Practical 8 Key - Case-control imbalance in GWAS
Last updated: 2024-06-14
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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(qqman)
library(ggplot2)Introduction
We will generate a simulated dataset consisting of 3 binary traits with different amounts of case-control imbalance, and a genetic data set of null SNPs to examine the distribution of the test statistics when scanning for associations.
Data preparation
We first need to define the path to the directory containing the PLINK 1.9 and PLINK2 binary.
plink_binary <- "/SISGM19/bin/plink1.9"
regenie_binary <- "/SISGM19/bin/regenie" If you don’t have REGENIE installed on your machine, download the R
implementation here
and change the path of the variable regenie_script to the
path of the script on your machine.
regenie_script <- "/SISGM19/data/run_regenie.r"
source(regenie_script)Simulate the data
We 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 to get the simulated data:
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
cmd <- sprintf("%s --make-bed --simulate sim.config --simulate-ncases %d --simulate-ncontrols 0 --simulate-prevalence 0.1 --out cc_imb_geno", plink_binary, N)
system(cmd)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 (casse-control ratios [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
fwrite(
data.frame(FID = sample.ids$V1, IID = sample.ids$V2, Y1 = y1, Y2 = y2, Y3 = y3),
"cc_imb_pheno.txt",
sep = "\t", na = NA, quote = FALSE
)You should now have a file named cc_imb_pheno.txt.
Exercises
We will now assess the null distribution of our test statistics when performing association testing using different models.
- Run the GWAS in REGENIE for the 3 traits.
cmd <- sprintf('%s --bed cc_imb_geno --phenoFile cc_imb_pheno.txt --bt --step 2 --bsize 2000 --ignore-pred --out test_regenie', regenie_binary)
system(cmd)This will produce three sumstats files (one for each phenotype) which you can read in R:
sumstats.y1 <- fread("test_regenie_Y1.regenie")
sumstats.y2 <- fread("test_regenie_Y2.regenie")
sumstats.y3 <- fread("test_regenie_Y3.regenie") To run the R implementation instead, run the following for each trait (this computes the association tests and stores it in the R variable directly)
sumstats.y1 <- run_regenie_step2_bt(
bedfile = "cc_imb_geno",
phenofile = "cc_imb_pheno.txt",
phenocol = "Y1",
bsize = 300
)
sumstats.y2 <- run_regenie_step2_bt(
bedfile = "cc_imb_geno",
phenofile = "cc_imb_pheno.txt",
phenocol = "Y2",
bsize = 300
)
sumstats.y3 <- run_regenie_step2_bt(
bedfile = "cc_imb_geno",
phenofile = "cc_imb_pheno.txt",
phenocol = "Y3",
bsize = 300
) - Make a QQ plot of the p-values for each phenotype. Since these are null SNPs, how does it compare to what we expect?
qq(10^-sumstats.y1$LOG10P)
| Version | Author | Date |
|---|---|---|
| 977dc7f | Joelle Mbatchou | 2024-06-14 |
qq(10^-sumstats.y2$LOG10P)
| Version | Author | Date |
|---|---|---|
| 977dc7f | Joelle Mbatchou | 2024-06-14 |
qq(10^-sumstats.y3$LOG10P)
| Version | Author | Date |
|---|---|---|
| 977dc7f | Joelle Mbatchou | 2024-06-14 |
- Make a histogram of the test statistics for each phenotype and overlay with a normal distribution. How well do they match? We will create a R function to easily make this plot for different phenotypes.
plot.sumstats.hist <- function(df, title = ""){
df$Z_STAT <- sign(df$BETA) * sqrt(df$CHISQ)
ggplot(df, aes(x = Z_STAT) ) +
geom_histogram(aes(y = after_stat(density)), colour="black", fill="white", bins = 100) +
stat_function(
fun = dnorm,
col = "red",
args = list(
mean = mean(df$Z_STAT, na.rm = TRUE),
sd = sd(df$Z_STAT, na.rm = TRUE)
)
) +
theme_bw(16) +
labs(title = title)
}Now make histogram plot for each trait.
# for Y1
plot.sumstats.hist(sumstats.y1, title = "Y1")
| Version | Author | Date |
|---|---|---|
| 977dc7f | Joelle Mbatchou | 2024-06-14 |
# for Y2
plot.sumstats.hist(sumstats.y2, title = "Y2")
| Version | Author | Date |
|---|---|---|
| 977dc7f | Joelle Mbatchou | 2024-06-14 |
# for Y3
plot.sumstats.hist(sumstats.y3, title = "Y3")
| Version | Author | Date |
|---|---|---|
| 977dc7f | Joelle Mbatchou | 2024-06-14 |
What do you observe as the case-control imbalance gets more severe?
- Re-do 3 but now separate the histogram for common and rare SNPs. We define a new function to generate the histogram for each class of variants.
plot.sumstats.hist.by.group <- function(df, title = ""){
df$Z_STAT <- sign(df$BETA) * sqrt(df$CHISQ)
df$group <- ifelse(grepl("rare", df$ID), "Rare SNPs", "Common SNPs")
# Step 2: Generate normal density data for each group
moment.ests <- with(df, tapply(Z_STAT, group, function(x) c(mean=mean(x, na.rm = TRUE), sd=sd(x, na.rm = TRUE))))
z_stat_seq <- seq(min(df$Z_STAT, na.rm = TRUE), max(df$Z_STAT, na.rm = TRUE), length.out = 100)
normal_curve_data <- do.call(rbind, lapply(unique(df$group), function(grp) {
mean <- moment.ests[[grp]]['mean']; sd <- moment.ests[[grp]]['sd']
density <- dnorm(z_stat_seq, mean = mean, sd = sd)
data.frame(Z_STAT = z_stat_seq, density = density, group = grp)
}))
ggplot(df, aes(x = Z_STAT) ) +
geom_histogram(aes(y = ..density..), colour="black", fill="white", bins = 100) +
geom_line(data = normal_curve_data, aes(x = Z_STAT, y = density), col = "red", size = 1) +
facet_wrap(~group) +
theme_bw(16) +
labs(title = title)
}- Make a histogram of the test statistics distribution at common/rare SNPs for each trait. What do you observe across the different case-control imbalances?
# for Y1
plot.sumstats.hist.by.group(sumstats.y1, "Y1")Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
ℹ Please use `linewidth` instead.
This warning is displayed once every 8 hours.
Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
generated.Warning: The dot-dot notation (`..density..`) was deprecated in ggplot2 3.4.0.
ℹ Please use `after_stat(density)` instead.
This warning is displayed once every 8 hours.
Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
generated.
| Version | Author | Date |
|---|---|---|
| 977dc7f | Joelle Mbatchou | 2024-06-14 |
# for Y2
plot.sumstats.hist.by.group(sumstats.y2, "Y2")
| Version | Author | Date |
|---|---|---|
| 977dc7f | Joelle Mbatchou | 2024-06-14 |
# for Y3
plot.sumstats.hist.by.group(sumstats.y3, "Y3")
| Version | Author | Date |
|---|---|---|
| 977dc7f | Joelle Mbatchou | 2024-06-14 |
What do you observe as the case-control imbalance gets more severe?
Extra
- Re-run GWAS in Questions 1 but now applying Firth correction. Make a QQ plot of the -log10 p-values for Y3. The command in PLINK to run GWAS with Firth is:
cmd <- sprintf('%s --bed cc_imb_geno --phenoFile cc_imb_pheno.txt --bt --step 2 --bsize 2000 --firth --approx --ignore-pred --out test_regenie_wFirth', regenie_binary)
system(cmd)This will produce three files (one for each phenotype) which you can read in R
sumstats.y1.firth <- fread("test_regenie_wFirth_Y1.regenie")
sumstats.y2.firth <- fread("test_regenie_wFirth_Y2.regenie")
sumstats.y3.firth <- fread("test_regenie_wFirth_Y3.regenie") To run the R implementation instead, run the following (this computes the association tests and stores it in the R variable directly)
sumstats.y1.firth <- run_regenie_step2_bt(
bedfile = "cc_imb_geno",
phenofile = "cc_imb_pheno.txt",
phenocol = "Y1",
bsize = 300,
firth = TRUE
)
sumstats.y2.firth <- run_regenie_step2_bt(
bedfile = "cc_imb_geno",
phenofile = "cc_imb_pheno.txt",
phenocol = "Y2",
bsize = 300,
firth = TRUE
)
sumstats.y3.firth <- run_regenie_step2_bt(
bedfile = "cc_imb_geno",
phenofile = "cc_imb_pheno.txt",
phenocol = "Y3",
bsize = 300,
firth = TRUE
) Looking at the test statistics and p-values:
qq(10^-sumstats.y1.firth$LOG10P)
| Version | Author | Date |
|---|---|---|
| 977dc7f | Joelle Mbatchou | 2024-06-14 |
plot.sumstats.hist(sumstats.y1.firth, title = "Y1 with Firth")
| Version | Author | Date |
|---|---|---|
| 977dc7f | Joelle Mbatchou | 2024-06-14 |
plot.sumstats.hist.by.group(sumstats.y1.firth, "Y1 with Firth")
| Version | Author | Date |
|---|---|---|
| 977dc7f | Joelle Mbatchou | 2024-06-14 |
qq(10^-sumstats.y2.firth$LOG10P)
| Version | Author | Date |
|---|---|---|
| 977dc7f | Joelle Mbatchou | 2024-06-14 |
plot.sumstats.hist(sumstats.y2.firth, title = "Y2 with Firth")
| Version | Author | Date |
|---|---|---|
| 977dc7f | Joelle Mbatchou | 2024-06-14 |
plot.sumstats.hist.by.group(sumstats.y2.firth, "Y2 with Firth")
| Version | Author | Date |
|---|---|---|
| 977dc7f | Joelle Mbatchou | 2024-06-14 |
qq(10^-sumstats.y3.firth$LOG10P)
| Version | Author | Date |
|---|---|---|
| 977dc7f | Joelle Mbatchou | 2024-06-14 |
plot.sumstats.hist(sumstats.y3.firth, title = "Y3 with Firth")
| Version | Author | Date |
|---|---|---|
| 977dc7f | Joelle Mbatchou | 2024-06-14 |
plot.sumstats.hist.by.group(sumstats.y3.firth, "Y3 with Firth")
| Version | Author | Date |
|---|---|---|
| 977dc7f | Joelle Mbatchou | 2024-06-14 |
sessionInfo()R version 4.3.0 (2023-04-21)
Platform: aarch64-apple-darwin20 (64-bit)
Running under: macOS 14.5
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: America/New_York
tzcode source: internal
attached base packages:
[1] parallel stats graphics grDevices utils datasets methods
[8] base
other attached packages:
[1] logistf_1.25.0 ggplot2_3.4.2 qqman_0.1.8 dplyr_1.1.2
[5] data.table_1.14.8
loaded via a namespace (and not attached):
[1] gtable_0.3.3 shape_1.4.6 xfun_0.39
[4] bslib_0.5.0 formula.tools_1.7.1 lattice_0.21-8
[7] vctrs_0.6.2 tools_4.3.0 generics_0.1.3
[10] tibble_3.2.1 fansi_1.0.4 highr_0.10
[13] pan_1.8 jomo_2.7-6 pkgconfig_2.0.3
[16] Matrix_1.5-4 lifecycle_1.0.3 farver_2.1.1
[19] compiler_4.3.0 stringr_1.5.0 git2r_0.32.0
[22] munsell_0.5.0 codetools_0.2-19 httpuv_1.6.11
[25] htmltools_0.5.5 sass_0.4.6 yaml_2.3.7
[28] glmnet_4.1-7 mice_3.16.0 crayon_1.5.2
[31] nloptr_2.0.3 later_1.3.1 pillar_1.9.0
[34] jquerylib_0.1.4 whisker_0.4.1 tidyr_1.3.0
[37] MASS_7.3-58.4 cachem_1.0.8 iterators_1.0.14
[40] rpart_4.1.19 boot_1.3-28.1 mitml_0.4-5
[43] foreach_1.5.2 nlme_3.1-162 tidyselect_1.2.0
[46] digest_0.6.31 stringi_1.7.12 purrr_1.0.1
[49] labeling_0.4.2 splines_4.3.0 operator.tools_1.6.3
[52] rprojroot_2.0.3 fastmap_1.1.1 grid_4.3.0
[55] colorspace_2.1-0 cli_3.6.1 magrittr_2.0.3
[58] survival_3.5-5 utf8_1.2.3 broom_1.0.5
[61] withr_2.5.0 scales_1.2.1 promises_1.2.0.1
[64] backports_1.4.1 calibrate_1.7.7 rmarkdown_2.22
[67] nnet_7.3-18 lme4_1.1-33 workflowr_1.7.0
[70] evaluate_0.21 knitr_1.43 mgcv_1.8-42
[73] rlang_1.1.1 Rcpp_1.0.10 glue_1.6.2
[76] minqa_1.2.5 rstudioapi_0.14 jsonlite_1.8.5
[79] R6_2.5.1 fs_1.6.2