Session 07 - Exercises Key
Last updated: 2023-07-24
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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(BEDMatrix)
library(SKAT)
library(ACAT)
library(ggplot2)Rare Variant Analysis
Introduction
We will look into a dataset collected on a quantitative phenotype which was first analyzed through GWAS and a signal was detected in chromosome 1. Let’s determine whether the signal is present when we focus on rare variation at the locus. In our analyses, we will define rare variants as those with \(MAF \leq 5\%\).
The file “rv_pheno.txt”” contains the phenotype measurements for a set of individuals and the file “rv_geno_chr1.bed” is a binary file in PLINK BED format with accompanying BIM and FAM files which contains the genotype data.
Exercises
Here are some things to try:
- Using PLINK, extract rare variants in a new PLINK BED file.
system("/data/SISG2023M15/exe/plink2 --bfile /data/SISG2023M15/data/rv_geno_chr1 --max-maf 0.05 --maj-ref force --make-bed --out chr1_region_rv")- Load the data in R:
- Read in the SNPs using R function
BEDMatrix()
G <- BEDMatrix("chr1_region_rv", simple_names = TRUE)Extracting number of samples and rownames from chr1_region_rv.fam...Extracting number of variants and colnames from chr1_region_rv.bim...- Load the phenotype data from
rv_pheno.txt
y <- fread("/data/SISG2023M15/data/rv_pheno.txt", header = TRUE)- Keep only samples who are present both in the genotype as well as phenotype data and who don’t have missing values for the phenotype
ids.keep <- y %>% drop_na(Pheno) %>% pull(IID)
length(ids.keep)[1] 9949G <- G[match(ids.keep, rownames(G)), ]
y <- y %>% drop_na(Pheno)
dim(G)[1] 9949 56- Examine the genotype data:
- Compute the minor allele frequency (MAF) for each SNP and plot histogram.
maf <- apply(G, 2, function(x) mean(x, na.rm=TRUE))/2
maf %>% hist(xlab = "Minor allele frequencies", main = "Distribution of MAF")
- Check for missing values.
sum(is.na(G))[1] 0- Run the single variant association tests in PLINK (only for the extracted variants).
system("/data/SISG2023M15/exe/plink2 --bfile chr1_region_rv --pheno /data/SISG2023M15/data/rv_pheno.txt --pheno-name Pheno --glm allow-no-covars --out sv_test")- What would be your significance threshold after applying Bonferroni correction for the multiple tests (assume the significance level is 0.05)? Is anything significant after this correction?
sv_pvals <- fread("sv_test.Pheno.glm.linear")
bonf.p <- 0.05 / length(sv_pvals$P)
bonf.p[1] 0.0008928571sv_pvals[P <= bonf.p, ] %>%
arrange(P) #CHROM POS ID REF ALT PROVISIONAL_REF? A1 OMITTED
1: 1 12639385 1:12639385:G:A A G Y G A
2: 1 12057950 1:12057950:C:T T C Y C T
3: 1 12734720 1:12734720:A:C C A Y A C
4: 1 12405413 1:12405413:T:C C T Y T C
5: 1 12360016 1:12360016:G:A A G Y G A
6: 1 12183493 1:12183493:G:A A G Y G A
A1_FREQ TEST OBS_CT BETA SE T_STAT P ERRCODE
1: 0.00567896 ADD 9949 0.391421 0.0955243 4.09761 4.20759e-05 .
2: 0.00789024 ADD 9949 -0.323574 0.0801934 -4.03492 5.50288e-05 .
3: 0.00849332 ADD 9949 -0.278236 0.0769709 -3.61482 3.02042e-04 .
4: 0.00487486 ADD 9949 0.359249 0.1019850 3.52258 4.29282e-04 .
5: 0.00643281 ADD 9949 -0.310260 0.0898433 -3.45335 5.55975e-04 .
6: 0.00773947 ADD 9949 0.274311 0.0814842 3.36643 7.64368e-04 .- Make a volcano plot (i.e. log10 p-values vs effect sizes).
sv_pvals %>%
ggplot(aes(x = sv_pvals$BETA, y = -log10(sv_pvals$P))) +
geom_point() +
labs(x = "Effect size", y = "-log10P")
- We will first compare three collapsing/burden approaches:
- CAST (Binary collapsing approach): for each individual, count where they have a rare allele at any of the sites
- MZ Test/GRANVIL (Count based collapsing): for each individual, count the total number of sites where a rare allele is present
- Weighted burden test: for each individual, take a weighted count of
the rare alleles across sites (for the weights, use
weights <- dbeta(MAF, 1, 25))
For each approach, first generate the burden scores vector then test
it for association with the phenotype using lm() R
function.
# CAST
# count number of rare alleles for each person and determine if it is > 0
burden.cast <- as.numeric( apply(G, 1, sum) > 0 )
lm(y$Pheno ~ burden.cast) %>% summary
Call:
lm(formula = y$Pheno ~ burden.cast)
Residuals:
Min 1Q Median 3Q Max
-3.9531 -0.6880 0.0012 0.6822 3.6581
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.002423 0.015317 0.158 0.874
burden.cast 0.017757 0.020422 0.870 0.385
Residual standard error: 1.01 on 9947 degrees of freedom
Multiple R-squared: 7.6e-05, Adjusted R-squared: -2.452e-05
F-statistic: 0.7561 on 1 and 9947 DF, p-value: 0.3846# MZ
# count number of sites with rare alleles for each person
burden.mz <- apply( G > 0 , 1, sum)
lm(y$Pheno ~ burden.mz) %>% summary
Call:
lm(formula = y$Pheno ~ burden.mz)
Residuals:
Min 1Q Median 3Q Max
-3.9521 -0.6894 -0.0013 0.6805 3.6591
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.001444 0.013700 0.105 0.916
burden.mz 0.013492 0.011346 1.189 0.234
Residual standard error: 1.01 on 9947 degrees of freedom
Multiple R-squared: 0.0001421, Adjusted R-squared: 4.162e-05
F-statistic: 1.414 on 1 and 9947 DF, p-value: 0.2344# Weighted burden
# weighted sum of genotype counts across sites
weights <- dbeta(maf, 1, 25)
burden.weighted <- G %*% weights
lm(y$Pheno ~ burden.weighted) %>% summary
Call:
lm(formula = y$Pheno ~ burden.weighted)
Residuals:
Min 1Q Median 3Q Max
-3.9519 -0.6896 -0.0014 0.6804 3.6593
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.0012244 0.0136778 0.090 0.929
burden.weighted 0.0006577 0.0005402 1.217 0.223
Residual standard error: 1.01 on 9947 degrees of freedom
Multiple R-squared: 0.000149, Adjusted R-squared: 4.846e-05
F-statistic: 1.482 on 1 and 9947 DF, p-value: 0.2235- Now use SKAT to test for an association.
# fit null model (no covariates)
skat.null <- SKAT_Null_Model(y$Pheno ~ 1 , out_type = "C")
# Run SKAT association test
SKAT(G, skat.null )$p.value[1] 8.745405e-11- Run the omnibus SKAT, but consider setting \(\rho\) (i.e.
r.corr) to 0 and then 1.
- Compare the results to using the CAST,MZ/GRANVIL and Weighted burden collapsing approaches in Question 5 as well as SKAT in Question 6. What tests do these \(\rho\) values correspond to?
# Run SKATO association test specifying rho
p.skato.r0 <- SKAT(G, skat.null, r.corr = 0)$p.value
p.skato.r1 <- SKAT(G, skat.null, r.corr = 1)$p.value
c(rho0 = p.skato.r0, rho1 = p.skato.r1) rho0 rho1
8.745405e-11 2.234603e-01 - Now the omnibus version of SKAT, but use the “optimal.adj” approach which searches across a range of rho values.
# Run SKATO association test using grid of rho values
SKAT(G, skat.null, method="optimal.adj")$p.value[1] 6.121784e-10- Run ACATV on the single variant p-values.
# `weights` vector is from Qesution 5
acat.weights <- weights^2 * maf * (1 - maf)
p.acatv <- ACAT(sv_pvals$P, weights = acat.weights)
p.acatv[1] 0.00112117- Run ACATO combining the SKAT and BURDEN p-values (from Question 7) with the ACATV p-value.
ACAT( c(p.skato.r0, p.skato.r1, p.acatv) )[1] 2.623621e-10
sessionInfo()R version 4.3.1 (2023-06-16)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 22.04.2 LTS
Matrix products: default
BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.10.0
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.10.0
locale:
[1] LC_CTYPE=C.UTF-8 LC_NUMERIC=C LC_TIME=C.UTF-8
[4] LC_COLLATE=C.UTF-8 LC_MONETARY=C.UTF-8 LC_MESSAGES=C.UTF-8
[7] LC_PAPER=C.UTF-8 LC_NAME=C LC_ADDRESS=C
[10] LC_TELEPHONE=C LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C
time zone: Etc/UTC
tzcode source: system (glibc)
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] ggplot2_3.4.2 ACAT_0.91 SKAT_2.2.5 RSpectra_0.16-1
[5] SPAtest_3.1.2 Matrix_1.5-4.1 BEDMatrix_2.0.3 tidyr_1.3.0
[9] dplyr_1.1.2 data.table_1.14.8
loaded via a namespace (and not attached):
[1] sass_0.4.6 utf8_1.2.3 generics_0.1.3 stringi_1.7.12
[5] lattice_0.21-8 digest_0.6.33 magrittr_2.0.3 evaluate_0.21
[9] grid_4.3.1 fastmap_1.1.1 rprojroot_2.0.3 workflowr_1.7.0
[13] jsonlite_1.8.7 whisker_0.4.1 promises_1.2.0.1 purrr_1.0.1
[17] fansi_1.0.4 scales_1.2.1 jquerylib_0.1.4 cli_3.6.1
[21] rlang_1.1.1 munsell_0.5.0 withr_2.5.0 cachem_1.0.8
[25] yaml_2.3.7 tools_4.3.1 colorspace_2.1-0 httpuv_1.6.11
[29] crochet_2.3.0 vctrs_0.6.3 R6_2.5.1 lifecycle_1.0.3
[33] git2r_0.32.0 stringr_1.5.0 fs_1.6.2 pkgconfig_2.0.3
[37] pillar_1.9.0 bslib_0.5.0 later_1.3.1 gtable_0.3.3
[41] glue_1.6.2 Rcpp_1.0.11 highr_0.10 xfun_0.39
[45] tibble_3.2.1 tidyselect_1.2.0 rstudioapi_0.15.0 knitr_1.43
[49] farver_2.1.1 htmltools_0.5.5 labeling_0.4.2 rmarkdown_2.23
[53] compiler_4.3.1