Partitioned Heritability from Continuous Annotations

!!! Note that bugs on scripts quantile_h2g.r and quantile_M.pl have been fixed on 8/10/18; check that you have the lastest versions!!!

Overview

Although ldsc software has been designed for binary annotations, the software allows taking continuous annotations as inputs for both --l2 and --h2 options. However, some result outputs of --h2 option are not meaningful anymore.

In this tutorial, you will partition the heritability of BMI by functional categories, using the baseline-LD model from Gazal et al. bioRxiv, which contains the baseline model as well as several continuous annotations. You will see how to interpret results for binary and continuous annotations. We will assume that you have already followed the previous tutorial on partitioned heritability, that you already generated the file BMI.sumstats.gz, and that you already installed python and the last version of ldsc.

Step 1: Running ldsc and interpreting outputs

The annotations and the LD scores from the baseline-LD model used in Gazal et al. bioRxiv can be downloaded here. The frequency and weight files (computed on European of Phase 3 of 1000 Genomes) can be downloaded here and here.

Run ldsc on BMI summary statistics using the command

python ldsc/ldsc.py \
  --h2 BMI.sumstats.gz \
  --ref-ld-chr baselineLD. \
  --frqfile-chr 1000G.EUR.QC. \
  --w-ld-chr weights.hm3_noMHC. \
  --overlap-annot \
  --print-coefficients \
  --print-delete-vals \
  --out BMI.baselineLD

The --print-coefficients flag outputs the estimated regression coefficients (i.e. the effect size of the annotation conditioned to all others) in the last column of the .result file. The --print-delete-vals flag outputs the 200 Jacknife coefficient estimates used to compute standard errors around the coefficient estimates in a .part_delete file (check that you have installed the last version of ldsc -after 11/09/2016- to access this output file).

The file BMI.baselineLD.results contains one row for each category and columns summarizing the results: Proportion of SNPs, Proportion of heritability, Enrichment, and standard errors. Enrichment is (Prop. heritability) / (Prop. SNPs). These outputs make sense only for binary annotations. Do not try to interpret them for continuous annotations. Using --print-coefficients flag outputs the regression coefficients and corresponding standard errors and Z score for each annotation. These coefficients measure the additional contribution of one annotation to the model and are interpretable for both binary and continuous annotations (see Finucane et al. 2015 Nat Genet and Gazal et al. bioRxiv for a discussion of the relationship between these regression coefficients and proportions of heritability).

Step 2: Computing heritability per quantile of one continuous annotation

Computing the proportion of heritability explained by each quantile of a continuous annotation provides a more intuitive interpretation of the magnitude of a continuous annotation effects. We released an R script quantile_h2g.r to compute these quantities. To compute the proportion of heritability explained by each quintile of MAF-adjusted predicted allele age in the baseline-LD model run the following command

Rscript quantile_h2g.r baselineLD.MAF_Adj_Predicted_Allele_Age.q5.M BMI.baselineLD BMI.baselineLD.Allele_Age.q5.txt

where the 3 arguments of the function need to be

1. the file containing the sum of each annotation by quantile of continuous annotations (here baselineLD.AlleleAge.q5.M; this file is available when downloading LD scores from the baseline-LD model, in addition to quintiles .q5.txt and deciles .q10.txt files of each LD-related annotations of the baseline-LD model). For example, the 3 first lines of baselineLD.AlleleAge.q5.M are

   head -3 baselineLD.MAF_Adj_Predicted_Allele_Age.q5.M | column -t N 1070940 1070943 1070946 1070941 1070947 base 1070940 1070943 1070946 1070941 1070947 Coding_UCSC 18830 16652 15737 14964 11810

and indicates the number of SNPs in each quintile (line starting with N), and the sum of the base and Coding_UCSC annotations in each quantile (here for example 18830 coding reference SNPs are in the quintile with the lowest MAF-adjusted predicted allele value, while 11810 coding reference SNPs are in the quintile with the highest MAF-adjusted predicted allele value). Note that these files are computed only on reference SNPs with MAF >= 5%, as stratified LD score regression only uses common SNPs to compute heritability estimates (see Finucane et al. 2015 Nat Genet for more details).

2. the header of the ldsc outputs (here BMI.baselineLD).

3. the output file name (here BMI.baselineLD.AlleleAge.q5.txt).

This output file has one row for each quantile (starting with lowest values) and column summarizing the heritability explained by each quantile, its enrichment and corresponding standard error and P value.

Step 3: Adding one continuous annotation to the baseline-LD model

Let’s now summarize the different steps to perform if you want to add one continuous the baseline-LD model.

1. Create 22 yourannot.*.annot.gz files with your continuous annotation of interest.

2. Compute LD scores for this annotation. List of HapMap 3 SNPs (that we recommend to perform regression) can be downloaded here. PLINK files of European of Phase 3 of 1000 Genomes can be downloaded here. The commands to compute LD scores on continuous annotations are the same as the ones to compute LD scores on binary annotations:

   awk '{if ($1!="SNP") {print $1} }' w_hm3.snplist > listHM3.txt for CHR in {1..22} do python ldsc/ldsc.py
   --l2
   --bfile 1000G.EUR.QC.$CHR
   --ld-wind-cm 1
   --print-snps listHM3.txt
   --annot yourannot.$CHR.annot.gz
   --out yourannot.$CHR done

3. Run ldsc on BMI summary statistics using baseline-LD model annotations and your new annotation using the command

   python ldsc/ldsc.py
   --h2 BMI.sumstats.gz
   --ref-ld-chr baselineLD.,yourannot.
   --frqfile-chr 1000G.EUR.QC.
   --w-ld-chr weights.hm3_noMHC.
   --overlap-annot
   --print-coefficients
   --print-delete-vals
   --out BMI.baselineLD_yourannot

and interpret the regression coefficient results of file BMI.baselineLD_yourannot.results. Remember that to combine two arguments to the -–ref-ld-chr flag, the corresponding files need to have the same SNPs in the same order.

4. To create the file containing the sum of each annotation by quantile of your continuous annotation, we released a perl script quantile_M.pl to compute these quantities. Run the command

   perl quantile_M.pl
   --ref-annot-chr baselineLD.,yourannot.
   --frqfile-chr 1000G.EUR.QC.
   --annot-header your_annot_header
   --nb-quantile 5
   --maf 0.05
   --out AlleleAge.baselineLD_yourannot.q5.M

where --ref-annot-chr indicates the annotation files to read, --frqfile-chr indicates the frq files to read, --annot-header indicates the header of your annotation in the yourannot.*.annot.gz files, --nb-quantile indicates the number of quantiles to generate (5 by default), --maf indicates the MAF threshold to use to include reference SNPs (0.05 by default), and --out indicates the ouput file. Type perl quantile_M.pl --help for more information. Note that perl module IO::Uncompress::Gunzip should be installed to run this script.

5. Compute heritability per quantile of one continuous annotation

   Rscript quantile_h2g.r baselineLD_yourannot.AlleleAge.q5.M BMI.baselineLD_yourannot BMI.baselineLD_yourannot.AlleleAge.q5.txt