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<h1 class="title toc-ignore">Quantile-normalize intensity measurements</h1>
<h4 class="author"><em>Joyce Hsiao</em></h4>
</div>
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<p><strong>Last updated:</strong> 2017-12-11</p>
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<p><strong>Code version:</strong> a5ec074</p>
<hr />
<div id="introduction" class="section level2">
<h2>Introduction</h2>
<p>Previously when investigating measurement variation (GFP/RFP/FAPI), we learned that there’s significant variation between batches in the distributions of background-corrected pixel intensites. See <a href="../docs/images-qc-labels.html">here</a>.</p>
<p><span class="math inline">\(~\)</span></p>
<p><strong>Approach:</strong></p>
<p>In this document, I apply quantile normalization to intensity measurements on a per-channel basis. The approach is as follows</p>
<ol style="list-style-type: decimal">
<li><p>Construct a reference intensity. Estimate k-quantiles of reference intensities <span class="math inline">\(Q^{R,k}= \big( {q^{R,k}_{[1]}, \dots, q^{R,k}_{[n_k]}} \big)\)</span>.</p></li>
<li><p>For each plate <span class="math inline">\(i\)</span>, estimate <span class="math inline">\(l\)</span>-quantiles of intensities on a per-plate basis <span class="math inline">\(Q^{i,l}= \big( {q^{i,l}_{[1]}, \dots, q^{i,l}_{[n_l]}} \big)\)</span>.</p></li>
<li><p>For each plate <span class="math inline">\(i\)</span>, compare the intensity value <span class="math inline">\(F_{ij}\)</span> with the quantile values <span class="math inline">\(\big( {q^{i,l}_{[1]}, \dots, q^{i,l}_{[n_l]}} \big)\)</span> and assign image/well <span class="math inline">\(j\)</span> with the quantile that has the closest intensity value, say <span class="math inline">\(q^{i,l}_{[m]}\)</span> if <span class="math inline">\(m= argmin_{(1,\dots,n_l)} |F_{ij}- q^{i,l}_{[n_l]}|\)</span>. Then subsitute the intensity value with the <span class="math inline">\(m\)</span>-th quantile value in the reference intensity <span class="math inline">\(q^{R,k}_{[m]}\)</span>.</p></li>
</ol>
<p><span class="math inline">\(~\)</span></p>
<p>I tried two methods for constructing reference intensity vector, and the results are vastly different depends on the method that we choose.</p>
<p><em>Method 1</em>: Aggregate intensity values aross plates.</p>
<p><em>Method 2</em>: Take the average of <span class="math inline">\(n\)</span>-quantiles across plates.</p>
<p><span class="math inline">\(~\)</span></p>
<p><strong>Results:</strong></p>
<ol style="list-style-type: decimal">
<li><p>We chose 1/.005 quantiles for all three channels. See the document for our exploratory analysis of intensities from all three channels.</p></li>
<li><p>Method 1 versus Method 2: Because in Method 1, the distribution of Green/Red is more dense toward low and high-valued intensities, we see that the normalized values are closer toward the boundaries.</p></li>
<li><p>Method 2 of constructing the reference produces better results. We see that the relationship between Green/Red is preserved before versus after normalization.</p></li>
<li><p>In Method 2, after normalization, the range of intensities is the same between plates for each of the three channels (Green, Red, DAPI). As a result, many of the images/wells with low intensties decreased in intensity values.</p></li>
<li><p>Because of 4, the distances between samples in many plates increase rather than decrease. We were looking for decrease in the distances between samples, i.e., tighter clusters or smaller within-cluster distance…</p></li>
</ol>
<hr />
</div>
<div id="load-packages-and-data" class="section level2">
<h2>Load packages and data</h2>
<pre class="r"><code>ints <- readRDS(file="/project2/gilad/joycehsiao/fucci-seq/data/intensity.rds")</code></pre>
<hr />
<p><span class="math inline">\(~\)</span></p>
</div>
<div id="densit-plots" class="section level2">
<h2>Densit plots</h2>
<p><span class="math inline">\(~\)</span></p>
<p>First, look at the distribution of all batches combined versus each batch.</p>
<p><span class="math inline">\(~\)</span></p>
<p><img src="figure/images-normalize-quantile.Rmd/unnamed-chunk-3-1.png" width="672" style="display: block; margin: auto;" /></p>
<hr />
<p><span class="math inline">\(~\)</span></p>
</div>
<div id="normalization" class="section level2">
<h2>Normalization</h2>
<p><span class="math inline">\(~\)</span></p>
<p>Code for one single sample</p>
<p><span class="math inline">\(~\)</span></p>
<pre class="r"><code>my_quantnorm <- function(reference, sample, span=.01) {
# quantiles for intensities all samples across plates
quants_reference <- quantile(reference, probs=seq(0,1,span))
# intensities for a given plate
# quantiles for intensities at each plate
quants_sample <- quantile(sample, probs=seq(0,1,span))
# empty vector for normalized values
sample_normed <- vector("numeric", length=length(sample))
for (index in 1:length(sample)) {
# for each sample, find the closest sample quantile
sample_order <- names(which.min(abs(sample[index]-quants_sample)))
# # get the reference intensity value of the closet quantile
ref_order_value <- reference[which(names(quants_reference)==sample_order)]
# assign the reference intensity value to the sample
sample_normed[index] <- ref_order_value
}
return(sample_normed)
}</code></pre>
<p><span class="math inline">\(~\)</span></p>
<div id="choosing-quantile-interval" class="section level3">
<h3>Choosing quantile interval</h3>
<p><span class="math inline">\(~\)</span></p>
<p><strong>RFP</strong></p>
<p><span class="math inline">\(~\)</span></p>
<p><img src="figure/images-normalize-quantile.Rmd/unnamed-chunk-5-1.png" width="672" style="display: block; margin: auto;" /></p>
<p><span class="math inline">\(~\)</span></p>
<p><strong>GFP</strong></p>
<p><span class="math inline">\(~\)</span></p>
<p><img src="figure/images-normalize-quantile.Rmd/unnamed-chunk-6-1.png" width="672" style="display: block; margin: auto;" /></p>
<p><span class="math inline">\(~\)</span></p>
<p><strong>DAPI</strong></p>
<p><span class="math inline">\(~\)</span></p>
<p><img src="figure/images-normalize-quantile.Rmd/unnamed-chunk-7-1.png" width="672" style="display: block; margin: auto;" /></p>
<p><span class="math inline">\(~\)</span></p>
</div>
<div id="method-1" class="section level3">
<h3>Method 1</h3>
<p>Method 1 constructs a vector of refernece intensity by aggregating all image intensity values across plates.</p>
<p><span class="math inline">\(~\)</span></p>
<p><span class="math inline">\(~\)</span></p>
<p><strong>Distribution of the reference</strong></p>
<p><span class="math inline">\(~\)</span></p>
<p><img src="figure/images-normalize-quantile.Rmd/unnamed-chunk-9-1.png" width="480" style="display: block; margin: auto;" /></p>
<p><span class="math inline">\(~\)</span></p>
<p><strong>After normalization</strong></p>
<p><span class="math inline">\(~\)</span></p>
<p><img src="figure/images-normalize-quantile.Rmd/unnamed-chunk-10-1.png" width="1152" style="display: block; margin: auto;" /></p>
<p><span class="math inline">\(~\)</span></p>
<p><strong>Green versus Red intensties by plate, labeled by DAPI</strong></p>
<p><span class="math inline">\(~\)</span></p>
<p><img src="figure/images-normalize-quantile.Rmd/unnamed-chunk-11-1.png" width="1152" style="display: block; margin: auto;" /></p>
<p><span class="math inline">\(~\)</span></p>
<p><strong>Green versus Red intensties by individual, labeled by DAPI</strong></p>
<p><span class="math inline">\(~\)</span></p>
<p><img src="figure/images-normalize-quantile.Rmd/unnamed-chunk-12-1.png" width="1152" style="display: block; margin: auto;" /></p>
<p><span class="math inline">\(~\)</span></p>
<p><strong>Green</strong></p>
<p><span class="math inline">\(~\)</span></p>
<p><img src="figure/images-normalize-quantile.Rmd/unnamed-chunk-13-1.png" width="1152" style="display: block; margin: auto;" /></p>
<p><span class="math inline">\(~\)</span></p>
<p><strong>Red</strong></p>
<p><span class="math inline">\(~\)</span></p>
<p><img src="figure/images-normalize-quantile.Rmd/unnamed-chunk-14-1.png" width="1152" style="display: block; margin: auto;" /></p>
<p><span class="math inline">\(~\)</span></p>
<p><strong>DAPI</strong></p>
<p><span class="math inline">\(~\)</span></p>
<p><img src="figure/images-normalize-quantile.Rmd/unnamed-chunk-15-1.png" width="1152" style="display: block; margin: auto;" /></p>
<hr />
<p><span class="math inline">\(~\)</span></p>
</div>
<div id="method-2" class="section level3">
<h3>Method 2</h3>
<p><span class="math inline">\(~\)</span></p>
<p>Reference intensity vector: average of quantile values across plates.</p>
<p><span class="math inline">\(~\)</span></p>
<p><span class="math inline">\(~\)</span></p>
<p><strong>After normalization</strong></p>
<p><span class="math inline">\(~\)</span></p>
<p><img src="figure/images-normalize-quantile.Rmd/unnamed-chunk-17-1.png" width="1152" style="display: block; margin: auto;" /></p>
<p><span class="math inline">\(~\)</span></p>
<p><strong>Green versus Red intensties by plate, labeled by DAPI</strong></p>
<p><span class="math inline">\(~\)</span></p>
<p><img src="figure/images-normalize-quantile.Rmd/unnamed-chunk-18-1.png" width="1152" style="display: block; margin: auto;" /></p>
<p><span class="math inline">\(~\)</span></p>
<p><strong>Green versus Red intensties by individual, labeled by DAPI</strong></p>
<p><span class="math inline">\(~\)</span></p>
<p><img src="figure/images-normalize-quantile.Rmd/unnamed-chunk-19-1.png" width="1152" style="display: block; margin: auto;" /></p>
<p><span class="math inline">\(~\)</span></p>
<p><strong>Green</strong></p>
<p><span class="math inline">\(~\)</span></p>
<p><img src="figure/images-normalize-quantile.Rmd/unnamed-chunk-20-1.png" width="1152" style="display: block; margin: auto;" /></p>
<p><span class="math inline">\(~\)</span></p>
<p><strong>Red</strong></p>
<p><span class="math inline">\(~\)</span></p>
<p><img src="figure/images-normalize-quantile.Rmd/unnamed-chunk-21-1.png" width="1152" style="display: block; margin: auto;" /></p>
<p><span class="math inline">\(~\)</span></p>
<p><strong>DAPI</strong></p>
<p><span class="math inline">\(~\)</span></p>
<p><img src="figure/images-normalize-quantile.Rmd/unnamed-chunk-22-1.png" width="1152" style="display: block; margin: auto;" /></p>
<hr />
</div>
</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-pc-linux-gnu (64-bit)
Running under: Scientific Linux 7.2 (Nitrogen)
Matrix products: default
BLAS: /home/joycehsiao/miniconda3/envs/fucci-seq/lib/R/lib/libRblas.so
LAPACK: /home/joycehsiao/miniconda3/envs/fucci-seq/lib/R/lib/libRlapack.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] Biobase_2.38.0 BiocGenerics_0.24.0 RColorBrewer_1.1-2
[4] wesanderson_0.3.2 cowplot_0.8.0 ggplot2_2.2.1
[7] dplyr_0.7.0 data.table_1.10.4
loaded via a namespace (and not attached):
[1] Rcpp_0.12.14 knitr_1.16 magrittr_1.5 munsell_0.4.3
[5] colorspace_1.3-2 R6_2.2.0 rlang_0.1.2 stringr_1.2.0
[9] plyr_1.8.4 tools_3.4.1 grid_3.4.1 gtable_0.2.0
[13] git2r_0.19.0 htmltools_0.3.6 lazyeval_0.2.0 yaml_2.1.14
[17] rprojroot_1.2 digest_0.6.12 assertthat_0.1 tibble_1.3.3
[21] glue_1.1.1 evaluate_0.10.1 rmarkdown_1.6 labeling_0.3
[25] stringi_1.1.2 compiler_3.4.1 scales_0.4.1 backports_1.0.5 </code></pre>
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