstance LD with multiple causal sites. Fortunately, much is known from external sources of data about whether variation at a particular site is likely to have biological consequences, and exploiting these resources is our general strategy for fine-mapping loci: nominating individual sites that may be causally responsible for the GWAS signals. Descriptions of genomic sites or regions based on external sources of data are known as annotations, and readers will not go far astray if they interpret this term rather literally (as referring to a note of explanation or comment added to a text in one of the margins). If we regard the type genome as the basic text, then annotations are additional comments describing the structural or functional properties of particular sites or the regions in which they reside. For example, all nonsynonymous sites that influence protein structures might be annotated as such. An annotation can be far more specific than this; for instance, all sites that fall in a regulatory region active in the fetal liver might bear an annotation to this effect. <!-- TODO http://biorxiv.org/content/biorxiv/early/2015/10/20/028688.full.pdf -->
> A given causal site will exert its phenotypic effect through altering the composition of a gene product or regulating its expression. Conceptually, once a causal site has been identified or at least nominated, the next question to pursue is the identity of the mediating gene. In practice, because only a handful of genes at most will typically overlap a GWAS locus, we can make\ some progress toward answering this question without precise knowledge of the causal site. The difficulty of the problem, however, should still not be underestimated. It is natural to assume that a lead GWAS SNP lying inside the boundaries of a particular gene must reflect a causal mechanism involving that gene itself, but in certain cases such a conclusion would be premature. It is possible for a causal SNP lying inside a certain gene to exert its phenotypic effect by regulating the expression of a nearby gene or for several genes to intervene between the SNP and its regulatory target.
> Supplementary Table 4.1 ranks each gene overlapping a DEPICT-defined locus by the number of discrete evidentiary items favoring that gene (see Supplementary Information section 4.5 for details regarding DEPICT). These lines of evidence are taken from a number of our analyses to be detailed in the following subsections. Our primary tool for gene prioritization is DEPICT, which can be used to calculate a P-value and associated FDR for each gene. It is important to keep in mind, however, that a gene-level P-value returned by DEPICT refers to the tail probability under the null hypothesis that random sampling of loci can account for annotations and patterns of co-expression shared by the focal gene with genes in all other GWAS-identified loci. Although it is very reasonable to expect that genes involved in the same phenotype do indeed share annotations and patterns of co-expression, it may be the case that certain causal genes do not conform to this expectation and thus fail to yield low DEPICT P-values. This is why we do not rely on DEPICT alone but also the other lines of evidence described in the caption of Supplementary Table 4.1.
>
> However, a priori we know that some SNPs are more likely to be associated with the phenotype than others; for example, it is often assumed that nonsynonymous SNPs are more likely to influence phenotypes than sites that fall far from all known genes. So a P-value of 5×10 −7 , say, though not typically considered significant at the genome-wide level, might merit a second look if the SNP in question is nonsynonymous.
> Formalizing this intuition can be done with Bayesian statistics, which combines the strength of evidence in favor of a hypothesis (in our case, that a genomic site is associated with a phenotype) with the prior probability of the hypothesis. Deciding how to set this prior is often subjective. However, if many hypotheses are being tested (for example, if there are thousands of nonsynonymous polymorphisms in the genome), then the prior can be estimated from the data themselves using what is called "empirical Bayes" methodology. For example, if it turns out that SNPs with low P-values tend to be nonsynonymous sites rather than other types of sites, then the prior probability of true association is increased at all nonsynonymous sites. In this way a nonsynonymous site that otherwise falls short of the conventional significance threshold can become prioritized once the empirically estimated prior probability of association is taken into account. Note that such favorable reweighting of sites within a particular class is not set a priori, but is learned from the GWAS results themselves. In our case, we split the genome into approximately independent blocks and estimate the prior probability that each block contains a causal SNP that influences the phenotype and (within each block) the conditional prior probability that each individual SNP is the causal one. Each such probability is allowed to depend on annotations describing structural or functional properties of the genomic region or the SNPs within it. We can then empirically estimate to extent to each annotation predicts association with the focal phenotype. For a complete description of the fgwas method, see ref. 1.
> 4.2.3
> Methods
> For application to the GWAS of EduYears, we used the same set of 450 annotations as ref. 1; these are available at https://github.com/joepickrell/1000-genomes.
> ...4.2.6
> Reweighted GWAS and Fine Mapping
> We reweighted the GWAS results using the functional-genomic results described above. Using a regional posterior probability of association (PPA) greater than 0.90 as the cutoff, we identified 102 regions likely to harbor a causal SNP with respect to EduYears (Extended Data Fig. 7c and Supplementary Table 4.2.1). All but two of our 74 lead EduYears-associated SNPs fall within one of these 102 regions. The exceptions are rs3101246 and rs2837992, which attained PPA > 0.80 (Extended Data Fig. 7c). In previous applications of fgwas, the majority of novel loci that attained the equivalent of genome-wide significance only upon reweighting later attained the conventional P < 5×10 −8 in larger cohorts 1 .
> Within each region attaining PPA > 0.90, each SNP received a conditional posterior probability of being the causal SNP (under the assumption that there is just one causal SNP in the region). The method of assigning this latter posterior probability is similar to that of ref. 6, except that the input Bayes factors are reweighted by annotation-dependent and hence SNP-varying prior probabilities. In essence, the likelihood of causality at an individual SNP derives from its Bayes factor with respect to phenotypic association (which is monotonically related to the P-value under reasonable assumptions), whereas the prior probability is derived from any empirical genome-wide tendency for the annotations borne by the SNP to predict evidence of association. Thus, the SNP with the largest posterior probabilities of causality tend to exhibit among the strongest P-values within their loci and functional annotations that predict association throughout the genome. Note that proper calibration of this posterior probability requires that all potential causal sites have been either genotyped or imputed, which may not be the case in our application; we did not include difficult-to-impute non-SNP sites such as insertions/deletions in the GWAS meta-analysis. With this caveat in mind, we identified 17 regions where fine mapping amassed over 50 percent of the posterior probability on a single SNP (Supplementary Table 4.2.2). Of our 74 lead EduYears SNPs, 9 are good candidates for being the causal sites driving their association signals [12%]. One of our top SNPs, rs4500960, is in nearly perfect LD with the causal candidate rs2268894 (and is indeed the second most likely causal SNP in this region according to fgwas). The causal candidate rs6882046 is within 75kb of two lead SNPs on chromosome 5 (rs324886 and rs10061788), but no two of these three SNPs show strong LD. Interestingly, the remaining 6 causal candidates lie in genomic regions that only attain the equivalent of genome-wide significance upon Bayesian reweighting. Of the 17 causal candidates, 9 lie in regions that are DNase I hypersensitive in the fetal brain.
>
> Table 4.2.2:
>
> Posterior probability of causality
> ----------------------------------
> 0.992035
> 0.766500
> 0.842271
> 0.567184
> 0.697862
> 0.524760
> 0.632536
> 0.885280
> 0.968627
> 0.781563
> 0.629610
> 0.837746
> 0.725158
> 0.755457
> 0.784373
> 0.682947
> 0.832675
>
>
> [mean(c(0.524760, 0.567184, 0.629610, 0.632536, 0.682947, 0.697862, 0.725158, 0.755457, 0.766500, 0.781563, 0.784373, 0.832675, 0.837746, 0.842271, 0.885280, 0.968627, 0.992035)) = 0.76, 0.76*19=14.4]
>
> The results from both approaches show that prediction accuracy increases as more SNPs are used to construct the score, with the maximum predictive power achieved when using all the genotyped SNPs (with Approach 1). In that case, the weighted average across the two cohorts of the incremental R 2 is ~3.85%.
>
> [Versus 2% from Rietveld's n=100k; this is in line with the rough doubling of the main SSGAC sample size. The additional UK Biobank sample of n=111k does not seem to have been used but if it was used, should boost the polygenic score to ~5.3%?]
>
> ...The magnitude of predictive power that we observe is less than one might have expected on the basis of statistical genetics calculations 6 and GCTA-GREML estimates of "SNP heritability" from individual cohorts. Indeed, Rietveld et al. (2013) 7 reported GCTA-GREML estimates of SNP heritability for each of two cohorts (STR and QIMR), and the mean estimate was 22.4%. Assuming that 22.4% is in fact the true SNP heritability, the calculations outlined in the SOM of Rietveld et al. (pp. 22-23) generate a prediction of R 2 = 11.0% for a score constructed from the GWAS estimates of this paper and of R 2 = 6.1% for a score constructed from the combined (discovery + replication cohorts, but excluding the validation cohorts) GWAS sample of N = ~117,000-119,000 in Rietveld et al.-substantially higher than the 3.85% that we achieve here (with the score based on all genotyped SNPs) and the 2.2% Rietveld et al. achieved, respectively.
> These discrepancies between the scores' predicted and estimated R 2 may be due to the failure of some of the assumptions underlying the calculation of the predicted R 2 . An alternative (or additional) explanation is that the true SNP heritability for the GWAS sample pooled across cohorts is lower than 22.4%. That would be the case if the true GWAS coefficients differ across cohorts, perhaps due to heterogeneity in phenotype measurement or gene-by-environment interactions. If so, then a polygenic score constructed from the pooled GWAS sample would be expected to have lower predictive power in an individual cohort than implied by the calculations above. Based on that reasoning, the R 2 of 2.2% observed by Rietveld et al. (2013) could be rationalized by assuming that the proportion of variance accounted for by common variants across the pooled Rietveld cohorts is only 12.7% 6 . (We obtain a similar estimate, 11.5% with a standard error of 0.45%, when we use LD Score regression 5 to estimate the SNP heritability using our pooled-sample meta-analysis results from this paper, excluding deCODE and without GC. While we believe this estimate is based on cohort results without GC, it is biased downward if any cohort in fact applied GC.) If we assume that the 12.7% is valid also for the cohorts considered in this study, we would predict an R 2 equal to 4.5%, somewhat higher than we observe in HRS and STR but much closer. However, the degree of correlation in coefficients across cohorts appears to be relatively high (Supplementary Table 1.10 reports estimates of the genetic correlation between selected cohorts and deCODE; although the correlation estimates vary a lot across cohorts, they tend to be large for the largest cohorts, and the weighted average is 0.76). We do not know whether a pooled-cohort SNP heritability of 12.7% or lower can be reconciled with the observed degree of correlation in coefficients across cohorts.
>
> The results are reported in Supplementary Tables 6.3 and 6.4. In both the STR and the HRS, cognitive performance significantly mediates the effect of PGS on EduYears; in the HRS, Openness to Experience is also a significant mediator. The indirect effects for the other mediating variables are not significant s .
> The results for cognitive performance are similar across STR and HRS. In both datasets, a one-standard deviation increase in PGS is associated with ~0.6-0.7 more years of education, and a one-standard deviation increase in cognitive performance is associated with ~0.15 more years of education. In both datasets, the direct effect (θ 1 ) of PGS on EduYears is ~0.3-0.4 and the total indirect effect (β 1 θ 2 ) is ~0.19-0.31. This implies that a one-standard-deviation increase in PGS is associated with ~0.3-0.4 more years of education, keeping the mediating variables constant, and that changing the mediating variables to the levels they would have attained had PGS increased by one standard deviation (but keeping PGS fixed) increases years of education by ~0.19-0.31 years. Lastly, in both datasets, the partial indirect effect (θ 21 β 11 ) of cognitive performance is large and very significant: the estimates are equal to 0.29 and 0.14-or 42% and 23% of the total effect (γ 1 )-in STR and HRS, respectively. The results also suggest that a one-standard deviation increase in Openness to Experience is associated with ~0.06 more years of education, and the estimated partial indirect effect for Openness to Experience is equal to 0.04-or 7% of the total effect (γ 1 ).

Fine-mapping:
"Association mapping of inflammatory bowel disease loci to single variant resolution", Huang et al 2017 http://biorxiv.org/content/early/2015/10/20/028688
[Farh et al 2015](http://www.nature.com/nature/journal/v518/n7539/full/nature13835.html "Genetic and epigenetic fine mapping of causal autoimmune disease variants")
[Gong et al 2013](http://www.sciencedirect.com/science/article/pii/S000292971300387X "Fine-mapping and Identification of BMI Loci in African Americans")
van de Bunt et al 2015 "Evaluating the Performance of Fine-Mapping Strategies at Common Variant GWAS Loci" 1http://journals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.1005535

---

let's say we have 74 SNP candidates with 2 levels each (on/off) which collectively determine the dependent variable IQ with an effect of +0.2 IQ points or +0.0133SDs each; we want power=0.80/alpha=0.05 to detect the main effect for each SNP to see if it has a non-zero effect. In factorial ANOVA terms, this would be a design with 74^2=5476 possible conditions (since we are only interested in main effects and not interactions, I think it could be a partial factorial design where many of those are dropped). As a multiple regression, it'd be something like `IQ ~ A + B + C + ... ZZ`. The effect of each variable is quite small, and so adding them all into a linear model will explain only a small amount of variance: (0.2/15)^2 * 74 = 0.0132.

G*Power 3.1 (http://www.gpower.hhu.de/ Windows version under Wine), test family 'F test', statistical test 'Linear multiple regression: Fixed model, R increase', a priori power analysis:

l = 0.0133766?
n=2711

Suppose we have a budget of 64 edits per embryo, and we want to be able to fill them all up with causal variants; we know that around half will already be the good variant, so we need to have at least 64*2=128 causal variants.  And since we know that each SNP candidate has a ~10% probability of being causal, we need to be testing 10 * 128 = >1280 SNPs to successfully winnow down to >128 causal SNPs which will yield >64 available edits.

We'll drop the mean effect to 0.1 points and consider sample size requirements testing 1280 SNPs. (0.1/15)^2 * 1280 = 0.05688888889

l=0.06032045
n=2954

What does 80% power and 5% alpha mean here? We know that ~10% are causal (our base rate for a true finding is 10%), so there are 128 causal SNPs and 1152 noncausal SNPs here. There is a 5% false positive rate, so there will be 0.05*1152=58 false positive SNPs. There is 80% power, so we will detect 0.8*128=102 causal SNPs. So we will have 58+102=160 apparently causal SNPs, but only 58/160=36% are actually causal. So we waste 64% of our edits. We need to do better.

let's try with 0.9 and 0.01

l=0.06032045
n=3987

0.9*0.1*1280=115
0.01*(1280-115)=11
115/(115+11)=0.91

0.1 average effect might be optimistic even though effect sizes decline slowly, so one last try with 0.05 mean effect size over those 1280 SNPs: (0.05/15)^2 * 1280 = 0.0142

l = 0.0144045
n=14197


~~~{.R}
n <- 1000
alpha <- 0.005
SNP_candidates <- 162
SNP_mean_effect <- 0.2
SNP_mean_frequency <- 0.5
SNP_causal_probability <- 0.12
SNP_effects <- sample(c(SNP_mean_effect, 0), SNP_candidates, replace=TRUE,
                      prob=c(SNP_causal_probability, 1-SNP_causal_probability))
which(SNP_effects>0)
r2 <- 0.01

generateSample <- function(n, SNP_effects, SNP_candidates=162, SNP_mean_frequency=0.5) {
    dm <- matrix(nrow=n, ncol=SNP_candidates+1)
    for (i in 1:n) {
        SNP_draw <- rbinom(SNP_candidates, 1, p=SNP_mean_frequency)
        SNPs_genetic <- sum(ifelse(SNP_draw, SNP_effects, 0))
        IQ <- rnorm(1, mean=100, sd=15) + SNPs_genetic
        dm[i,] <- c(round(IQ), SNP_draw)
        }
    df <- as.data.frame(dm)
    colnames(df) <- c("IQ", paste("SNP.", as.character(1:SNP_candidates), sep=""))
    return(df)
}
df <- generateSample(n, SNP_effects, SNP_candidates, SNP_mean_frequency)

power <- sapply(seq(1, n, by=500), function(i) {
    l <- summary(lm(IQ ~ ., data=df[1:i,]))
    # coefficients <- l$coefficients[,1]
    pvalues <- l$coefficients[,4][-1]
    causalPvalues <- na.omit(ifelse(SNP_effects>0, pvalues, NA))
    noncausalPvalues <- na.omit(ifelse(SNP_effects==0, pvalues, NA))

    alphas <- seq(from=0.001, to=0.05, by=0.001)
    alphaYields <- sapply(alphas, function(alpha) { sum(causalPvalues<alpha) / (sum(pvalues<alpha)) })
    alpha <- alphas[which.max(alphaYields)]

    positives <- sum(pvalues<alpha)
    falsePositives <- sum(noncausalPvalues<alpha)
    truePositives <- sum(causalPvalues<alpha)
    truePositiveFraction <- truePositives / length(causalPvalues)
    causalFraction <- (truePositives + falsePositives) / positives
    return(causalFraction) })




library(BGLR)
# n <- 1000
ns <- seq(100, 50000, by=400)
recovery <- sapply(ns, function(n) {
  mean(replicate(100, {
    ## bootstrap a new dataset
    d <- df[sample(nrow(df), n, replace=TRUE),]

    b <- BGLR(d$IQ, ETA=list(list(X=d[-1], model="BayesB", probIn=SNP_causal_probability)), R2=0.01, burnIn=0, verbose=FALSE)
    # plot((b$ETA[[1]]$b), SNP_effects!=0)
    estimate <- data.frame(Causal=SNP_effects!=0, Estimate=(b$ETA[[1]]$b))
    estimate <- estimate[order(estimate$Estimate),]
    truePositives <- sum(estimate$Causal[1:64])
    falseNegatives <- sum(estimate$Causal[-(1:64)])
    # truePositives;falseNegatives
    causalFraction <- truePositives / (truePositives+falseNegatives)
    print(causalFraction)
    return(causalFraction)
    })) })
recovery
library(ggplot2)
qplot(ns, recovery) + geom_smooth(method=lm)


library(glmnet)
cv <- cv.glmnet(as.matrix(df[-1]), df$IQ)
g <- glmnet(as.matrix(df[-1]), df$IQ, lambda=cv$lambda.min)
coef(g)
causalSNPs <- which(SNP_effects>0)
ridgeSNPs <- which(as.matrix(coef(g)[-1,])!=0)
intersect(causalSNPs, ridgeSNPs)

length(intersect(causalSNPs, ridgeSNPs)) / length(causalSNPs)
length(intersect(causalSNPs, ridgeSNPs)) / length(ridgeSNPs)



Thompson sampling with a subset/edit budget:

SNP_edit_limit <- 100
SNP_candidates <- 500
verbose <- TRUE
SNP_mean_effect <- 0.2
SNP_mean_frequency <- 0.5
SNP_causal_probability <- 0.12
r2 <- 0.05
iqError <- 0.55 ## 5yo IQ scores correlate r=0.55 with adult
SNP_effects <- sample(c(SNP_mean_effect, 0), SNP_candidates, replace=TRUE,
                      prob=c(SNP_causal_probability, 1-SNP_causal_probability))
which(SNP_effects>0)

measurementError <- function(r, IQ) {
    IQ.true.std <- (IQ-100)/15
    IQ.measured.std <- r*IQ.true.std + rnorm(length(IQ), mean=0, sd=sqrt(1 - r^2))
    IQ.measured <- 100 + 15 * IQ.measured.std
    return(IQ.measured) }
generateExperimentalSample <- function(n, r, SNP_effects, SNP_candidates, SNP_mean_frequency, SNP_draw_generator) {
    dm <- matrix(nrow=n, ncol=SNP_candidates+1+1) ## allocate space for all SNPs, true IQ, and measured IQ
    for (i in 1:n) {
        SNP_draw <- SNP_draw_generator() # which SNPs to toggle
        SNPs <- ifelse(SNP_draw, SNP_effects, 0) ## convert to effects
        SNP_genetic_score <- sum(SNPs, na.rm=TRUE)
        ## generate a N(100,15) - minus however much our candidate genes explain
        IQ <- round(rnorm(1, mean=100, sd= sqrt((15^2) * (1-r2))) + SNP_genetic_score)
        IQ_measured <- round(measurementError(r, IQ))
        dm[i,] <- c(IQ, IQ_measured, SNP_draw)
        }
    df <- as.data.frame(dm)
    colnames(df) <- c("IQ", "IQ.measured", paste("SNP.", as.character(1:SNP_candidates), sep=""))
    return(df)
}
generateRandomSample <- function(n, r=1, SNP_effects, SNP_candidates, SNP_mean_frequency) {
    generateExperimentalSample(n, r, SNP_effects, SNP_candidates, SNP_mean_frequency,
                               function() { rbinom(SNP_candidates, 1, p=SNP_mean_frequency) })
}

d <- generateRandomSample(1000, iqError, SNP_effects, SNP_candidates, SNP_mean_frequency)
summary(d)

library(BGLR)
library(ggplot2)
maximumDays <- 10000
batch <- 10
lag <- 5*365
jumpForward <- lag*5
## initialize with a seed of n>=2; with less or an empty dataframe, BGLR will crash
d <- generateRandomSample(jumpForward, iqError, SNP_effects, SNP_candidates, SNP_mean_frequency)
d$Date <- 1:jumpForward
# d$Date <- -lag # available immediately
regretLog <- data.frame(N=integer(), N.eff=integer(), Regret=numeric(), Fraction.random=numeric(), Fraction.causals=numeric(), Causal.found=integer(), Causal.notfound=integer())
for (i in jumpForward:maximumDays) {

    ## i=date; day 1, day 2, etc. A datapoint is only available if it was created more than 'lag' days ago; ie if we do 1 a day, then on day 20 with lag 18
    ## we will have 20-18=2 datapoints available. With a 5 year lag, we will go 1825 time-steps before any new data starts becoming available.
    dAvailable <- d[i >= (d$Date+lag),]
    ## quick Bayesian model of our data up to now, using Lasso priors and our SNP setup
    ## BGLR will randomly crash with a gamma/lambda range error every ~5k calls, so catch & retry until it succeeds:
    while(TRUE) {
    tryCatch({
      b <- BGLR(dAvailable$IQ.measured, ETA=list(list(X=dAvailable[-c(1, 2, length(colnames(dAvailable)))],
                                          model="BL", type="beta", probIn=0.12, counts=162, R2=r2, lambda=202, max=500)),
                verbose=FALSE)
      means <- b$ETA[[1]]$b; sds <- b$ETA[[1]]$SD.b
      break;
      }, error = function(e) { print(e) })
      }

    ## Thompson sampling: for Thompson sampling, we sample 1 possible value of each parameter from that parameter's
    ## posterior distribution. Normally, we would sample from the posterior samples returned by JAGS, but BGLR returns
    ## instead a mean+SD, so we sample from each parameter's normal distribution defined by the mean/sd. Then we see if it
    ## was positive (and hence worth editing); if it is positive, then we choose to edit it and toggle it to '1' (since
    ## we set the problem up as 1=increasing). This boolean is then passed into the simulation and a fresh datapoint generated according to
    ## that intervention. In the next loop, this new datapoint will be incorporated into the posterior and so on.
    ## For multiple-edit Thompson sampling where we can only edit _l_ out of _k_ possible SNPs, we sample 1 possible value
    ## as before, then we sort and take the top _l_ out of _k_ actions;
    ## then to decide whether to sample 1 or 0 in each arm, we do a second Thompson sample within each arm.
    ##
    ## To save computations while simulating, or to be more realistic, we might have batches: multiple datapoints in between
    ## updates. If batch=1, it is the conventional Thompson sample (and most data-efficient) but computationally demanding
    ## In the delayed-updates setting, 'batch' is how many get created each day
    for (j in 1:batch) {
     SNPs_Thompson_sampled <- function () {
         ## select the _l_ arms
         samplesArms <- rnorm(n=SNP_candidates, mean=means, sd=sds)
         cutoff <- sort(samplesArms, decreasing=TRUE)[SNP_edit_limit]
         l <- which(samplesArms>=cutoff)

         ## for each winner, do another Thompson sample, and record the losers as NA/not-played
         choices <- rep(NA, SNP_candidates)
         samplesActions <- rnorm(n=SNP_edit_limit, mean=means[l], sd=sds[l]) > 0
         choices[l] <- samplesActions
         return(choices)
         }
     newD <- generateExperimentalSample(1, iqError, SNP_effects, SNP_candidates, SNP_mean_frequency, SNPs_Thompson_sampled)
     newD$Date <- i
     d <- rbind(d, newD)
     }

    ## reports, evaluations, logging:
    estimate <- data.frame(Causal=SNP_effects!=0, Effect=SNP_effects, Estimate=(b$ETA[[1]]$b), SD=b$ETA[[1]]$SD.b)
    estimate <- estimate[order(estimate$Estimate, decreasing=TRUE),]
    regretLog[i,]$Causal.found <- sum(estimate$Causal[1:SNP_edit_limit])
    regretLog[i,]$Causal.notfound <- sum(estimate$Causal[-(1:SNP_edit_limit)])
    regretLog[i,]$Fraction.random  <- sum(estimate$Causal!=0) / SNP_candidates  ## base rate: random guessing
    regretLog[i,]$Fraction.causals <- round(regretLog[i,]$Causal.found / (regretLog[i,]$Causal.found+regretLog[i,]$Causal.notfound), digits=2)
    regretLog[i,]$Regret <- (sum(estimate$Effect) - sum(estimate$Effect[1:SNP_edit_limit])) * SNP_mean_frequency
    regretLog[i,]$N <- nrow(d)
    regretLog[i,]$N.eff <- nrow(dAvailable)

    if(verbose) { print(regretLog[i,]) }
}
qplot(regretLog$N, jitter(regretLog$Regret), xlab="Total N (not effective N)", ylab="Regret (expected lost IQ points compared to omniscience)", main=paste("Edits:", SNP_edit_limit, "; Candidates:", SNP_candidates)) + stat_smooth()

b <- BGLR(d$IQ.measured, ETA=list(list(X=d[-c(1, 2, length(colnames(d)))], model="BL", type="beta", probIn=0.12, counts=162, R2=r2, lambda=202, max=500)), verbose=FALSE)
means <- b$ETA[[1]]$b; sds <- b$ETA[[1]]$SD.b; qplot(SNP_effects, b$ETA[[1]]$b, color=b$ETA[[1]]$SD.b, main=paste("Edits:", SNP_edit_limit, "; Candidates:", SNP_candidates))
image(as.matrix(d[-c(1, 2, length(colnames(d)))]), col=heat.colors(2))
~~~