Calculating Precision Weights for Screens

 

Calculating precision weights first requires that screen data and annotations be combined in a Bioconductor ExpressionSet object. It also requires that the replicate_group column be set in the phenoData slot of the ExpressionSet.

 

Here’s what that looks like for the BREAST SCREENS FROM MARCOTTE et al. 2016:

### To install required packages, uncomment and run this
# source("http://www.bioconductor.org/biocLite.R")
# biocLite(c("Biobase", "preprocessCore", "genefilter"))
# install.packages(c("blme", "doMC", "ggplot2", "locfit", "MASS", "plyr", "reshape"))

suppressPackageStartupMessages(library("Biobase"))
suppressPackageStartupMessages(library("preprocessCore"))
suppressPackageStartupMessages(library("locfit"))
suppressPackageStartupMessages(library("blme"))
suppressPackageStartupMessages(library("reshape"))
suppressPackageStartupMessages(library("plyr"))
suppressPackageStartupMessages(library("genefilter"))
suppressPackageStartupMessages(library("ggplot2"))
suppressPackageStartupMessages(library("MASS"))
suppressPackageStartupMessages(library("doMC"))

source("../../R/data_format_lib.R")
source("../../R/model_lib.R")
source("../../R/simem_lib.R")

load("../../data/shrna/breast_screens.eset")
phenoBreast = pData(breast_screens)
# The 'phenoBreast$replicate_group' column needs to be present for the mean-variance function calculation. Since the Breast screens are measured at 3 time-points, we group the screens by both cell line and time-points for the purposes of calculating the mean-variance function
table(phenoBreast$replicate_group)[1:21]

## 
##  184a1_t0  184a1_t1  184a1_t2  184b5_t0  184b5_t1  184b5_t2 600mpe_t0 
##         2         3         3         2         3         3         2 
## 600mpe_t1 600mpe_t2  au565_t0  au565_t1  au565_t2   bt20_t0   bt20_t1 
##         3         3         2         3         3         3         3 
##   bt20_t2  bt474_t0  bt474_t1  bt474_t2  bt483_t0  bt483_t1  bt483_t2 
##         3         3         3         3         2         3         3

 

Here’s the same grouping for the ACHILLES SCREENS FROM CHEUNG et al. 2011:

load("../../data/shrna/achilles_screens.eset")
phenoAchilles = pData(achilles_screens)
# The 'phenoAchilles$replicate_group' column needs to be present for the mean-variance function calculation. Since the Achilles screens are measured at an end-point, we group the screens by cell line for the purposes of calculating the mean-variance function
table(phenoAchilles$replicate_group)[1:21]

## 
##    786o    a204   a2058   a2780    a549     ags   aspc1   bxpc3  c2bbe1 
##       4       3       4       4       4       4       3       4       4 
##   caov3   caov4  cfpac1 ch157mn colo205 colo704 colo741  cov362  cov434 
##       4       3       4       4       4       4       3       4       3 
##  cov504    dld1   efo21 
##       4       4       4

 

Once the screens are loaded, the precision (mean-variance) weights are calculated for the measurements using the

simem::addPrecisionWeights()

as follows:

# Calculate the precision weights by grouping samples using the values in the 'phenoBreast$replicate_group' column. This process takes several minutes. The 'printProgress=TRUE' parameter prints a line of output for each 'replicate_group' as it is processed; printProgress=FALSE by default.
breast_screens = addPrecisionWeights(breast_screens, printProgress=FALSE)

## Beginning calculation of replicate means, and smoothed mean-variance function for grouped/replicate samples...
## Finalizing mean-variance function calculations and assigning precision weights to data points...
## Done.

# Save the ExpressionSet with added weights so that the calculation doesn't need to be rerun
# save(breast_screens, file="../../data/breast_screens_with_weights.eset")

 

Here’s the mean-variance calculation for the Achilles data:

# Calculate the precision weights by grouping samples using the values in the 'phenoBreast$replicate_group' column. This process takes several minutes. The 'printProgress=TRUE' parameter prints a line of output for each 'replicate_group', and is set to FALSE by default.
achilles_screens = addPrecisionWeights(achilles_screens, printProgress=FALSE)

## Beginning calculation of replicate means, and smoothed mean-variance function for grouped/replicate samples...
## Finalizing mean-variance function calculations and assigning precision weights to data points...
## Done.

# Save the ExpressionSet with added weights
# save(achilles_screens, file="../../data/achilles_screens_with_weights.eset")

 

The calculated group means, variances and smoothed mean-variance function can be accessed and plotted for the breast data. MCF7 T0, T1 and T2 values are plotted below - notice how the sqrt variance increases as time increases as a result of the independent evolution of the replicates after T0:

meansBr = assayData(breast_screens)[["groupMeans"]]
varsBr = assayData(breast_screens)[["groupVars"]]
# calculate 1/precision weights to get the smoothed variance function for plotting purposes
smoothedBr = 1/assayData(breast_screens)[["varWeights"]]

# The matrices have the samples in the same order, and the values for replicates a, b, and c are identical, so we need only plot one of the replicates for each of the time-points
mcfT0 = grep("mcf7_t0_a", colnames(meansBr))
mcfT1 = grep("mcf7_t1_a", colnames(meansBr))
mcfT2 = grep("mcf7_t2_a", colnames(meansBr))

# Create a data frame with values to be visualized, using the MCF7 screen as an example
plotDatT0 = cbind.data.frame(means=meansBr[,mcfT0], vars=varsBr[,mcfT0], smoothed=smoothedBr[,mcfT0])
plotDatT1 = cbind.data.frame(means=meansBr[,mcfT1], vars=varsBr[,mcfT1], smoothed=smoothedBr[,mcfT1])
plotDatT2 = cbind.data.frame(means=meansBr[,mcfT2], vars=varsBr[,mcfT2], smoothed=smoothedBr[,mcfT2])

# For T0, plot mean vs. sqrt(variance) and sqrt(smoothed variance). We plot the sqrt of the variance to highlight differences
plT0 = ggplot(data=plotDatT0)
plT0 = plT0 + geom_point(aes(x=means, y=sqrt(vars)), size=2)
plT0 = plT0 + geom_line(aes(x=means, y=sqrt(smoothed)), colour="red", size=1)
plT0 = plT0 + scale_y_continuous(limits=c(0,4))
plT0 = plT0 + theme_bw()
plT0 = plT0 + xlab("MCF7 T0 replicate means") 
plT0 = plT0 + ylab("MCF7 T0 sqrt replicate variances\nand smoothed variance function")
plT0 = plT0 + theme(axis.title.x=element_text(size=16), 
                axis.title.y=element_text(size=16),
                axis.text.x=element_text(size=16), 
                axis.text.y=element_text(size=16)
                )

# For T1, plot mean vs. sqrt(variance) and sqrt(smoothed variance). We plot the sqrt of the variance to highlight differences
plT1 = ggplot(data=plotDatT1)
plT1 = plT1 + geom_point(aes(x=means, y=sqrt(vars)), size=2)
plT1 = plT1 + geom_line(aes(x=means, y=sqrt(smoothed)), colour="red", size=1)
plT1 = plT1 + scale_y_continuous(limits=c(0,4))
plT1 = plT1 + theme_bw()
plT1 = plT1 + xlab("MCF7 T1 replicate means") 
plT1 = plT1 + ylab("MCF7 T1 sqrt replicate variances\nand smoothed variance function")
plT1 = plT1 + theme(axis.title.x=element_text(size=16), 
                axis.title.y=element_text(size=16),
                axis.text.x=element_text(size=16), 
                axis.text.y=element_text(size=16)
                )

# For T2, plot mean vs. sqrt(variance) and sqrt(smoothed variance). We plot the sqrt of the variance to highlight differences
plT2 = ggplot(data=plotDatT2)
plT2 = plT2 + geom_point(aes(x=means, y=sqrt(vars)), size=2)
plT2 = plT2 + geom_line(aes(x=means, y=sqrt(smoothed)), colour="red", size=1)
plT2 = plT2 + scale_y_continuous(limits=c(0,4))
plT2 = plT2 + theme_bw()
plT2 = plT2 + xlab("MCF7 T2 replicate means")
plT2 = plT2 + ylab("MCF7 T2 sqrt replicate variances\nand smoothed variance function")
plT2 = plT2 + theme(axis.title.x=element_text(size=16), 
                axis.title.y=element_text(size=16),
                axis.text.x=element_text(size=16), 
                axis.text.y=element_text(size=16)
                )

plT0

plT1

plT2

 

And the plot of the smoothed mean-variance function for one of the Achilles screens follows:

meansAch = assayData(achilles_screens)[["groupMeans"]]
varsAch = assayData(achilles_screens)[["groupVars"]]
# calculate 1/precision weights to get the smoothed variance function for plotting purposes
smoothedAch = 1/assayData(achilles_screens)[["varWeights"]]

# The matrices have the samples in the same order, and the values for replicates a, b, and c are identical, so we need only plot one of the replicates
a549 = grep("a549_a", colnames(meansAch))

# Create a data frame with values to be visualized, using the MCF7 screen as an example
plotDat = cbind.data.frame(means=meansAch[,a549], vars=varsAch[,a549], smoothed=smoothedAch[,a549])

# Plot mean vs. sqrt(variance) and sqrt(smoothed variance). We plot the sqrt of the variance to highlight differences
pl = ggplot(data=plotDat)
pl = pl + geom_point(aes(x=means, y=sqrt(vars)), size=2)
pl = pl + geom_line(aes(x=means, y=sqrt(smoothed)), colour="red", size=1)
pl = pl + theme_bw()
pl = pl + xlab("A549 replicate means") 
pl = pl + ylab("A549 sqrt replicate variances\nand variance smoothed function")
pl = pl + theme(axis.title.x=element_text(size=16), 
                  axis.title.y=element_text(size=16),
                  axis.text.x=element_text(size=16), 
                  axis.text.y=element_text(size=16)
                  )
pl