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<h1 class="title toc-ignore">parametric cellcycleR for image intensities: convergence assessment</h1>
<h4 class="author"><em>Joyce Hsiao</em></h4>
</div>
<!-- The file analysis/chunks.R contains chunks that define default settings
shared across the workflowr files. -->
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<p><strong>Last updated:</strong> 2018-01-25</p>
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package git2r is installed -->
<p><strong>Code version:</strong> a62292e</p>
<hr />
<div id="introductionsummary" class="section level2">
<h2>Introduction/Summary</h2>
<p>In this document, we assess the convergence of <code>cellcycleR</code> across all samples and all batches on fitting intensity data - three intensity vectors for ~1,200 single cell samples.</p>
<p><strong>Results</strong>:</p>
<p>20 runs of <code>sin_cell_ordering_class</code> on 20 different random seeds. Each 500 iterations. We assess the range of log-likelihood, and model estimates <span class="math inline">\(\hat{\alpha}_g\)</span>, <span class="math inline">\(\hat{\phi}_g\)</span>, and <span class="math inline">\(\hat{\sigma}_g\)</span>.</p>
<ol style="list-style-type: decimal">
<li><p>Large deviation in the estimates of <span class="math inline">\(\phi_g\)</span>: because <span class="math inline">\(\phi_g\)</span> is not identifiable.</p></li>
<li><p>Not much deviation between the 20 runs in the estimates for <span class="math inline">\(\alpha_g\)</span> amplitude or <span class="math inline">\(\sigma_g\)</span> or log-likelihood.</p></li>
<li><p>Re. speed of convergence, across random seeds, it takes about less than 50 iterations to reach convergence. Note that the observation vector of each cell is a three-dimensional vector (green, red, and dapi). The number of iterations will go up as we increase the dimension of the observations (e.g., number of genes).</p></li>
</ol>
<hr />
</div>
<div id="data" class="section level2">
<h2>Data</h2>
<p>Combined intensity data (see <a href="/project2/gilad/joycehsiao/fucci-seq/code/combine-intensity-data.R">combine-intensity-data.R</a>).</p>
<hr />
</div>
<div id="model-overview" class="section level2">
<h2>Model overview</h2>
<p>For <span class="math inline">\(S\)</span> cells, let the vector of true cell time be <span class="math inline">\(t_S\)</span>. We use an iterative scheme to estimate cell time parameters <span class="math inline">\(t_S\)</span>, and curve parameters <span class="math inline">\(\alpha_g\)</span>, <span class="math inline">\(\phi_g\)</span>, and <span class="math inline">\(\sigma_g\)</span>. First, we consider <span class="math inline">\(T\)</span> time classes which is a set of uniformly spaced time points on <span class="math inline">\((0, 2\pi)\)</span>. In the first iteration, we assign each cell <span class="math inline">\(s\)</span> to a time class <span class="math inline">\(t_s^{(0)}\)</span> and estimate the curve parameters <span class="math inline">\(\alpha_g\)</span>, <span class="math inline">\(\phi_g\)</span>, and <span class="math inline">\(\sigma_g\)</span>. In the second iteratio, we estimate <span class="math inline">\(t_s^{(1)}\)</span> based on the model estimates from the first iteration (<span class="math inline">\(\hat{\alpha}_g\)</span>, <span class="math inline">\(\hat{\phi}_g\)</span>, and <span class="math inline">\(\hat{\sigma}_g\)</span>). We continue this iterative scheme until convergence. For any <span class="math inline">\(n\)</span> iterations, starting from 0, we fit the following model for gene <span class="math inline">\(g\)</span> and and cell <span class="math inline">\(s\)</span>.</p>
<p><span class="math display">\[
Y_{sg} = \alpha_g sin(t_s^{(n)} + \phi_g) + \epsilon_{sg}
\]</span> where <span class="math inline">\(\epsilon_{sg} \sim N(0, \sigma^2_g)\)</span>, and frequency is 1.</p>
<hr />
</div>
<div id="analysis" class="section level2">
<h2>Analysis</h2>
<p>20 runs of <code>sin_cell_ordering_class</code> on 20 different random seeds. Each 500 iterations.</p>
<p>We assess the range of log-likelihood, and model estimates <span class="math inline">\(\hat{\alpha}_g\)</span>, <span class="math inline">\(\hat{\phi}_g\)</span>, and <span class="math inline">\(\hat{\sigma}_g\)</span>.</p>
<pre class="r"><code>summary(loglik)</code></pre>
<pre><code> Min. 1st Qu. Median Mean 3rd Qu. Max.
-3350 -3312 -3290 -3290 -3262 -3244 </code></pre>
<pre class="r"><code>summary(amp)</code></pre>
<pre><code> Red Green DAPI
Min. :1.289 Min. :1.060 Min. :1.002
1st Qu.:1.301 1st Qu.:1.081 1st Qu.:1.019
Median :1.318 Median :1.093 Median :1.036
Mean :1.316 Mean :1.090 Mean :1.035
3rd Qu.:1.324 3rd Qu.:1.099 3rd Qu.:1.047
Max. :1.346 Max. :1.106 Max. :1.068 </code></pre>
<pre class="r"><code>summary(phi)</code></pre>
<pre><code> Red Green DAPI
Min. :0.4663 Min. :0.1580 Min. :0.06544
1st Qu.:1.2966 1st Qu.:0.6726 1st Qu.:0.64207
Median :3.9793 Median :3.4906 Median :3.48495
Mean :3.5329 Mean :2.9224 Mean :2.89855
3rd Qu.:5.4010 3rd Qu.:4.5465 3rd Qu.:4.47567
Max. :5.9765 Max. :6.1127 Max. :6.01985 </code></pre>
<pre class="r"><code>summary(sigma)</code></pre>
<pre><code> Red Green DAPI
Min. :0.3654 Min. :0.6702 Min. :0.6928
1st Qu.:0.3774 1st Qu.:0.6745 1st Qu.:0.7085
Median :0.3854 Median :0.6814 Median :0.7141
Mean :0.3876 Mean :0.6815 Mean :0.7133
3rd Qu.:0.3971 3rd Qu.:0.6873 3rd Qu.:0.7180
Max. :0.4120 Max. :0.6990 Max. :0.7230 </code></pre>
<p>log-liklihood distribution</p>
<pre class="r"><code>plot(loglik)</code></pre>
<p><img src="figure/images-cellcycleR-convergence.Rmd/unnamed-chunk-5-1.png" width="672" style="display: block; margin: auto;" /></p>
<pre class="r"><code>par(mfrow=c(5,4), mar=c(1,1,2.5,1), oma=rep(1,4))
for (i in 1:length(objs)) {
plot(objs[[i]]$loglik_iter[-1],
main = paste("round no.", i))
}
title("log-likelihood", outer=TRUE)</code></pre>
<p><img src="figure/images-cellcycleR-convergence.Rmd/unnamed-chunk-6-1.png" width="960" style="display: block; margin: auto;" /></p>
<p>speed of convergence</p>
<pre class="r"><code>maxiter <- vector("numeric", length(objs))
for (i in 1:length(maxiter)) {
maxiter[i] <- which.max(objs[[i]]$loglik_iter[-1])
}
boxplot(maxiter, outpch = NA, main = "no. iterations reached for convergence")
stripchart(maxiter,
vertical = TRUE, method = "jitter",
pch = 21, col = "maroon", bg = "bisque",
add = TRUE) </code></pre>
</div>
<div id="section" class="section level2">
<h2><img src="figure/images-cellcycleR-convergence.Rmd/unnamed-chunk-7-1.png" width="672" style="display: block; margin: auto;" /></h2>
</div>
<div id="session-information" class="section level2">
<h2>Session information</h2>
<pre><code>R version 3.4.1 (2017-06-30)
Platform: x86_64-redhat-linux-gnu (64-bit)
Running under: Scientific Linux 7.2 (Nitrogen)
Matrix products: default
BLAS/LAPACK: /usr/lib64/R/lib/libRblas.so
locale:
[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
[3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
[5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
[7] LC_PAPER=en_US.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
attached base packages:
[1] parallel stats graphics grDevices utils datasets methods
[8] base
other attached packages:
[1] plotrix_3.7 Biobase_2.38.0 BiocGenerics_0.24.0
[4] RColorBrewer_1.1-2 wesanderson_0.3.4 cowplot_0.9.2
[7] dplyr_0.7.4 data.table_1.10.4-3 cellcycleR_0.1.6
[10] zoo_1.8-1 binhf_1.0-1 adlift_1.3-3
[13] EbayesThresh_1.4-12 wavethresh_4.6.8 MASS_7.3-47
[16] ggplot2_2.2.1
loaded via a namespace (and not attached):
[1] Rcpp_0.12.14 compiler_3.4.1 git2r_0.20.0 plyr_1.8.4
[5] bindr_0.1 tools_3.4.1 digest_0.6.13 evaluate_0.10.1
[9] tibble_1.3.4 gtable_0.2.0 lattice_0.20-35 pkgconfig_2.0.1
[13] rlang_0.1.4 yaml_2.1.16 bindrcpp_0.2 stringr_1.2.0
[17] knitr_1.17 rprojroot_1.3-1 grid_3.4.1 glue_1.2.0
[21] R6_2.2.2 rmarkdown_1.8 magrittr_1.5 backports_1.1.2
[25] scales_0.5.0 htmltools_0.3.6 assertthat_0.2.0 colorspace_1.3-2
[29] stringi_1.1.6 lazyeval_0.2.1 munsell_0.4.3 </code></pre>
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