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adds test_left_censorship, and all the docs to do it
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44 changes: 32 additions & 12 deletions DESCRIPTION
Original file line number Diff line number Diff line change
@@ -1,24 +1,44 @@
Package: ICIKendallTau
Title: Calculates information-content-informed Kendall-tau
Version: 1.0.5
Date: 2024-04-08
Authors@R: c(person(given = c("Robert", "M"), family = "Flight", role =
c("aut", "cre"), email = "rflight79@gmail.com", comment =
c(ORCID = "0000-0001-8141-7788")), person(given = c("Hunter",
"NB"), family = "Moseley", role = "aut", comment = c(ORCID =
"0000-0003-3995-5368")))
Version: 1.1.0
Authors@R: c(
person(
given = c("Robert", "M"),
family = "Flight",
role = c("aut", "cre"),
email = "rflight79@gmail.com",
comment = c(ORCID = "0000-0001-8141-7788")),
person(
given = c("Hunter", "NB"),
family = "Moseley",
role = "aut",
comment = c(ORCID = "0000-0003-3995-5368")))
Description: Provides functions for calculating
information-content-informed Kendall-tau. This version of
Kendall-tau allows for the inclusion of missing values.
VignetteBuilder: knitr
LazyData: true
License: MIT + file LICENSE
Encoding: UTF-8
Roxygen: list(markdown = TRUE)
RoxygenNote: 7.3.1
LinkingTo: Rcpp
Imports: Rcpp, purrr, utils, stringr
Suggests: furrr, future, testthat (>= 3.0.0), microbenchmark,
rmarkdown, knitr, dplyr, logger
URL: https://moseleybioinformaticslab.github.io/ICIKendallTau
https://github.com/moseleybioinformaticslab/ICIKendallTau
Imports: Rcpp,
purrr,
utils,
stringr,
stats
Suggests: furrr,
future,
testthat (>= 3.0.0),
microbenchmark,
rmarkdown,
knitr,
dplyr,
logger,
withr,
naniar
URL: https://moseleybioinformaticslab.github.io/ICIKendallTau/
https://github.com/moseleybioinformaticslab/ICIKendallTau/
BugReports: https://github.com/moseleybioinformaticslab/ICIKendallTau/issues
Config/testthat/edition: 3
4 changes: 4 additions & 0 deletions NEWS.md
Original file line number Diff line number Diff line change
@@ -1,3 +1,7 @@
# ICIKendallTau 1.1.0

- adds the function `test_left_censorship` to verify if `ici_kendalltau` is appropriate to use on the data or not.

# ICIKendallTau 1.0.0

- Calculates correlation between columns of the matrix, **not** the rows.
Expand Down
16 changes: 10 additions & 6 deletions R/kendalltau.R
Original file line number Diff line number Diff line change
Expand Up @@ -12,11 +12,9 @@
#' @param check_timing logical to determine should we try to estimate run time for full dataset? (default is FALSE)
#' @param return_matrix logical, should the data.frame or matrix result be returned?
#'
#' @seealso [vignette("ici-kendalltau", package = "ICIKendallTau")] [test_left_censorship()]
#' @seealso [test_left_censorship()] [pairwise_completeness()] [kt_fast()]
#'
#' @details For more details, see the ICI-Kendall-tau vignette
#'
#' \code{browseVignettes("ICIKendallTau")}
#' @details For more details, see the vignette `vignette("ici-kendalltau", package = "ICIKendallTau"))`
#'
#' The default for \code{global_na} includes what values in the data to replace with NA for the Kendall-tau calculation. By default these are \code{global_na = c(NA, Inf, 0)}. If you want to replace something other than 0, for example, you might use \code{global_na = c(NA, Inf, -2)}, and all values of -2 will be replaced instead of 0.
#'
Expand All @@ -30,6 +28,10 @@
#' * taumax: the theoretical maximum kendall-tau value possible
#'
#' Eventually, we plan to provide two more parameters for replacing values, \code{feature_na} for feature specific NA values and \code{sample_na} for sample specific NA values.
#'
#' If you want to know if the missing values in your data are possibly due to
#' left-censorship, we recommend testing that hypothesis with [test_left_censorship()]
#' first.
#'
#' @return list with cor, raw, pval, taumax
#'
Expand Down Expand Up @@ -315,8 +317,8 @@ ici_kendalltau = function(data_matrix,
#' @param use an optional character string giving a method for computing correlations in the presence of missing values. This must be (an abbreviation of) one of the strings "everything", "all.obs", "complete.obs", or "pairwise.complete.obs".
#' @param return_matrix Should the matrices of values be returned, or a long data.frame
#'
#' @details Although the interface is *mostly* identical to the built-in `stats::cor` method,
#' there are some differences.
#' @details Although the interface is *mostly* identical to the built-in
#' [stats::cor()] method, there are some differences.
#'
#' * if providing both `x` and `y`, it is assumed they are both
#' single vectors.
Expand Down Expand Up @@ -535,6 +537,8 @@ kt_fast = function(x, y = NULL, use = "everything", return_matrix = TRUE)
#' @param include_only is there certain comparisons to do?
#' @param return_matrix should the matrix or data.frame be returned?
#'
#' @seealso [ici_kendalltau()]
#'
#' @export
#'
#' @return matrix of degree of completeness
Expand Down
4 changes: 3 additions & 1 deletion R/left_censorship.R
Original file line number Diff line number Diff line change
Expand Up @@ -17,7 +17,9 @@
#' instances (minus missing values) as the number of trials, and the number of
#' of features below the sample medians as the number of successes.
#'
#' @seealso [vignette("testing-for-left-censorship", package = "ICIKendallTau")]
#' There is a bit more detail in the vignette: `vignette("testing-for-left-censorship", package = "ICIKendallTau")`
#'
#' @seealso [ici_kendalltau()]
#'
#' @examples
#' # this example has 80% missing due to left-censorship
Expand Down
8 changes: 5 additions & 3 deletions README.Rmd
Original file line number Diff line number Diff line change
Expand Up @@ -21,7 +21,7 @@ knitr::opts_chunk$set(
[![ICIKendallTau status badge](https://moseleybioinformaticslab.r-universe.dev/badges/ICIKendallTau)](https://moseleybioinformaticslab.r-universe.dev)
<!-- badges: end -->

You can see the pkgdown site [here](https://moseleybioinformaticslab.github.io/ICIKendallTau).
You can see the pkgdown site [here](https://moseleybioinformaticslab.github.io/ICIKendallTau/).

## Installation

Expand Down Expand Up @@ -49,7 +49,7 @@ install.packages("ICIKendallTau")
* In these cases, NA is informative.
* Therefore, in **most** analytical measurements (gene expression, proteomics, metabolomics), missing measurements should be included, and contribute to the correlation.

If you want to read more on **how** we solve this problem, see the package vignette.
If you want to read more on **how** we solve this problem, see the package [vignette](https://moseleybioinformaticslab.github.io/ICIKendallTau/articles/ici-kendalltau.html).

## Package Functions

Expand All @@ -65,6 +65,8 @@ The functions that implement this include:
* `plan(multiprocess)`
* Otherwise will only use a single core.

We've also included a function for testing if the missingness in your data comes from left-censorship, `test_left_censorship`. We walk through creating example data and testing it in the vignette [Testing for Left Censorship](https://moseleybioinformaticslab.github.io/ICIKendallTau/articles/testing-for-left-censorship).

## Examples

The most common case is a large matrix of independent samples (columns) and measured features in each of the samples (i.e. gene expression).
Expand Down Expand Up @@ -158,7 +160,7 @@ r_3 = ici_kendalltau(matrix_2)
In the case of hundreds of thousands of comparisons to be done, the result matrices can become very, very large, and require lots of memory for storage.
They are also inefficient, as both the lower and upper triangular components are stored.
An alternative storage format is as a `data.frame`, where there is a single row for each comparison performed.
This is actually how the results are stored internally, and then they are converted to a matrix form if requested (the default).s
This is actually how the results are stored internally, and then they are converted to a matrix form if requested (the default).
To keep the `data.frame` output, add the argument `return_matrix=FALSE` to the call of `ici_kendalltau`.

```{r}
Expand Down
26 changes: 13 additions & 13 deletions README.html
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Expand Up @@ -606,10 +606,10 @@
<h1 id="icikendalltau">ICIKendallTau</h1>
<!-- badges: start -->

<p><a href="https://moseleybioinformaticslab.r-universe.dev"><img src="data:image/svg+xml; charset=utf-8;base64,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" alt="ICIKendallTau status badge" /></a></p>
<p><a href="https://moseleybioinformaticslab.r-universe.dev"><img src="data:image/svg+xml; charset=utf-8;base64,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" alt="ICIKendallTau status badge" /></a></p>
<!-- badges: end -->

<p>You can see the pkgdown site <a href="https://moseleybioinformaticslab.github.io/ICIKendallTau">here</a>.</p>
<p>You can see the pkgdown site <a href="https://moseleybioinformaticslab.github.io/ICIKendallTau/">here</a>.</p>
<h2 id="installation">Installation</h2>
<p>You can install the current version of ICIKendallTau via GitHub:</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" tabindex="-1"></a>remotes<span class="sc">::</span><span class="fu">install_github</span>(<span class="st">&quot;MoseleyBioinformaticsLab/ICIKendallTau&quot;</span>)</span></code></pre></div>
Expand Down Expand Up @@ -639,7 +639,7 @@ <h2 id="problem">Problem</h2>
</ul></li>
</ul>
<p>If you want to read more on <strong>how</strong> we solve this
problem, see the package vignette.</p>
problem, see the package <a href="https://moseleybioinformaticslab.github.io/ICIKendallTau/articles/ici-kendalltau.html">vignette</a>.</p>
<h2 id="package-functions">Package Functions</h2>
<p>The functions that implement this include:</p>
<ul>
Expand All @@ -662,6 +662,10 @@ <h2 id="package-functions">Package Functions</h2>
<li>Otherwise will only use a single core.</li>
</ul></li>
</ul>
<p>We’ve also included a function for testing if the missingness in your
data comes from left-censorship, <code>test_left_censorship</code>. We
walk through creating example data and testing it in the vignette <a href="https://moseleybioinformaticslab.github.io/ICIKendallTau/articles/testing-for-left-censorship">Testing
for Left Censorship</a>.</p>
<h2 id="examples">Examples</h2>
<p>The most common case is a large matrix of independent samples
(columns) and measured features in each of the samples (i.e. gene
Expand Down Expand Up @@ -721,14 +725,10 @@ <h2 id="is-it-fast">Is It Fast?</h2>
<span id="cb5-14"><a href="#cb5-14" tabindex="-1"></a> <span class="at">times =</span> <span class="dv">5</span></span>
<span id="cb5-15"><a href="#cb5-15" tabindex="-1"></a>)</span>
<span id="cb5-16"><a href="#cb5-16" tabindex="-1"></a><span class="co">#&gt; Unit: microseconds</span></span>
<span id="cb5-17"><a href="#cb5-17" tabindex="-1"></a><span class="co">#&gt; expr min lq mean median uq max</span></span>
<span id="cb5-18"><a href="#cb5-18" tabindex="-1"></a><span class="co">#&gt; cor(x, y, method = &quot;kendall&quot;) 11506.697 11670.094 12169.6628 12006.418 12482.883 13182.222</span></span>
<span id="cb5-19"><a href="#cb5-19" tabindex="-1"></a><span class="co">#&gt; ici_kt(x, y, &quot;global&quot;) 243.866 250.125 294.6542 275.104 320.058 384.118</span></span>
<span id="cb5-20"><a href="#cb5-20" tabindex="-1"></a><span class="co">#&gt; ici_kt(x2, y2, &quot;global&quot;) 13467.011 13739.312 14658.5050 14945.446 14987.140 16153.616</span></span>
<span id="cb5-21"><a href="#cb5-21" tabindex="-1"></a><span class="co">#&gt; neval</span></span>
<span id="cb5-22"><a href="#cb5-22" tabindex="-1"></a><span class="co">#&gt; 5</span></span>
<span id="cb5-23"><a href="#cb5-23" tabindex="-1"></a><span class="co">#&gt; 5</span></span>
<span id="cb5-24"><a href="#cb5-24" tabindex="-1"></a><span class="co">#&gt; 5</span></span></code></pre></div>
<span id="cb5-17"><a href="#cb5-17" tabindex="-1"></a><span class="co">#&gt; expr min lq mean median uq max neval</span></span>
<span id="cb5-18"><a href="#cb5-18" tabindex="-1"></a><span class="co">#&gt; cor(x, y, method = &quot;kendall&quot;) 11685.244 12730.878 12860.9060 13071.630 13406.514 13410.264 5</span></span>
<span id="cb5-19"><a href="#cb5-19" tabindex="-1"></a><span class="co">#&gt; ici_kt(x, y, &quot;global&quot;) 263.306 268.503 332.1288 274.858 283.589 570.388 5</span></span>
<span id="cb5-20"><a href="#cb5-20" tabindex="-1"></a><span class="co">#&gt; ici_kt(x2, y2, &quot;global&quot;) 14110.743 14322.836 15782.6490 16053.907 16595.979 17829.780 5</span></span></code></pre></div>
<p>In the case of 40,000 features, the average time on a modern CPU is
14 milliseconds.</p>
<p>Of course, if you want to use it to calculate Kendall-tau-b without
Expand Down Expand Up @@ -757,7 +757,7 @@ <h2 id="many-many-comparisons">Many Many Comparisons</h2>
triangular components are stored. An alternative storage format is as a
<code>data.frame</code>, where there is a single row for each comparison
performed. This is actually how the results are stored internally, and
then they are converted to a matrix form if requested (the default).s To
then they are converted to a matrix form if requested (the default). To
keep the <code>data.frame</code> output, add the argument
<code>return_matrix=FALSE</code> to the call of
<code>ici_kendalltau</code>.</p>
Expand All @@ -770,7 +770,7 @@ <h2 id="many-many-comparisons">Many Many Comparisons</h2>
<span id="cb9-7"><a href="#cb9-7" tabindex="-1"></a><span class="co">#&gt; 3 s4 s4 0 1.0000000 0 1.000000 1.0000000</span></span>
<span id="cb9-8"><a href="#cb9-8" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb9-9"><a href="#cb9-9" tabindex="-1"></a><span class="co">#&gt; $run_time</span></span>
<span id="cb9-10"><a href="#cb9-10" tabindex="-1"></a><span class="co">#&gt; [1] 0.01606894</span></span></code></pre></div>
<span id="cb9-10"><a href="#cb9-10" tabindex="-1"></a><span class="co">#&gt; [1] 0.01747489</span></span></code></pre></div>
<h2 id="code-of-conduct">Code of Conduct</h2>
<p>Please note that the ICIKendallTau project is released with a <a href="https://contributor-covenant.org/version/2/0/CODE_OF_CONDUCT.html">Contributor
Code of Conduct</a>. By contributing to this project, you agree to abide
Expand Down
26 changes: 14 additions & 12 deletions README.md
Original file line number Diff line number Diff line change
Expand Up @@ -10,7 +10,7 @@ badge](https://moseleybioinformaticslab.r-universe.dev/badges/ICIKendallTau)](ht
<!-- badges: end -->

You can see the pkgdown site
[here](https://moseleybioinformaticslab.github.io/ICIKendallTau).
[here](https://moseleybioinformaticslab.github.io/ICIKendallTau/).

## Installation

Expand Down Expand Up @@ -47,7 +47,8 @@ install.packages("ICIKendallTau")
and contribute to the correlation.

If you want to read more on **how** we solve this problem, see the
package vignette.
package
[vignette](https://moseleybioinformaticslab.github.io/ICIKendallTau/articles/ici-kendalltau.html).

## Package Functions

Expand All @@ -66,6 +67,11 @@ The functions that implement this include:
- `plan(multiprocess)`
- Otherwise will only use a single core.

We’ve also included a function for testing if the missingness in your
data comes from left-censorship, `test_left_censorship`. We walk through
creating example data and testing it in the vignette [Testing for Left
Censorship](https://moseleybioinformaticslab.github.io/ICIKendallTau/articles/testing-for-left-censorship).

## Examples

The most common case is a large matrix of independent samples (columns)
Expand Down Expand Up @@ -136,14 +142,10 @@ microbenchmark(
times = 5
)
#> Unit: microseconds
#> expr min lq mean median uq max
#> cor(x, y, method = "kendall") 11506.697 11670.094 12169.6628 12006.418 12482.883 13182.222
#> ici_kt(x, y, "global") 243.866 250.125 294.6542 275.104 320.058 384.118
#> ici_kt(x2, y2, "global") 13467.011 13739.312 14658.5050 14945.446 14987.140 16153.616
#> neval
#> 5
#> 5
#> 5
#> expr min lq mean median uq max neval
#> cor(x, y, method = "kendall") 11685.244 12730.878 12860.9060 13071.630 13406.514 13410.264 5
#> ici_kt(x, y, "global") 263.306 268.503 332.1288 274.858 283.589 570.388 5
#> ici_kt(x2, y2, "global") 14110.743 14322.836 15782.6490 16053.907 16595.979 17829.780 5
```

In the case of 40,000 features, the average time on a modern CPU is 14
Expand Down Expand Up @@ -188,7 +190,7 @@ for storage. They are also inefficient, as both the lower and upper
triangular components are stored. An alternative storage format is as a
`data.frame`, where there is a single row for each comparison performed.
This is actually how the results are stored internally, and then they
are converted to a matrix form if requested (the default).s To keep the
are converted to a matrix form if requested (the default). To keep the
`data.frame` output, add the argument `return_matrix=FALSE` to the call
of `ici_kendalltau`.

Expand All @@ -202,7 +204,7 @@ r_4
#> 3 s4 s4 0 1.0000000 0 1.000000 1.0000000
#>
#> $run_time
#> [1] 0.01606894
#> [1] 0.01747489
```

## Code of Conduct
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