Last updated: 2019-11-20

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Knit directory: finemap-uk-biobank/

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    Ignored:    data/height.ADAMTS17.XtX.Xty.rds
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    Ignored:    data/height.CDK6.XtX.Xty.rds
    Ignored:    data/height.DLEU1.XtX.Xty.rds
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    Ignored:    data/height.ZBTB38.removeCS1.XtX.Xty.rds
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    Ignored:    output/height.CABLES1.removeCS1.XtX.Xty.rds
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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 rs7235010 and rs12327253 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)
p1

Version Author Date
9e4fee7 zouyuxin 2019-11-19

The first credible set contains

cs1 = ss.dat$pos[unlist(mod_bhat$sets$cs$L1),]
cs1$gene = sapply(cs1$POS/1e6, function(i){
  id = intersect(which(gene.pos.map$start <= i), which(gene.pos.map$end >= i))
  gene.pos.map$geneName[id]
})
cs1
     #CHROM      POS        ID REF ALT      maf    gene
1293     18 20724810 rs7235010   A   G 0.216373 CABLES1
1294     18 20724931 rs4392169   T   A 0.216218 CABLES1
1296     18 20727611 rs4800452   T   C 0.216717 CABLES1
1299     18 20728223 rs7236494   A   G 0.216449 CABLES1
1301     18 20729714 rs7244464   C   A 0.216409 CABLES1

The second credible set contains

cs2 = ss.dat$pos[unlist(mod_bhat$sets$cs$L2),]
cs2$gene = sapply(cs2$POS/1e6, function(i){
  id = intersect(which(gene.pos.map$start <= i), which(gene.pos.map$end >= i))
  gene.pos.map$geneName[id]
})
cs2
     #CHROM      POS         ID REF ALT      maf    gene
1281     18 20719164 rs12327253   G   A 0.286795 CABLES1
1282     18 20719585 rs57772091   C   T 0.187854 CABLES1

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
f1c45e9 zouyuxin 2019-11-19
8aef62b zouyuxin 2019-11-19
ac423f0 zouyuxin 2019-11-19
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 rs12327253 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
8aef62b zouyuxin 2019-11-19
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')
grid.arrange(p3, p4, ncol=2)

Version Author Date
f1c45e9 zouyuxin 2019-11-19
9e4fee7 zouyuxin 2019-11-19
3db8ace zouyuxin 2019-11-18

Simulation under the estimated model

In the following simulation, we treat rs7235010 and rs12327253 as true signals. The effect sizes are from estimated model. We use the fitted residual variance in the simulation. The response y is simulated from \[ y \sim N_n(Xb, \sigma^2 I) \] , where X the genotype matrix that column centered, scaled, and removed the effect of covariates.

# ON CRI
library(data.table)
library(readr)
library(Matrix)
library(susieR)
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"

# 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, data = pheno)

# Remove intercept
Z = Z[,-1]
Z = scale(Z, center=TRUE, scale=FALSE)
# 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

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

A   <- crossprod(Z)
# chol decomposition for (Z'Z)^(-1)
R = chol(solve(A))
W = R %*% t(Z) %*% X

# Remove Covariates from X
X   <- as.matrix(X - Z %*% crossprod(R,W))

# Get estimated parameters
ss.dat = readRDS('height.CABLES1.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))))
R = as.matrix(t(ss.dat$XtX * (1/sqrt(diag(ss.dat$XtX)))) * (1/ sqrt(diag(ss.dat$XtX))))
mod_bhat.ld = susie_bhat(bhat = betas, shat = se, R = R, n = ss.dat$n, var_y = as.numeric(ss.dat$yty/(ss.dat$n-1)), standardize = F)
sigma2 = mod_bhat.ld$sigma2
b2 = c(mod_bhat.ld$mu[1, 1293], mod_bhat.ld$mu[2, 1281])
Xb = as.vector(X[, c(1293, 1281)] %*% b2)

n = nrow(X)
result = vector("list", 1000)
set.seed(201910)
for(i in 1:1000){
  ## generate y
  y = Xb + rnorm(n, 0, sqrt(sigma2))
  
  ## compute Xty, yty
  Xty = as.vector(y %*% X)
  yty = sum(y^2)
  
  ## compute summary stats
  betas = as.vector(Xty/diag(ss.dat$XtX))
  rss = yty - betas * Xty
  se = as.vector(sqrt(rss/((n-1)*diag(ss.dat$XtX))))
  z = betas/se
  
  result[[i]] = susie_bhat(betas, se, R=R, n=n, var_y = as.numeric(yty/(n-1)), standardize = F)
}
saveRDS(result, 'height.CABLES1.simulation1000.rds')

Load simulation results:

result = readRDS('output/height.CABLES1.simulation1000.rds')

In 1000 simulations, 753 runs have 2 CSs. The rests have 1 CS.

table(sapply(result, function(mod) length(mod$sets$cs)))

  1   2 
247 753

677 runs contain both true signals.

contain.true = sapply(result, function(mod) all(c(1293, 1281) %in% unlist(mod$sets$cs)))
sum(contain.true)
[1] 677

974 runs contain rs7235010.

contain.true.1 = sapply(result, function(mod) all( 1293 %in% unlist(mod$sets$cs)))
sum(contain.true.1)
[1] 974

699 runs contain rs12327253.

contain.true.2 = sapply(result, function(mod) all( 1281 %in% unlist(mod$sets$cs)))
sum(contain.true.2)
[1] 699

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_1.0.3       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