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<h1 class="title toc-ignore">Batch effect in RNA-seq data</h1>
<h4 class="author"><em>Joyce Hsiao</em></h4>
</div>
<!-- The file analysis/chunks.R contains chunks that define default settings
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<p><strong>Last updated:</strong> 2018-02-14</p>
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<p><strong>Code version:</strong> 3267559</p>
<hr />
<div id="introductionsummary" class="section level2">
<h2>Introduction/summary</h2>
<p>The experimental design for our study is commonly known as “incomplete block design”. The individuals are grouped into combinations of two, and no two individuals appear in the same combination twice. In our study, combination refers to C1 plates, so the combination of cell lines on each C1 plate is thereofre unique.</p>
<p>In notations,</p>
<p><span class="math inline">\(N\)</span>: number of individuals <span class="math inline">\(k\)</span>: combination size (in our case, each combinatino is a plate) <span class="math inline">\(B\)</span>: number of plates <span class="math inline">\(r_i\)</span>: number of replicates for individual <span class="math inline">\(i\)</span> in the entire design</p>
<p>For now assume <span class="math inline">\(r_i=r\)</span> for all individuals. Then, in our design each individual replicate can pair up with <span class="math inline">\(N-1/k-1\)</span> possible number of individuals. And since the pairs consist of unique individuals, so there can be <span class="math inline">\(N-1/k-1\)</span> possible number of replicates for each individual. We have <span class="math inline">\(N=6, k=2\)</span> which gives 5 replicates per individual cell line.</p>
<p>Our design is in principle balanced, i.e., each pair of individuals occurs together one time in the study. But at the end of the experiment, we collected an additional C1 plate on the first pair of individuals processed. This gives us a total of 16 plates (pairs or blocks).</p>
<p>I performed <strong>analysis of variance</strong> for intensity data using the following model</p>
<p><span class="math display">\[
y_{ij} = \mu + \tau_i + \beta_j + \epsilon_{ij}
\]</span> where <span class="math inline">\(i = 1,2,..., N\)</span> and <span class="math inline">\(j = 1,2,..., B\)</span>. The parameters are estimated under sum-to-zero constraints <span class="math inline">\(\sum \tau_i = 0\)</span> and <span class="math inline">\(\sum \beta_j = 0\)</span>.</p>
<p>Note that in this model 1) not all <span class="math inline">\(y_{ij}\)</span> exists due to the incompleteness of the design, 2) the effects of individual and block are nonorthogonal, 3) the effects are additive due to the block design.</p>
<p>We analyzed data normalized to log2CPM and used the <code>ibd</code> package for each gene to</p>
<ol style="list-style-type: decimal">
<li><p>Estimate prop of variance explained by individual and plate.</p></li>
<li><p>Estimate mean effect from each plate and remove this estimated effect from each gene</p></li>
</ol>
<p><strong>TO DO: apply shrinkage to the estimated mean effect??</strong></p>
<hr />
</div>
<div id="load-data" class="section level2">
<h2>Load data</h2>
<p><span class="math inline">\(~\)</span></p>
<pre class="r"><code>library(data.table)
library(dplyr)
library(ggplot2)
library(cowplot)
library(wesanderson)
library(RColorBrewer)
library(Biobase)
library(scales)
library(stringr)
library(heatmap3)
# note that ibd is not in the fucci-seq conda environment
library(ibd)</code></pre>
<p>Read in filtered data.</p>
<pre class="r"><code>df <- readRDS(file="../data/eset-filtered.rds")
pdata <- pData(df)
fdata <- fData(df)
counts <- exprs(df)</code></pre>
<p>library size variation</p>
<pre class="r"><code>boxplot(pdata$molecules~pdata$experiment,
xlab = "Plate", ylab = "log10 library size")</code></pre>
<p><img src="figure/seqdata-batch-correction.Rmd/unnamed-chunk-3-1.png" width="672" style="display: block; margin: auto;" /></p>
<pre class="r"><code>boxplot(pdata$molecules~pdata$chip_id,
xlab = "Plate", ylab = "log10 library size")</code></pre>
<p><img src="figure/seqdata-batch-correction.Rmd/unnamed-chunk-3-2.png" width="672" style="display: block; margin: auto;" /></p>
<p>counts to log2cpm</p>
<pre class="r"><code>log2cpm <- t(log2(1+(10^6)*(t(counts)/pdata$molecules)))</code></pre>
<p>save log2cpm</p>
<pre class="r"><code>saveRDS(log2cpm, file = "../output/seqdata-batch-correction.Rmd/log2cpm.rds")</code></pre>
<p>convert sample well to two labels: rows and columns</p>
<pre class="r"><code>pdata$well_row <- str_sub(pdata$well,1,1)
pdata$well_col <- str_sub(pdata$well,2,3)</code></pre>
<hr />
</div>
<div id="batch-variation" class="section level2">
<h2>batch variation</h2>
<p>total molecules significant differs between individuals and batch</p>
<pre class="r"><code>ibd_mol <- aov.ibd(log10(molecules)~factor(chip_id)+factor(experiment),data=pdata)</code></pre>
<p><img src="figure/seqdata-batch-correction.Rmd/unnamed-chunk-8-1.png" width="1056" style="display: block; margin: auto;" /></p>
<p>per gene log2cpm anova</p>
<pre class="r"><code>ibd_genes <- lapply(1:nrow(log2cpm), function(i) {
aov.ibd(log2cpm[i,]~factor(chip_id)+factor(experiment),data=pdata)
})
saveRDS(ibd_genes, file = "../output/seqdata-batch-correction.Rmd/ibd-genes.rds")</code></pre>
<p>This seems to suggest that there’s no relationship between proportion of variance explained by indivdiual and by plate. Note that in these per-gene analysis, intercept explains a significant large portion of the variance, suggesting an overall large deviation of sample log2cpm from the mean.</p>
<pre class="r"><code>ibd_genes <- readRDS("../output/seqdata-batch-correction.Rmd/ibd-genes.rds")
ind_varprop <- sapply(ibd_genes, function(x) x[[1]]$`Sum Sq`[2]/sum(x[[1]]$`Sum Sq`))
plate_varprop <- sapply(ibd_genes, function(x) x[[1]]$`Sum Sq`[3]/sum(x[[1]]$`Sum Sq`))
plot(log10(ind_varprop), log10(plate_varprop), xlim=c(-4,0), ylim=c(-4,0),
pch=16, cex=.7)</code></pre>
<p><img src="figure/seqdata-batch-correction.Rmd/unnamed-chunk-10-1.png" width="672" style="display: block; margin: auto;" /></p>
<p>Estimate plate effect</p>
<pre class="r"><code># make contrast matrix
n_plates <- uniqueN(pdata$experiment)
contrast_plates <- matrix(-1, nrow=n_plates, ncol=n_plates)
diag(contrast_plates) <- n_plates-1
log2cpm.adjust <- log2cpm
for (i in 1:nrow(log2cpm)) {
ibd_exp <- aov.ibd(log2cpm[i,]~factor(chip_id)+factor(experiment),
data=pdata, spec="experiment", contrast=contrast_plates)
ibd_est <- ibd_exp$LSMEANS
exps <- unique(pdata$experiment)
for (j in 1:uniqueN(exps)) {
exp <- exps[j]
ii_exp <- which(pdata$experiment == exp)
est_exp <- ibd_est$lsmean[which(ibd_est$experiment==exp)]
log2cpm.adjust[i,ii_exp] <- log2cpm[i,ii_exp] - est_exp
}
}
saveRDS(log2cpm.adjust, file = "../output/seqdata-batch-correction.Rmd/log2cpm.adjust.rds")</code></pre>
<pre class="r"><code>log2cpm.adjust <- readRDS("../output/seqdata-batch-correction.Rmd/log2cpm.adjust.rds")</code></pre>
<p>PCA after adjustment. Somehow now well has significant contribution to PC1…</p>
<pre class="r"><code>pca_log2cpm_adjust <- prcomp(t(log2cpm.adjust), center = TRUE)
covariates <- pdata %>% dplyr::select(experiment, well_row, well_col, chip_id,
concentration, raw:unmapped,
starts_with("detect"), molecules)
## look at the first 6 PCs
pcs <- pca_log2cpm_adjust$x[, 1:6]
## generate the data
get_r2 <- function(x, y) {
stopifnot(length(x) == length(y))
model <- lm(y ~ x)
stats <- summary(model)
return(stats$adj.r.squared)
}
r2 <- matrix(NA, nrow = ncol(covariates), ncol = ncol(pcs),
dimnames = list(colnames(covariates), colnames(pcs)))
for (cov in colnames(covariates)) {
for (pc in colnames(pcs)) {
r2[cov, pc] <- get_r2(covariates[, cov], pcs[, pc])
}
}
## plot heatmap
heatmap3(r2, cexRow=1, cexCol=1, margins=c(8,8), scale = "none",
col=brewer.pal(9,"YlGn"), showColDendro = F, Colv = NA,
ylab="technical factor", main = "Batch-corrected data")</code></pre>
<p><img src="figure/seqdata-batch-correction.Rmd/unnamed-chunk-13-1.png" width="672" style="display: block; margin: auto;" /></p>
<p>PCA before adjustment.</p>
<pre class="r"><code>pca_log2cpm <- prcomp(t(log2cpm), center = TRUE)
covariates <- pdata %>% dplyr::select(experiment, well_row, well_col, chip_id,
concentration, raw:unmapped,
starts_with("detect"), molecules)
## look at the first 6 PCs
pcs <- pca_log2cpm$x[, 1:6]
## generate the data
get_r2 <- function(x, y) {
stopifnot(length(x) == length(y))
model <- lm(y ~ x)
stats <- summary(model)
return(stats$adj.r.squared)
}
r2 <- matrix(NA, nrow = ncol(covariates), ncol = ncol(pcs),
dimnames = list(colnames(covariates), colnames(pcs)))
for (cov in colnames(covariates)) {
for (pc in colnames(pcs)) {
r2[cov, pc] <- get_r2(covariates[, cov], pcs[, pc])
}
}
## plot heatmap
heatmap3(r2, cexRow=1, cexCol=1, margins=c(8,8), scale = "none",
col=brewer.pal(9,"YlGn"), showColDendro = F, Colv = NA,
ylab="technical factor", main = "Before batch correction")</code></pre>
<p><img src="figure/seqdata-batch-correction.Rmd/unnamed-chunk-14-1.png" width="672" style="display: block; margin: auto;" /></p>
<hr />
</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] ibd_1.2 multcompView_0.1-7 lsmeans_2.27-61
[4] car_2.1-6 MASS_7.3-47 lpSolve_5.6.13
[7] heatmap3_1.1.1 stringr_1.2.0 scales_0.5.0
[10] Biobase_2.38.0 BiocGenerics_0.24.0 RColorBrewer_1.1-2
[13] wesanderson_0.3.4 cowplot_0.9.2 ggplot2_2.2.1
[16] dplyr_0.7.4 data.table_1.10.4-3
loaded via a namespace (and not attached):
[1] fastcluster_1.1.24 zoo_1.8-1 splines_3.4.1
[4] lattice_0.20-35 colorspace_1.3-2 htmltools_0.3.6
[7] yaml_2.1.16 mgcv_1.8-17 survival_2.41-3
[10] rlang_0.1.6 pillar_1.1.0 nloptr_1.0.4
[13] glue_1.2.0 bindrcpp_0.2 multcomp_1.4-8
[16] bindr_0.1 plyr_1.8.4 MatrixModels_0.4-1
[19] munsell_0.4.3 gtable_0.2.0 mvtnorm_1.0-7
[22] coda_0.19-1 codetools_0.2-15 evaluate_0.10.1
[25] labeling_0.3 knitr_1.19 SparseM_1.77
[28] quantreg_5.35 pbkrtest_0.4-7 TH.data_1.0-8
[31] Rcpp_0.12.15 xtable_1.8-2 backports_1.1.2
[34] lme4_1.1-15 digest_0.6.15 stringi_1.1.6
[37] grid_3.4.1 rprojroot_1.3-2 tools_3.4.1
[40] sandwich_2.4-0 magrittr_1.5 lazyeval_0.2.1
[43] tibble_1.4.2 pkgconfig_2.0.1 Matrix_1.2-10
[46] estimability_1.2 assertthat_0.2.0 minqa_1.2.4
[49] rmarkdown_1.8 R6_2.2.2 nnet_7.3-12
[52] nlme_3.1-131 git2r_0.21.0 compiler_3.4.1 </code></pre>
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