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alleledb_calcOverdispersion.R
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#20170212 cjieming/alleleDB alleledb_v2.0 script
#Chen J et al. (2016). Nat Commun. 7:11101
# with minor modifications to incorporate into the pipeline
#library(VGAM)
library(VGAM, lib.loc="~/R_libs/")
## weighted beta/binomial distribution
# d.combined collects all results and correspond it to an allelic ratio:
# col1=ref_allele_ratio (based on binomial n=6, ar=0,1/6,2/6...)
# col2=corresponding weighted value in binomial distribution, i.e. pdf(n,k,p)*(num of empirical SNPs at n counts)
nulldistrib <- function(minN,maxN,p,w,binSize,yuplimit,distrib="binomial",b=0)
{
d.combined = matrix(0,sum(seq(minN+1,maxN+1)),2)
ptr = 1
for (i in minN:maxN)
{
## doing the distribution
k=seq(0,i)
if(distrib == "binomial")
{
d = dbinom(k,i,p) ## binomial
}
else if(distrib == "betabinomial")
{
d = dbetabinom(k,i,p,b)
}
## weight each with actual counts in empirical
d.w = d*w[i,1]
if(i == minN)
{
d.combined[ptr:length(k),1] = k/i
d.combined[ptr:length(k),2] = d.w
colnames(d.combined) = c('ref_allele_ratio','wBinDist')
}
else
{
d.combined[ptr:(ptr+length(k)-1),1] = k/i
d.combined[ptr:(ptr+length(k)-1),2] = d.w
}
ptr = ptr + length(k)
}
## sort the d.combined distribution of all the n's
d.combined.sorted = d.combined[ order(d.combined[,1],d.combined[,2]), ]
## bin it according to empirical distribution
bins=pretty(0:1,binSize)
start=0
end=0
d.combined.sorted.binned = matrix(0,length(bins)-1,2)
for (z in 2:length(bins)) ##skip 0
{
start=bins[z-1]
end=bins[z]
row=z-1
d.combined.sorted.binned[row,1] = (end-start)/2 +start ## equi of a $mid in hist
d.combined.sorted.binned[row,2] = sum(d.combined.sorted[(d.combined.sorted[,1]<=end &
d.combined.sorted[,1]>start),2])
## empirical right closed, left open ?hist; right=TRUE
## (range] so no double counts
## but zero gets excluded!!
if(row==1)
{
d.combined.sorted.binned[row,2] = sum(d.combined.sorted[(d.combined.sorted[,1]<=end &
d.combined.sorted[,1]>=start),2])
}
## empirical right closed, left open ?hist; right=TRUE
## (range] so no double counts
## but zero gets excluded!!
if(row==1)
{
d.combined.sorted.binned[row,2] = sum(d.combined.sorted[(d.combined.sorted[,1]<=end &
d.combined.sorted[,1]>=start),2])
}
}
## change "counts" into density
d.combined.sorted.binned[,2] = d.combined.sorted.binned[,2]/sum(d.combined.sorted.binned[,2])
return(d.combined.sorted.binned)
}
################################## MAIN #######################################
### set parameters
args = commandArgs(trailingOnly=TRUE)
filename = args[1]
data = read.table(filename, header=T, stringsAsFactors=F, comment.char="%", check.names=FALSE)
#print (head(data))
#dir.create("betabinomial")
dir.create(args[2])
#folder = args[3]
#setwd(paste(folder,"/betabinomial",sep=''))
#setwd(paste(folder, "/", args[2],sep=''))
setwd(args[2])
colors <- c("green","blue","orange","cyan","pink","purple",
"brown","black","slategray1","violetred","tan","deeppink","darkgreen",
"orchid","darksalmon","antiquewhite3","magenta","darkblue","peru","slateblue",
"thistle","tomato","rosybrown1","royalblue","olivedrab") ##Set of 26 colours (no red) to use for all plots
## binomial parameters
p=0.5 #null probability
minN=6 #min total num of reads (since it's left open right closed)
# maxN=max(data$sum_ref_n_alt_cnts) #max total num of reads
if(max(data$sum_ref_n_alt_cnts) < 2500){ maxN=max(data$sum_ref_n_alt_cnts) }else { maxN=2500 }
apropor = length(data$sum_ref_n_alt_cnts[data$sum_ref_n_alt_cnts <= 2500]) / nrow(data)
yuplimit=0.15
binSize=40
bins=pretty(0:1,binSize)
r.min = 0
r.max = 1
## graded weights for SSE calculation
r = seq(r.min,r.max,(r.max - r.min)/((length(bins) - 1)/2))
r = r[2:length(r)]
if((length(bins)-1)%%2 != 0){ w.grad=c(r,sort(r[1:(length(r)-1)],decreasing=TRUE))
}else { w.grad=c(r,sort(r[1:length(r)],decreasing=TRUE)) }
## empirical allelic Ratio
data.match=data[data$sum_ref_n_alt_cnts <= maxN & data$sum_ref_n_alt_cnts >= minN, ]
h = hist(data.match$ref_allele_ratio, xlim=range(0,1),breaks=bins,right=TRUE)
# plot right closed interval left open (range] for x axis
# note that you have pseudozeroes as counts in your data so thats fine
empirical = h$counts/sum(h$counts)
### weighted expected binomial
## plot the binomial distribution for each n
## dbinom(seq(0,500),n=500,p=0.5) gives the pdf of 0-500, at n=500, p=0.5 in binomial distrib
## weight each probability by the number of SNPs with n reads
# weight by empirical counts
t = as.data.frame(table(data$sum_ref_n_alt_cnts), stringsAsFactors=F)
w = matrix(0,max(data$sum_ref_n_alt_cnts),1)
for (jj in 1:nrow(t))
{
w[as.integer(t[jj,1]),1] = t[jj,2]
}
d.combined.sorted.binned = nulldistrib(minN,maxN,p,w,binSize,yuplimit,distrib="binomial")
### weighted betabinomial distribution
# very naive way of automating the process of finding b parameter automatically
# using least sum of squares of errors (between the density plots of empirical and
# the expected distributions)
# sse for the binomial distrib
# x11(width=17,height=9)
# par(cex.axis=1.5, cex.lab=2, cex.main=2, mar=c(5,5,5,5))
# barplot(empirical, ylab='density', xlab='ref_allele_ratio',names.arg=h$mids, ylim=c(0,yuplimit), main=paste("n=",minN,'-',maxN))
# par(new=TRUE)
# plot(d.combined.sorted.binned,ylim=c(0,yuplimit),pch=16,type='b',col='red',bty='n',ylab='',xlab='',yaxt='n',xaxt='n',yaxs="i")
r.sta = 0
r.end = 0.99
r.by = 0.1
b.range = seq(r.sta,r.end,by=r.by)
labels = matrix(0,50,1)
ctr = 1
sse = sum((empirical-d.combined.sorted.binned[,2])^2)
b.choice = 0
b.and.sse = matrix(0,50,2)
colnames(b.and.sse) <- c('b','sse')
for (k in b.range)
{
e.combined.sorted.binned = nulldistrib(minN,maxN,p,w,binSize,yuplimit,distrib="betabinomial",b=k)
# par(new=TRUE)
# plot(e.combined.sorted.binned,ylim=c(0,yuplimit),pch=16,type='b',col=colors[ctr],bty='n',ylab='',xlab='',yaxt='n',xaxt='n',yaxs="i")
## minimize sse for betabinomials
if(b.choice==0){ b.and.sse[1,1]=b.choice; b.and.sse[1,2]=sse }
sse.bbin = sum(w.grad*((empirical-e.combined.sorted.binned[,2])^2))
b.and.sse[ctr+1,1] = k
b.and.sse[ctr+1,2] = sse.bbin
labels[ctr] = paste("betabin,b=",signif(k,2),"; SSE=",signif(sse.bbin,2))
if(sse.bbin < sse){ sse = sse.bbin; b.choice = k }
else if(sse.bbin > sse){ break }
ctr = ctr + 1
}
# print(paste("b.chosen=",b.choice,", SSE.chosen=",sse))
# legend(0.01,0.14,c("empirical","binomial",
# labels[1:ctr]),
# col=c("grey","red",colors[1:ctr]), cex=2, pt.cex=2,
# text.col = "black", pch = 15, bg = 'white')
# dev.copy2pdf(file = paste("allele_readdepth_table_betabinomial_distribution_compare_NA10847_sa1",minN,"-",maxN,".pdf", sep=""))
##################################################################################
# sum of squares
# after picking b.choice with the sse, use a Newton-Raphson idea to optimize
# b.choice
ctr.ori = ctr ##debug
b.and.sse.ori = b.and.sse ##debug
# x11()
# par(cex.axis=1.5, cex.lab=2, cex.main=2, mar=c(5,5,5,5))
# plot(b.and.sse[1:(ctr+1),],type='b',pch=16)
b.chosen = b.choice
sse.chosen = sse
flag = 3
if(b.chosen >= 0.9){flag = 0; newctr = ctr}
while(flag)
{
r.sta = max(0,(b.choice - r.by/2))
r.end = b.choice + r.by/2
r.by = r.by/4
b.range = seq(r.sta,r.end,by=r.by)
labels = matrix(0,50,1)
newctr = 1
sse = b.and.sse[1,2]
b.choice = 0
for (k in b.range)
{
e.combined.sorted.binned = nulldistrib(minN,maxN,p,w,binSize,yuplimit,distrib="betabinomial",b=k)
## minimize sse for betabinomials
sse.bbin = sum(w.grad*((empirical-e.combined.sorted.binned[,2])^2))
b.and.sse[(ctr+2),1] = k
b.and.sse[(ctr+2),2] = sse.bbin
labels[newctr] = paste("betabin,b=",signif(k,3),"; SSE=",signif(sse.bbin,3))
if(sse.bbin < sse){ sse = sse.bbin; b.choice = k }
else if(sse.bbin > sse){ break }
ctr = ctr + 1
newctr = newctr + 1
}
print(paste("b.chosen=",b.choice,", SSE.chosen=",sse))
labels = labels[1:(newctr+1),]
## pseudofinal fit plot
# x11(width=17, height=9)
# par(cex.axis=1.5, cex.lab=2, cex.main=2, mar=c(5,5,5,5))
# barplot(empirical, ylab='density', xlab='ref_allele_ratio',
# names.arg=h$mids, ylim=c(0,yuplimit), main=paste("n=",minN,'-',maxN))
# par(new=TRUE)
# plot(d.combined.sorted.binned,ylim=c(0,yuplimit),pch=16,type='b',col='red',
# bty='n',ylab='',xlab='',yaxt='n',xaxt='n',yaxs="i")
# par(new=TRUE)
# plot(e.combined.sorted.binned,ylim=c(0,yuplimit),pch=16,type='b',col='blue',
# bty='n',ylab='',xlab='',yaxt='n',xaxt='n',yaxs="i")
#
# legend(0.01,0.14,c("empirical","binomial",
# labels[1:newctr]),
# col=c("grey","red",colors[1:newctr]), cex=2, pt.cex=2,
# text.col = "black", pch = 15, bg = 'white')
if(signif(b.and.sse[ctr+2,2],3) == signif(b.and.sse[ctr+1,2],3)){ flag = 0 }
}
## print empirical, binomial and betabinomial fit
# x11(width=17, height=9)
pdf(paste(filename,"-checkgrad-",minN,"-",maxN,".pdf", sep=""),width=17, height=9)
par(cex.axis=1.5, cex.lab=2, cex.main=2, mar=c(5,5,5,5))
barplot(empirical, ylab='density', xlab='ref_allele_ratio',
names.arg=h$mids, ylim=c(0,yuplimit), main=paste("n=",minN,'-',maxN))
par(new=TRUE)
plot(d.combined.sorted.binned,ylim=c(0,yuplimit),pch=16,type='b',col='red',
bty='n',ylab='',xlab='',yaxt='n',xaxt='n',yaxs="i")
par(new=TRUE)
plot(e.combined.sorted.binned,ylim=c(0,yuplimit),pch=16,type='b',col='blue',
bty='n',ylab='',xlab='',yaxt='n',xaxt='n',yaxs="i")
legend(0.01,0.14,c("empirical","binomial",
labels[1:(newctr-1)]),
col=c("grey","red",colors[1:(newctr-2)],"blue"), cex=2, pt.cex=2,
text.col = "black", pch = 15, bg = 'white')
# dev.copy2pdf(file = paste(filename,"-check-",minN,"-",maxN,".pdf", sep=""))
dev.off()
## print sse
# x11(width=10, height=7)
pdf(paste(filename,"-checksse.grad-",minN,"-",maxN,".pdf", sep=""), width=10, height=7)
par(cex.axis=1.5, cex.lab=2, cex.main=2, mar=c(5,5,5,5))
b.and.sse = b.and.sse[1:(ctr+2),]
plot(b.and.sse[order(b.and.sse[,1]),],type='b',
pch=16,xlim=c(min(b.and.sse[,1]), max(b.and.sse[,1])),
ylim=c(min(b.and.sse[,2]), max(b.and.sse[,2])))
par(new=TRUE)
par(cex.axis=1.5, cex.lab=2, cex.main=2, mar=c(5,5,5,5))
plot(b.choice,sse,bty='n',ylab='',xlab='',yaxt='n',xaxt='n',
col='red',pch=8,xlim=c(min(b.and.sse[,1]), max(b.and.sse[,1])),
ylim=c(min(b.and.sse[,2]), max(b.and.sse[,2])))
text(b.choice,sse+(r.by*2),paste("b.chosen=",signif(b.choice,3),"\nSSE.chosen=",signif(sse,3)),cex=1.5)
# dev.copy2pdf(file = paste(filename,"-checksse-",minN,"-",maxN,".pdf", sep=""))
dev.off()
## print to files
write.table(b.and.sse,"b_and_sse.grad.txt", row.names=FALSE, sep="\t")
write.table(cbind(maxN,apropor),"percentageOfData.grad.txt", row.names=FALSE, sep="\t")
write.table(cbind(b.choice,sse),"b_chosen.grad.txt", row.names=FALSE,sep="\t")
##################################################################################
# parameter estimation
# estimate the parameters of the betabinomial
# library(fitdistrplus)
# library(MASS)
#
# mu = mean(data.match$ref_allele_ratio)
# V = var(data.match$ref_allele_ratio)
# ## estimation using Jing's formulae, fixing mu=0.5
# # V = n * mu * (1-mu) * b
# b = V/0.25
# b
#
# ## estimation using beta pdf paramter formalisms
# a = (((1-mu) / V) - 1/mu ) * mu^2
# a
# b = a * (1/mu - 1)
# b
#
# ## estimation using 2-parameter fitting
# countdata = cbind(data.match$cA,data.match$cC,data.match$cG,data.match$cT,data.match$total)
# totalcount = apply(countdata,1, function(x,n=1) sort(x,decreasing=TRUE)[n])
# dominantAl = apply(countdata,1, function(x,n=2) sort(x,decreasing=TRUE)[n])
#
# fit = vglm(cbind(dominantAl,totalcount-dominantAl) ~ 1, betabinomial.ab, trace=TRUE)
# coef(fit,matrix=TRUE)
# Coef(fit)
# head(fit@misc$rho)
# head(cbind(depvar(fit)))
# ##################################################################################
# # finding the b parameter automatically
#
# # this is the log likelihood function
# # we fix alpha = 0.5
# loglikelihood <- function(b)
# {
# R = apply(cbind(dominantAl,totalcount),1,dbetabinom)
#
# # product of the function of the parameters you are estimating
# # is sum of the log
# -sum(log(R))
# }
#
# # max likelihood function
# library(stats4)
# mle(loglikelihood, start=list(b=0.01))