Last updated: 2019-11-18

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We perform some check for the SuSiE result on region around CABLES1

Load pacakges:

library(readr)
library(dplyr)
library(gridExtra)
library(susieR)

Load plotting functions:

knitr::read_chunk("scripts/plots.R")
library(ggplot2)

#' plot gene name annotations
#' @param dat a matrix of gene names with 'start' and 'end' base-pair position
#' @param xrange range of x axis, base-pair position
plot_geneName = function(dat, xrange, chr){
  ngene = 2:nrow(dat)
  line = 1
  dat$lines = NA
  dat$lines[1] = 1
  gene.end = dat[1, 'end']
  while(length(ngene) != 0){
    id = which(dat[ngene, 'start'] > gene.end + 0.02)[1]
    if(!is.na(id)){
      dat$lines[ngene[id]] = line
      gene.end = dat[ngene[id],'end']
      ngene = ngene[-id]
    }else{
      line = line + 1
      dat$lines[ngene[1]] = line
      gene.end = dat[ngene[1],'end']
      ngene = ngene[-1]
    }
  }
  
  dat$start = pmax(dat$start, xrange[1])
  dat$end = pmin(dat$end, xrange[2])
  dat$mean = rowMeans(dat[,c('start', 'end')])
  
  pl = ggplot(dat, aes(xmin = xrange[1], xmax = xrange[2])) + xlim(xrange[1], xrange[2]) + ylim(min(-dat$lines-0.6), -0.8) + 
    geom_rect(aes(xmin = start, xmax = end, ymin = -lines-0.05, ymax = -lines+0.05), fill='blue') +
    geom_text(aes(x = mean, y=-lines-0.4, label=geneName), size=4) + 
                xlab(paste0('base-pair position (Mb) on chromosome ', chr)) + ylab('Gene') + 
    theme_bw() + theme(axis.text.x=element_blank(),
                       axis.ticks = element_blank(),
                       axis.text.y=element_blank(),
                       axis.title = element_text(size=15),
                       plot.title=element_text(size=11),
                       panel.grid.major = element_blank(),
                       panel.grid.minor = element_blank())
  pl
}

discrete_gradient_pal <- function(colours, bins = 5) {
  ramp <- scales::colour_ramp(colours)
  
  function(x) {
    if (length(x) == 0) return(character())
    
    i <- floor(x * bins)
    i <- ifelse(i > bins-1, bins-1, i)
    ramp(i/(bins-1))
  }
}

scale_colour_discrete_gradient <- function(..., colours, bins = 5, na.value = "grey50", guide = "colourbar", aesthetics = "colour", colors)  {
  colours <- if (missing(colours)) 
    colors
  else colours
  continuous_scale(
    aesthetics,
    "discrete_gradient",
    discrete_gradient_pal(colours, bins),
    na.value = na.value,
    guide = guide,
    ...
  )
}

#' Locuszoom plot
#' @param z a vector of z scores with SNP names
#' @param pos base-pair positions
#' @param gene.pos.map a matrix of gene names with 'start' and 'end' base-pair position
#' @param z.ref.name the reference SNP
#' @param ld correlations between teh reference SNP and the rests
#' @param title title of the plot
#' @param title.size the size of the title
#' @param true the true value
#' @param y.height height of -log10(p) plot and height of the gene name annotation plot
#' @param y.lim range of y axis
locus.zoom = function(z, pos, chr, gene.pos.map=NULL, z.ref.name=NULL, ld=NULL, 
                      title = NULL, title.size = 10, true = NULL, 
                      y.height=c(5,1.5), y.lim=NULL, y.type='logp',xrange=NULL){
  if(is.null(xrange)){
    xrange = c(min(pos), max(pos))
  }
  tmp = data.frame(POS = pos, p = -(pnorm(-abs(z), log.p = T) + log(2))/log(10), z = z)
  
  if(!is.null(ld) && !is.null(z.ref.name)){
    tmp$ref = names(z) == z.ref.name
    tmp$r2 = ld^2
    if(y.type == 'logp'){
      pl_zoom = ggplot(tmp, aes(x = POS, y = p, shape = ref, size=ref, color=r2)) + geom_point() + 
        ylab("-log10(p value)") + ggtitle(title) + xlim(xrange[1], xrange[2]) +
        scale_color_gradientn(colors = c("darkblue", "deepskyblue", "lightgreen", "orange", "red"),
                              values = seq(0,1,0.2), breaks=seq(0,1,0.2)) +
        # scale_colour_discrete_gradient(
        #   colours = c("darkblue", "deepskyblue", "lightgreen", "orange", "red"),
        #   limits = c(0, 1.01),
        #   breaks = c(0,0.2,0.4,0.6,0.8,1),
        #   guide = guide_colourbar(nbin = 100, raster = FALSE, frame.colour = "black", ticks.colour = NA)
        # ) + 
        scale_shape_manual(values=c(20, 18), guide=FALSE) + scale_size_manual(values=c(2,5), guide=FALSE) + 
        theme_bw() + theme(axis.title.x=element_blank(),
                           axis.title.y = element_text(size=15),axis.text = element_text(size=15),
                           plot.title = element_text(size=title.size))
    }else if(y.type == 'z'){
      pl_zoom = ggplot(tmp, aes(x = POS, y = z, shape = ref, size=ref, color=r2)) + geom_point() + 
        ylab("z score") + ggtitle(title) + xlim(xrange[1], xrange[2]) +
        scale_color_gradientn(colors = c("darkblue", "deepskyblue", "lightgreen", "orange", "red"),
                              values = seq(0,1,0.2), breaks=seq(0,1,0.2)) +
        # scale_colour_discrete_gradient(
        #   colours = c("darkblue", "deepskyblue", "lightgreen", "orange", "red"),
        #   limits = c(0, 1.01),
        #   breaks = c(0,0.2,0.4,0.6,0.8,1),
        #   guide = guide_colourbar(nbin = 100, raster = FALSE, frame.colour = "black", ticks.colour = NA)
        # ) + 
        scale_shape_manual(values=c(20, 18), guide=FALSE) + scale_size_manual(values=c(2,5), guide=FALSE) + 
        theme_bw() + theme(axis.title.x=element_blank(),
                           axis.title.y = element_text(size=15),axis.text = element_text(size=15),
                           plot.title = element_text(size=title.size))
    }
  }else{
    if(y.type == 'logp'){
      pl_zoom = ggplot(tmp, aes(x = POS, y = p)) + geom_point(color = 'darkblue') + 
        ylab("-log10(p value)") + ggtitle(title) + xlim(xrange[1], xrange[2]) +
        theme_bw() + theme(axis.title.x=element_blank(),
                           plot.title = element_text(size=title.size))
    }else if(y.type == 'z'){
      pl_zoom = ggplot(tmp, aes(x = POS, y = z)) + geom_point(color = 'darkblue') + 
        ylab("z scores") + ggtitle(title) + xlim(xrange[1], xrange[2]) +
        theme_bw() + theme(axis.title.x=element_blank(),
                           plot.title = element_text(size=title.size))
    }
  }
  
  if(!is.null(y.lim)){
    pl_zoom = pl_zoom + ylim(y.lim[1], y.lim[2])
  }
  # pl_zoom = pl_zoom + geom_hline(yintercept=-log10(5e-08), linetype='dashed', color = 'red')
  if(!is.null(true)){
    tmp.true = data.frame(POS = which(true!=0), p = tmp$p[which(true!=0)], 
                          ref = (names(z) == z.ref.name)[which(true!=0)],
                          label = paste0('SNP',1:length(which(true!=0))))
    pl_zoom = pl_zoom + geom_point(data=tmp.true, aes(x=POS, y=p), 
                                   color='red', show.legend = FALSE, shape=1, stroke = 1) + 
      geom_text(data=tmp.true, aes(x = POS-30, y=p+1, label=label), size=3, color='red')
  }
  if(!is.null(gene.pos.map)){
    pl_gene = plot_geneName(gene.pos.map, xrange = xrange, chr=chr)
    g = egg::ggarrange(pl_zoom, pl_gene, nrow=2, heights = y.height, draw=FALSE)
  }else{
    g = pl_zoom
  }
  g
}

#' SuSiE plot with Locuszoom plot
#' @param z a vector of z scores with SNP names
#' @param model the fitted SuSiE model
#' @param pos base-pair positions
#' @param gene.pos.map a matrix of gene names with 'start' and 'end' base-pair position
#' @param z.ref.name the reference SNP
#' @param ld correlations between teh reference SNP and the rests
#' @param title title of the plot
#' @param title.size the size of the title
#' @param true the true value
#' @param plot.locuszoom whether to plot locuszoom plot
#' @param y.lim range of y axis
#' @param y.susie the y axis of the SuSiE plot, 'PIP' or 'p' or 'z', 'p' refers to -log10(p)
susie_plot_locuszoom = function(z, model, pos, chr, gene.pos.map = NULL, z.ref.name, ld, 
                                title = NULL, title.size = 10, true = NULL, 
                                plot.locuszoom = TRUE, y.lim=NULL, y.susie='PIP', xrange=NULL){
  if(is.null(xrange)){
    xrange = c(min(pos), max(pos))
  }
  if(plot.locuszoom){
    if(y.susie == 'z'){
      y.type = 'z'
    }else{
      y.type = 'logp'
    }
    pl_zoom = locus.zoom(z, pos = pos, chr = chr, ld=ld, z.ref.name = z.ref.name, title = title, title.size = title.size, y.lim=y.lim, y.type=y.type, xrange=xrange)
  }
  pip = model$pip
  tmp = data.frame(POS = pos, PIP = pip, p = -(pnorm(-abs(z), log.p = T) + log(2))/log(10), z = z)
  if(y.susie == 'PIP'){
    pl_susie = ggplot(tmp, aes(x = POS, y = PIP)) + geom_point(show.legend = FALSE, size=3) + 
      xlim(xrange[1], xrange[2]) + 
      theme_bw() + theme(axis.title.x=element_blank(), axis.text.x=element_blank(),axis.text = element_text(size=15),
                         axis.title.y = element_text(size=15))
    if(!plot.locuszoom){
      pl_susie = pl_susie + ggtitle(title) + theme(plot.title = element_text(size=title.size))
    }
  }else if(y.susie == 'p'){
    pl_susie = ggplot(tmp, aes(x = POS, y = p)) + geom_point(show.legend = FALSE, size=3) + 
      ylab("-log10(p value)") + xlim(xrange[1], xrange[2]) + 
      theme_bw() + theme(axis.title.x=element_blank(), axis.text.x=element_blank(),axis.text = element_text(size=15),
                         axis.title.y = element_text(size=15))
    if(!plot.locuszoom){
      pl_susie = pl_susie + ggtitle(title) + theme(plot.title = element_text(size=title.size))
      # pl_susie = pl_susie + geom_hline(yintercept=-log10(5e-08), linetype='dashed', color = 'red')
    }
  }else if(y.susie == 'z'){
    pl_susie = ggplot(tmp, aes(x = POS, y = z)) + geom_point(show.legend = FALSE, size=3) + 
      ylab("z scores") + xlim(xrange[1], xrange[2]) + 
      theme_bw() + theme(axis.title.x=element_blank(), axis.text.x=element_blank(),axis.text = element_text(size=15),
                         axis.title.y = element_text(size=15))
    if(!plot.locuszoom){
      pl_susie = pl_susie + ggtitle(title) + theme(plot.title = element_text(size=title.size))
    }
  }
  
  if(!is.null(true)){
    tmp.true = data.frame(POS = pos[which(true!=0)], PIP = pip[which(true!=0)])
    pl_susie = pl_susie + geom_point(data=tmp.true, aes(x=POS, y=PIP), 
                                     color='red', size=3, show.legend = FALSE)
  }
  
  model.cs = model$sets$cs
  if(!is.null(model.cs)){
    tmp$CS = numeric(length(z))
    for(i in 1:length(model.cs)){
      tmp$CS[model.cs[[i]]] = gsub('L', 'CS', names(model.cs)[i])
    }
    tmp.cs = tmp[unlist(model.cs),]
    tmp.cs$CS = factor(tmp.cs$CS)
    levels(tmp.cs$CS) = paste0('CS', 1:length(model.cs))
    colors = c('red', 'cyan', 'green', 'orange', 'dodgerblue', 'violet', 'gold',
               '#FF00FF', 'forestgreen', '#7A68A6')
    if(y.susie == 'PIP'){
      pl_susie = pl_susie + geom_point(data=tmp.cs, aes(x=POS, y=PIP, color=CS), 
                                       size=3, shape=1, stroke = 2) + 
        scale_color_manual(values=colors)
    }else if(y.susie == 'p'){
      pl_susie = pl_susie + geom_point(data=tmp.cs, aes(x=POS, y=p, color=CS), 
                                       shape=1, size=3, stroke=1.5) + 
        scale_color_manual(values=colors)
    }else if(y.susie == 'z'){
      pl_susie = pl_susie + geom_point(data=tmp.cs, aes(x=POS, y=z, color=CS), 
                                       shape=1, size=3, stroke=1.5) + 
        scale_color_manual(values=colors)
    }
  }
  
  if(!is.null(gene.pos.map)){
    pl_gene = plot_geneName(gene.pos.map, xrange = xrange, chr=chr)
    if(plot.locuszoom){
      g = egg::ggarrange(pl_zoom, pl_susie, pl_gene, nrow=3, heights = c(4,4,1.5), draw=FALSE)
    }else{
      g = egg::ggarrange(pl_susie, pl_gene, nrow=2, heights = c(5.5,1.5), draw=FALSE)
    }
    
  }else{
    if(plot.locuszoom){
      g = egg::ggarrange(pl_zoom, pl_susie, nrow=2, heights = c(4,4), draw=FALSE)
    }else{
      g = pl_susie
    }
  }
  g
}
locus.zoom.cs = function(z, cs, pos, chr, gene.pos.map=NULL, z.ref.name=NULL, ld=NULL, title = NULL, title.size = 10, xrange = NULL, y.lab='-log10(p value)', y.type = 'logp'){

  if(is.null(xrange)){
    xrange = c(min(pos), max(pos))
  }
  tmp = data.frame(POS = pos, log10p = -(pnorm(-abs(z), log.p = T) + log(2))/log(10), z = z)
  tmp$ref = names(z) == z.ref.name
  tmp$r2 = ld^2
  tmp$CS = rep(4, length(z))
  tmp$CS[cs] = 16
  tmp$CS = as.factor(tmp$CS)
  if(y.type == 'logp'){
    pl_zoom = ggplot(tmp, aes(x = POS, y = log10p, shape = CS, color = r2, size=CS)) + 
    geom_point() + ylab(y.lab)
  }else if(y.type == 'z'){
    pl_zoom = ggplot(tmp, aes(x = POS, y = z, shape = CS, color = r2, size=CS)) + 
    geom_point() + ylab(y.lab)
  }
  pl_zoom = pl_zoom + scale_color_gradientn(colors = c("darkblue", "deepskyblue", "lightgreen", "orange", "red"),
                          values = seq(0,1,0.2), breaks=seq(0,1,0.2)) + 
    # scale_colour_discrete_gradient(
    #     colours = c("darkblue", "deepskyblue", "lightgreen", "orange", "red"),
    #     limits = c(0, 1.01),
    #     breaks = c(0,0.2,0.4,0.6,0.8,1),
    #     guide = guide_colourbar(nbin = 100, raster = FALSE, frame.colour = "black", ticks.colour = NA)) +
    scale_shape_manual(values = c(4, 19), guide=FALSE) + 
    scale_size_manual(values=c(1.5,4), guide=FALSE) + 
    ggtitle(title) + 
    theme_bw() + theme(axis.title.x=element_blank(), axis.text=element_text(size=15),
                       axis.title.y=element_text(size=12),
                       plot.title = element_text(size=title.size))
  tmp.sub = tmp[cs,]
  if(y.type == 'logp'){
    pl_zoom = pl_zoom + geom_point(data = tmp.sub, aes(x=POS, y=log10p), shape=1, size=4, color='black', stroke=0.1)
  }else if(y.type == 'z'){
    pl_zoom = pl_zoom + geom_point(data = tmp.sub, aes(x=POS, y=z), shape=1, size=4, color='black', stroke=0.1)
  }
  
  if(!is.null(xrange)){
    pl_zoom = pl_zoom + xlim(xrange[1], xrange[2])
  }
  
  pl_gene = plot_geneName(gene.pos.map, xrange = xrange, chr=chr)
  g = egg::ggarrange(pl_zoom, pl_gene, nrow=2, heights = c(5.5,1.5), draw=FALSE)
  g
}

Get summary statistics:

ss.dat = readRDS('data/height.CABLES1.XtX.Xty.rds')
betas = as.vector(ss.dat$Xty/diag(ss.dat$XtX))
rss = c(ss.dat$yty) - betas * as.vector(ss.dat$Xty)
se = sqrt(rss/((ss.dat$n-1)*diag(ss.dat$XtX)))
z = betas/se
pval = 2*pnorm(-abs(z))
R = as.matrix(t(ss.dat$XtX * (1/sqrt(diag(ss.dat$XtX)))) * (1/ sqrt(diag(ss.dat$XtX))))
names(z) = rownames(R)

Get gene data:

genes        <- read_delim("data/seq_gene.md.gz",delim = "\t",quote = "")
class(genes) <- "data.frame"
genes        <- subset(genes,
                       group_label == "GRCh37.p5-Primary Assembly" &
                       feature_type == "GENE")
start.pos <- min(ss.dat$pos$POS)
stop.pos  <- max(ss.dat$pos$POS)
plot.genes <- subset(genes,
                     chromosome == 18 &
                     ((chr_start > start.pos & chr_start < stop.pos) |
                      (chr_stop > start.pos & chr_start < stop.pos)) & feature_type == 'GENE')
gene.pos.map = plot.genes %>% select(feature_name, chr_start, chr_stop)
colnames(gene.pos.map) = c('geneName', 'start', 'end')
gene.pos.map = as.data.frame(gene.pos.map)
gene.pos.map = gene.pos.map %>% mutate(start = start/1e6, end = end/1e6)
gene.pos.map = gene.pos.map[-c(1),]

SuSiE bhat result: the top panel shows the r2 with respect to the top hit (diamond shape); the lower panel plots the credible sets in PIP, -log10(p value) and z scores.

mod_bhat = susie_bhat(bhat = betas, shat = se, R = R, n = ss.dat$n, var_y = as.numeric(ss.dat$yty/(ss.dat$n-1)), track_fit=TRUE, standardize=FALSE)
z.max = which.max(abs(z))
p1 = susie_plot_locuszoom(z, mod_bhat, pos = ss.dat$pos$POS/1e6, chr=18, gene.pos.map = gene.pos.map, ld = R[z.max,], z.ref.name = names(z.max))
p2 = susie_plot_locuszoom(z, mod_bhat, pos = ss.dat$pos$POS/1e6, chr=18, gene.pos.map = gene.pos.map, ld = R[z.max,], z.ref.name = names(z.max), y.susie ='p')
p3 = susie_plot_locuszoom(z, mod_bhat, pos = ss.dat$pos$POS/1e6, chr=18, gene.pos.map = gene.pos.map, ld = R[z.max,], z.ref.name = names(z.max), y.susie ='z')
grid.arrange(p1, p2, p3, ncol=3)

Version Author Date
9e4fee7 zouyuxin 2019-11-19

For 1Mb region about CABLES1, SuSiE found 2 CSs. The SNP with the strongest marginal p value in CS1 is rs7235010 (p = 1.3394e-113). For CS2, the SNP with the strongest marginal p value is rs12327253 (p = 0.1015).

The correlation between rs2871960 and rs11919556 is 0.3082546. The average correlation between SNPs in CS1 and CS2 is

round(mean(abs(R[mod_bhat$sets$cs$L1, mod_bhat$sets$cs$L2])), 4)
[1] 0.2764

Zoom in plot:

p1 = susie_plot_locuszoom(z, mod_bhat, pos = ss.dat$pos$POS/1e6, chr=18, gene.pos.map = gene.pos.map, z.ref.name = names(z), ld = R[z.max,], title='CABLES1 Credible Sets', plot.locuszoom = FALSE, y.susie = 'p', xrange=c(20.5, 21), title.size = 20)
Warning: Removed 1129 rows containing missing values (geom_point).
Warning: Removed 4 rows containing missing values (geom_rect).
Warning: Removed 4 rows containing missing values (geom_text).
p1

Version Author Date
9e4fee7 zouyuxin 2019-11-19

CS 1

  • Option 1. We remove effect of top SNP in CS 2.
library(data.table)
library(readr)
library(Matrix)
geno.file = 'height.CABLES1.raw.gz'
cat("Reading genotype data.\n")
geno <- fread(geno.file,sep = "\t",header = TRUE,stringsAsFactors = FALSE)
class(geno) <- "data.frame"

# Extract the genotypes.
X <- as(as.matrix(geno[-(1:6)]),'dgCMatrix')

pheno.file <- "/gpfs/data/stephens-lab/finemap-uk-biobank/data/raw/height.csv.gz"
out.pheno.file <- "pheno.height.txt"
out.covar.file <- "covar.removeCS2.height.txt"

# LOAD PHENOTYPE and COVARIATES DATA
# -------------------
# Read the phenotype data from the CSV file.
cat("Reading phenotype data.\n")
pheno        <- suppressMessages(read_csv(pheno.file))
class(pheno) <- "data.frame"
pheno$sex = factor(pheno$sex)
pheno$assessment_centre = factor(pheno$assessment_centre)
pheno$genotype_measurement_batch = factor(pheno$genotype_measurement_batch)
pheno$age2 = pheno$age^2
# match individual order with genotype file
ind = fread('height.CABLES1.psam')
match.idx = match(ind$IID, pheno$id)
pheno = pheno[match.idx,]

Z = model.matrix(~ sex + age + age2 + assessment_centre + genotype_measurement_batch +
                   pc_genetic1 + pc_genetic2 + pc_genetic3 + pc_genetic4 + pc_genetic5 +
                   pc_genetic6 + pc_genetic7 + pc_genetic8 + pc_genetic9 + pc_genetic10 +
                   pc_genetic11 + pc_genetic12 + pc_genetic13 + pc_genetic14 + pc_genetic15 +
                   pc_genetic16 + pc_genetic17 + pc_genetic18 + pc_genetic19 + pc_genetic20 + X[,1281], data = pheno)

# Remove intercept
Z = Z[,-1]
colnames(Z)[150] = 'X'
Z = scale(Z, center=T, scale=F)
# standardize quantitative columns
cols = which(colnames(Z) %in% c("age","pc_genetic1","pc_genetic2","pc_genetic3","pc_genetic4",
                                "pc_genetic5","pc_genetic6","pc_genetic7","pc_genetic8","pc_genetic9", 
                                "pc_genetic10","pc_genetic11","pc_genetic12","pc_genetic13","pc_genetic14",
                                "pc_genetic15","pc_genetic16","pc_genetic17","pc_genetic18","pc_genetic19","pc_genetic20"))
Z[,cols] = scale(Z[,cols])
Z[,'age2'] = Z[,'age']^2

# Compute XtX and Xty
y = pheno$height
names(y) = pheno$id

# Center y
y = y - mean(y)
# Center X
X = scale(X, center=T, scale=FALSE)
xtxdiag = colSums(X^2)

A   <- crossprod(Z) # Z'Z
# chol decomposition for (Z'Z)^(-1)
R = chol(solve(A)) # R'R = (Z'Z)^(-1)
W = R %*% crossprod(Z, X) # RZ'X
S = R %*% crossprod(Z, y) # RZ'y

# Load LD matrix from raw genotype
ld.matrix = as.matrix(fread(paste0('height.CABLES1.matrix')))
# X'X
XtX = sqrt(xtxdiag) * t(ld.matrix*sqrt(xtxdiag)) - crossprod(W) # W'W = X'ZR'RZ'X = X'Z(Z'Z)^{-1}Z'X
rownames(XtX) = colnames(XtX) = colnames(X)
# X'y
Xty = as.vector(y %*% X)
Xty = Xty - crossprod(W, S) # W'S = X'ZR'RZ'y = X'Z(Z'Z)^{-1}Z'y

## SNP info
maf <- read.delim('height.CABLES1.afreq')
pos <- fread('height.CABLES1.pvar')
pos$maf = pmin(maf$ALT_FREQS, 1-maf$ALT_FREQS)

saveRDS(list(XtX = XtX, Xty = Xty, yty = sum(y^2) - crossprod(S), n = length(y), pos=pos),
        paste0('height.CABLES1.removeCS2.XtX.Xty.rds'))

After removing the effect of rs12327253 (p = 0.1015), the p values and z scores are plotted below. The color is correspongding to LD, the shape is corresponding to CS. The SNP in CS is labeled with filled circle.

ss.dat = readRDS('output/height.CABLES1.removeCS2.XtX.Xty.rds')
betas = as.vector(ss.dat$Xty/diag(ss.dat$XtX))
rss = c(ss.dat$yty) - betas * ss.dat$Xty
se = as.vector(sqrt(rss/((ss.dat$n-1)*diag(ss.dat$XtX))))
z = betas/se
pval = 2*pnorm(-abs(z))
R = as.matrix(t(ss.dat$XtX * (1/sqrt(diag(ss.dat$XtX)))) * (1/ sqrt(diag(ss.dat$XtX))))
names(z) = rownames(R)
z.max = which.max(abs(z))
p1 = locus.zoom.cs(z, cs = mod_bhat$sets$cs$L1, pos=ss.dat$pos$POS/1e6, chr=18, gene.pos.map = gene.pos.map, z.ref.name = names(z)[z.max], ld = R[z.max,], xrange=c(20.5,21), title='CABLES1 CS1', y.lab = '-log10(p value condition on CS2)')
p2 = locus.zoom.cs(z, cs = mod_bhat$sets$cs$L1, pos=ss.dat$pos$POS/1e6, chr=18, gene.pos.map = gene.pos.map, z.ref.name = names(z)[z.max], ld = R[z.max,], xrange=c(20.5,21), title='CABLES1 CS1', y.lab = 'z scores condition on CS2', y.type = 'z')
grid.arrange(p1, p2, ncol=2)

Version Author Date
9e4fee7 zouyuxin 2019-11-19
  • Option 2. We remove effect of all other CSs.

Instead of removing the effect of top SNP from other CSs, we do exactly what SuSiE does here. In SuSiE, we estimate effects using residuals that are obtained by removing the effects of all other CSs.

The residuals after removing the effects from CSs other than CS1 is \[ r = y - \mathbf{X} \sum_{l=2}^{L}\hat{\mathbf{b}}_{l}. \]

ss.dat = readRDS('data/height.CABLES1.XtX.Xty.rds')
# remove 1-st effect from fitted values
XtXr = mod_bhat$XtXr - ss.dat$XtX %*% (mod_bhat$alpha[1,] * mod_bhat$mu[1,]) 
Xtr = ss.dat$Xty - XtXr
betas = Xtr/diag(ss.dat$XtX)
b_2 = colSums(mod_bhat$alpha[-1,]*mod_bhat$mu[-1,])
rss = c(ss.dat$yty - 2*sum(ss.dat$Xty * b_2) + sum(XtXr * b_2)) - betas * Xtr
se = as.vector(sqrt(rss/((ss.dat$n-1)*diag(ss.dat$XtX))))
z.CS1 = betas/se
R = as.matrix(t(ss.dat$XtX * (1/sqrt(diag(ss.dat$XtX)))) * (1/ sqrt(diag(ss.dat$XtX))))
names(z.CS1) = colnames(R)
z.cs1.max = which.max(abs(z.CS1))
p1 = locus.zoom.cs(z.CS1, mod_bhat$sets$cs$L1, pos=ss.dat$pos$POS/1e6, chr = 18, gene.pos.map = gene.pos.map, z.ref.name = names(z.cs1.max), ld = R[z.cs1.max,], xrange=c(20.5,21), title='CABLES1 Credible Set 1', y.lab = '-log10(p value condition on other CSs)', title.size = 20)
p2 = locus.zoom.cs(z.CS1, mod_bhat$sets$cs$L1, pos=ss.dat$pos$POS/1e6, chr = 18, gene.pos.map = gene.pos.map, z.ref.name = names(z.cs1.max), ld = R[z.cs1.max,], xrange=c(20.5,21), title='CABLES1 Credible Set 1', y.lab = 'z scores condition on other CSs', title.size = 20, y.type='z')
grid.arrange(p1, p2, ncol=2)

Version Author Date
9e4fee7 zouyuxin 2019-11-19
3db8ace zouyuxin 2019-11-18

CS 2

  • Option 1. We remove effect of top SNP in CS 1.
library(data.table)
library(readr)
library(Matrix)
geno.file = 'height.CABLES1.raw.gz'
cat("Reading genotype data.\n")
geno <- fread(geno.file,sep = "\t",header = TRUE,stringsAsFactors = FALSE)
class(geno) <- "data.frame"

# Extract the genotypes.
X <- as(as.matrix(geno[-(1:6)]),'dgCMatrix')

pheno.file <- "/gpfs/data/stephens-lab/finemap-uk-biobank/data/raw/height.csv.gz"
out.pheno.file <- "pheno.height.txt"
out.covar.file <- "covar.removeCS1.height.txt"

# LOAD PHENOTYPE and COVARIATES DATA
# -------------------
# Read the phenotype data from the CSV file.
cat("Reading phenotype data.\n")
pheno        <- suppressMessages(read_csv(pheno.file))
class(pheno) <- "data.frame"
pheno$sex = factor(pheno$sex)
pheno$assessment_centre = factor(pheno$assessment_centre)
pheno$genotype_measurement_batch = factor(pheno$genotype_measurement_batch)
pheno$age2 = pheno$age^2
# match individual order with genotype file
ind = fread('height.CABLES1.psam')
match.idx = match(ind$IID, pheno$id)
pheno = pheno[match.idx,]

Z = model.matrix(~ sex + age + age2 + assessment_centre + genotype_measurement_batch +
                   pc_genetic1 + pc_genetic2 + pc_genetic3 + pc_genetic4 + pc_genetic5 +
                   pc_genetic6 + pc_genetic7 + pc_genetic8 + pc_genetic9 + pc_genetic10 +
                   pc_genetic11 + pc_genetic12 + pc_genetic13 + pc_genetic14 + pc_genetic15 +
                   pc_genetic16 + pc_genetic17 + pc_genetic18 + pc_genetic19 + pc_genetic20 + X[,1293], data = pheno)

# Remove intercept
Z = Z[,-1]
colnames(Z)[150] = 'X'
Z = scale(Z, center=T, scale = F)
# standardize quantitative columns
cols = which(colnames(Z) %in% c("age","pc_genetic1","pc_genetic2","pc_genetic3","pc_genetic4",
                                "pc_genetic5","pc_genetic6","pc_genetic7","pc_genetic8","pc_genetic9", 
                                "pc_genetic10","pc_genetic11","pc_genetic12","pc_genetic13","pc_genetic14",
                                "pc_genetic15","pc_genetic16","pc_genetic17","pc_genetic18","pc_genetic19","pc_genetic20"))
Z[,cols] = scale(Z[,cols])
Z[,'age2'] = Z[,'age']^2

# Compute XtX and Xty
y = pheno$height
names(y) = pheno$id

# Center y
y = y - mean(y)
# Center X
X = scale(X, center=TRUE, scale = FALSE)
xtxdiag = colSums(X^2)

A   <- crossprod(Z) # Z'Z
# chol decomposition for (Z'Z)^(-1)
R = chol(solve(A)) # R'R = (Z'Z)^(-1)
W = R %*% crossprod(Z, X) # RZ'X
S = R %*% crossprod(Z, y) # RZ'y

# Load LD matrix from raw genotype
ld.matrix = as.matrix(fread('height.CABLES1.matrix'))
# X'X
XtX = sqrt(xtxdiag) * t(ld.matrix*sqrt(xtxdiag)) - crossprod(W) # W'W = X'ZR'RZ'X = X'Z(Z'Z)^{-1}Z'X
rownames(XtX) = colnames(XtX) = colnames(X)
# X'y
Xty = as.vector(y %*% X)
Xty = Xty - crossprod(W, S) # W'S = X'ZR'RZ'y = X'Z(Z'Z)^{-1}Z'y

## SNP info
maf <- read.delim('height.CABLES1.afreq')
pos <- fread('height.CABLES1.pvar')
pos$maf = pmin(maf$ALT_FREQS, 1-maf$ALT_FREQS)

saveRDS(list(XtX = XtX, Xty = Xty, yty = sum(y^2) - crossprod(S), n = length(y), pos=pos),
        paste0('height.CABLES1.removeCS1.XtX.Xty.rds'))

After removing the effect of rs7235010 (p = 1.3394e-113), the conditional p value for rs57772091 becomes 1.9404e-08!

ss.dat = readRDS('output/height.CABLES1.removeCS1.XtX.Xty.rds')
betas = as.vector(ss.dat$Xty/diag(ss.dat$XtX))
rss = c(ss.dat$yty) - betas * ss.dat$Xty
se = as.vector(sqrt(rss/((ss.dat$n-1)*diag(ss.dat$XtX))))
z = betas/se
pval = 2*pnorm(-abs(z))
R = as.matrix(t(ss.dat$XtX * (1/sqrt(diag(ss.dat$XtX)))) * (1/ sqrt(diag(ss.dat$XtX))))
names(z) = rownames(R)
z.max = which.max(abs(z))
p1 = locus.zoom.cs(z, cs = mod_bhat$sets$cs$L2, pos=ss.dat$pos$POS/1e6, chr=18, gene.pos.map = gene.pos.map, z.ref.name = names(z)[z.max], ld = R[z.max,], xrange=c(20.5,21), title='CABLES1 CS2', y.lab = '-log10(p value condition on CS1)')
p2 = locus.zoom.cs(z, cs = mod_bhat$sets$cs$L2, pos=ss.dat$pos$POS/1e6, chr=18, gene.pos.map = gene.pos.map, z.ref.name = names(z)[z.max], ld = R[z.max,], xrange=c(20.5,21), title='CABLES1 CS2', y.lab = 'z scores condition on CS1)', y.type = 'z')
grid.arrange(p1, p2, ncol=2)

Version Author Date
9e4fee7 zouyuxin 2019-11-19
  • Option 2. We remove effect of all other CSs.

Instead of removing the effect of top SNP from other CSs, we do exactly what SuSiE does here. In SuSiE, we estimate effects using residuals that are obtained by removing the effects of all other CSs.

The residuals after removing the effects from CSs other than CS2 is \[ r = y - \mathbf{X} \sum_{l\neq 2}^{L}\hat{\mathbf{b}}_{l}. \]

ss.dat = readRDS('data/height.CABLES1.XtX.Xty.rds')
XtXr = mod_bhat$XtXr - ss.dat$XtX %*% (mod_bhat$alpha[2,] * mod_bhat$mu[2,]) 
Xtr = ss.dat$Xty - XtXr
betas = Xtr/diag(ss.dat$XtX)
b_2 = colSums(mod_bhat$alpha[-2,]*mod_bhat$mu[-2,])/mod_bhat$X_column_scale_factors
rss = c(ss.dat$yty - 2*sum(ss.dat$Xty * b_2) + sum(XtXr * b_2)) - betas * Xtr
se = as.vector(sqrt(rss/((ss.dat$n-1)*diag(ss.dat$XtX))))
z.CS2 = betas/se
R = as.matrix(t(ss.dat$XtX * (1/sqrt(diag(ss.dat$XtX)))) * (1/ sqrt(diag(ss.dat$XtX))))
names(z.CS2) = colnames(R)
z.cs2.max = which.max(abs(z.CS2))
p3 = locus.zoom.cs(z.CS2, mod_bhat$sets$cs$L2, pos=ss.dat$pos$POS/1e6, chr=18, gene.pos.map = gene.pos.map, z.ref.name = names(z.cs2.max), ld = R[z.cs2.max,], xrange=c(20.5, 21), title='CABLES1 Credible Set 2', y.lab = '-log10(p value condition on other CSs)', title.size = 20)
p4 = locus.zoom.cs(z.CS2, mod_bhat$sets$cs$L2, pos=ss.dat$pos$POS/1e6, chr=18, gene.pos.map = gene.pos.map, z.ref.name = names(z.cs2.max), ld = R[z.cs2.max,], xrange=c(20.5, 21), title='CABLES1 Credible Set 2', y.lab = 'z scores condition on other CSs', title.size = 20, y.type='z')
p3

Version Author Date
9e4fee7 zouyuxin 2019-11-19
3db8ace zouyuxin 2019-11-18 

sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Scientific Linux 7.4 (Nitrogen)

Matrix products: default
BLAS/LAPACK: /software/openblas-0.2.19-el7-x86_64/lib/libopenblas_haswellp-r0.2.19.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] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] ggplot2_3.1.1     susieR_0.8.1.0545 gridExtra_2.3     dplyr_0.8.0.1    
[5] readr_1.3.1      

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.1       plyr_1.8.4       pillar_1.3.1     compiler_3.5.1  
 [5] later_0.7.5      git2r_0.26.1     workflowr_1.5.0  tools_3.5.1     
 [9] digest_0.6.18    evaluate_0.12    tibble_2.0.1     gtable_0.2.0    
[13] lattice_0.20-38  egg_0.4.5        pkgconfig_2.0.2  rlang_0.3.1     
[17] Matrix_1.2-15    yaml_2.2.0       withr_2.1.2      stringr_1.3.1   
[21] knitr_1.20       fs_1.3.1         hms_0.4.2        rprojroot_1.3-2 
[25] grid_3.5.1       tidyselect_0.2.5 glue_1.3.0       R6_2.3.0        
[29] rmarkdown_1.10   purrr_0.3.2      magrittr_1.5     whisker_0.3-2   
[33] backports_1.1.2  scales_1.0.0     promises_1.0.1   htmltools_0.3.6 
[37] assertthat_0.2.1 colorspace_1.4-0 httpuv_1.4.5     labeling_0.3    
[41] stringi_1.2.4    lazyeval_0.2.1   munsell_0.5.0    crayon_1.3.4