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Before you begin:

  • Make sure that R is installed on your computer
  • For this lab, we will use the following R libraries:
library(data.table)
library(dplyr)
library(tidyr)
library(GWASTools)
library(ggplot2)
library(patchwork)

The R template to do the exercises is here.

Note: if on the online server, set your working directory to your home directory using in R

setwd("home/<username>/")

The data files are in the folder /data/SISG2023M15/data/.

Case-control imbalance in GWAS

Introduction

We will use a simulated dataset consisting of 3 binary traits with different amounts of case-control imbalance, as well as a genetic data set of null SNPs to examine the null distribution of the test statistics from GWAS.

Simulate the data

We can use PLINK1.9 to simulate the genetic dataset. For \(N=10,000\) samples, Let’s simulate 10,000 variants where 5,000 are common with MAF chosen from a Uniform(0.05, 0.5) distribution and for the rare variants, we will use a Uniform(0.001, 0.01) distribution. Run the following command in R:

N <- 10e3
# Generate a configuration file specifying allele frequencies (a,b) for Uniform(a,b) distribution
write(paste0("5000 common 0.05 0.5 1 1"), "sim.config")
write(paste0("5000 rare 0.001 0.01 1 1"), "sim.config", append = TRUE)
# Run PLINK1.9
system(paste0("/data/SISG2023M15/exe/plink --make-bed --simulate sim.config --simulate-ncases ", N, " --simulate-ncontrols 0 --simulate-prevalence 0.1  --out cc_imb_geno"))

You should now have files cc_imb_geno.{bed,bim,fam}.

For the phenotype data simulation, we will simulate 3 phenotypes with different levels of case-control imbalance (CCR 1:9, 1:99, and 1:199). Run the following code

# get FID/IID from FAM file
sample.ids <- fread("cc_imb_geno.fam", header = FALSE)
N <- nrow(sample.ids)

## Set prevalence = 10% (CCR 1:9)
y1 <- rbinom(N, 1, prob = 0.1 )
## Set prevalence = 1% (CCR 1:99)
y2 <- rbinom(N, 1, prob = 0.01 )
## Set prevalence = 0.5% (CCR 1:199)
y3 <- rbinom(N, 1, prob = 0.005 )

# write to file
data.frame(FID = sample.ids$V1, IID = sample.ids$V2, Y1 = y1, Y2 = y2, Y3 = y3) %>%
  fwrite("cc_imb_pheno.txt", sep = "\t", na = NA, quote = FALSE)

You should now have file cc_imb_pheno.txt.

Exercises

We will assess the null distribution of our test statistics when performing association mapping using different models. Here are some things to try:

  1. Run GWAS in REGENIE (step 2) analyzing all 3 traits. The basic command would be
system("/data/SISG2023M15/exe/regenie --bed cc_imb_geno --phenoFile cc_imb_pheno.txt --step 2 --bsize 400 --bt  --ignore-pred --out <output_prefix>")

This will produce three files (one for each phenotype): <output_prefix>_Y1.regenie, <output_prefix>_Y2.regenie, <output_prefix>_Y3.regenie

  1. Read in the three summary statistics files in R and make a QQ plot of the p-values for each phenotype. Since these are null SNPs, how does it compare to what we expect? The basic command for one phenotype would be
sumstats.y1 <- fread("<output_prefix>_Y1.regenie") %>% mutate(Pval = 10^(-LOG10P), Z = sign(BETA) * sqrt(CHISQ))
qqPlot( pval = sumstats.y1$Pval )
  1. Make a histogram of the test statistics for each phenotype and overlay with a normal distribution. How well do they match? We will create a R function to easily make this plot for different phenotypes. The basic command for one phenotype would be
plot.sumstats.hist <- function(df, title = ""){
  df %>%
  ggplot( aes(x = Z) ) +
  geom_histogram(aes(y = ..density..), colour="black", fill="white", bins = 100) +
  stat_function(
    fun = dnorm, 
    col = "red",
    args = list(mean = mean(df$Z), sd = sd(df$Z))
  ) +
    labs(title = title)
}

# for Y1
plot.sumstats.hist(sumstats.y1, title = "Y1")

What do you observe as the case-control imbalance gets more severe?

  1. Re-do 3 but now separate the histogram for common and rare SNPs.
  • First separate the data frame based on common/rare simulated SNPs. For example for trait Y1:
sumstats.y1.common <- sumstats.y1[ grepl("common", ID), ]
sumstats.y1.rare <- sumstats.y1[ grepl("rare", ID), ]
  • Make a histogram of the test statistics distribution at common/rare SNPs. What do you observe across the different case-control imbalances? To easily make side-by-side plots, we can use functionality from the R patchwork library (e.g. p1|p2). For example
plot.sumstats.hist(sumstats.y1.common, title = "Y1 - Common SNPs") | plot.sumstats.hist(sumstats.y1.rare, title = "Y1 - Rare SNPs")

Extra: 5. Re-run GWAS in Questions 1 but now applying Firth correction. Make a QQ plot of the -log10 p-values for Y3. The REGENIE command with Firth would be

system("/data/SISG2023M15/exe/regenie --bed cc_imb_geno --phenoFile cc_imb_pheno.txt --step 2 --bsize 400 --bt  --ignore-pred --firth --out --out <output_prefix>")

sessionInfo()
R version 4.3.0 (2023-04-21)
Platform: aarch64-apple-darwin20 (64-bit)
Running under: macOS Ventura 13.4

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.11.0

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

time zone: Australia/Brisbane
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

loaded via a namespace (and not attached):
 [1] vctrs_0.6.2      cli_3.6.1        knitr_1.43       rlang_1.1.1     
 [5] xfun_0.39        stringi_1.7.12   promises_1.2.0.1 jsonlite_1.8.5  
 [9] workflowr_1.7.0  glue_1.6.2       rprojroot_2.0.3  git2r_0.32.0    
[13] htmltools_0.5.5  httpuv_1.6.11    sass_0.4.6       fansi_1.0.4     
[17] rmarkdown_2.22   evaluate_0.21    jquerylib_0.1.4  tibble_3.2.1    
[21] fastmap_1.1.1    yaml_2.3.7       lifecycle_1.0.3  whisker_0.4.1   
[25] stringr_1.5.0    compiler_4.3.0   fs_1.6.2         Rcpp_1.0.10     
[29] pkgconfig_2.0.3  rstudioapi_0.14  later_1.3.1      digest_0.6.31   
[33] R6_2.5.1         utf8_1.2.3       pillar_1.9.0     magrittr_2.0.3  
[37] bslib_0.5.0      tools_4.3.0      cachem_1.0.8