Last updated: 2024-04-30

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Here, we provide an example of using XMAP for correcting confounding bias in cross-population GWAS data. We simulated GWAS data with confounding effects. For demonstration, we assume that we have estimated the inflation constants \(c_1=1.636171\) and \(c_2=1.791455\), and the polygenic parameters \(\Omega\) using bi-variate LDSC (See next section for details in estimating these parameters in real GWAS data).

We first fit XMAP without correcting confounding bias by setting \(c_1=c_2=1\):

library(susieR)
library(XMAP)
data("example_data_confound")
c1 <- 1.636171
c2 <- 1.791455
fit_xmapI <- XMAP(simplify2array(list(R1,R2)), cbind(zs1,zs2),
                  n=c(15000,20000), K = 5,
                  Omega = OmegaHat,
                  Sig_E = c(1,1),
                  tol = 1e-6,
                  maxIter = 200, estimate_residual_variance = F, estimate_prior_variance = T,
                  estimate_background_variance = F)
# Get credible set based on R1
cs1 <- get_CS(fit_xmapI, Xcorr = R1, coverage = 0.95, min_abs_corr = 0.1)
# Get credible set based on R2
cs2 <- get_CS(fit_xmapI, Xcorr = R2, coverage = 0.95, min_abs_corr = 0.1)
# Get joint credible set
cs <- cs1$cs[intersect(names(cs1$cs), names(cs2$cs))]
pip <- get_pip(fit_xmapI$gamma)
plot_CS(pip, cs, Beta_true[,1], main = "XMAP (C=I)")

Version Author Date
64b7578 mxcai 2024-04-29

In the above figure, the red dot is the only causal SNP, level-95% credible sets are colored circles. Without correcting for confounding bias, some null SNPs on the left region of the locus can have high PIP. These are false positives.

Now, we use the estimated LDSC intercepts to correct the confounding bias in XMAP:

c1 <- 1.636171
c2 <- 1.791455
fit_xmap <- XMAP(simplify2array(list(R1,R2)), cbind(zs1,zs2),
                 n=c(15000,20000), K = 5,
                 Omega = OmegaHat,
                 Sig_E = c(c1,c2),
                 tol = 1e-6,
                 maxIter = 200, estimate_residual_variance = F, estimate_prior_variance = T,
                 estimate_background_variance = F)
# Get credible set based on R1
cs1 <- get_CS(fit_xmap, Xcorr = R1, coverage = 0.95, min_abs_corr = 0.1)
# Get credible set based on R2
cs2 <- get_CS(fit_xmap, Xcorr = R2, coverage = 0.95, min_abs_corr = 0.1)
# Get joint credible set
cs <- cs1$cs[intersect(names(cs1$cs), names(cs2$cs))]
pip <- get_pip(fit_xmap$gamma)
plot_CS(pip, cs, Beta_true[,1], main = "XMAP")

Version Author Date
64b7578 mxcai 2024-04-29

As we can observe, XMAP effectively reduces the PIP of spurious signals and correctly excludes them from the level-95% credible sets.


sessionInfo()
R version 4.1.2 (2021-11-01)
Platform: aarch64-apple-darwin20 (64-bit)
Running under: macOS 13.6.3

Matrix products: default
BLAS:   /opt/homebrew/Cellar/openblas/0.3.19/lib/libopenblasp-r0.3.19.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.1-arm64/Resources/lib/libRlapack.dylib

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

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

other attached packages:
[1] XMAP_1.0       susieR_0.12.35

loaded via a namespace (and not attached):
 [1] tidyselect_1.2.0   xfun_0.32          bslib_0.4.0        lattice_0.20-45   
 [5] colorspace_2.0-2   vctrs_0.6.3        generics_0.1.1     htmltools_0.5.4   
 [9] yaml_2.3.5         utf8_1.2.2         rlang_1.1.1        mixsqp_0.3-43     
[13] jquerylib_0.1.4    later_1.3.0        pillar_1.9.0       glue_1.6.2        
[17] RcppZiggurat_0.1.6 matrixStats_0.61.0 lifecycle_1.0.3    plyr_1.8.6        
[21] stringr_1.4.1      munsell_0.5.0      gtable_0.3.0       workflowr_1.7.0   
[25] evaluate_0.16      knitr_1.40         fastmap_1.1.0      httpuv_1.6.5      
[29] parallel_4.1.2     irlba_2.3.5        fansi_0.5.0        highr_0.9         
[33] Rfast_2.0.6        Rcpp_1.0.10        promises_1.2.0.1   scales_1.1.1      
[37] cachem_1.0.6       jsonlite_1.8.0     fs_1.5.2           ggplot2_3.3.5     
[41] digest_0.6.29      stringi_1.7.8      dplyr_1.1.2        rprojroot_2.0.2   
[45] grid_4.1.2         cli_3.6.1          tools_4.1.2        magrittr_2.0.3    
[49] sass_0.4.2         tibble_3.2.1       crayon_1.5.1       whisker_0.4       
[53] pkgconfig_2.0.3    Matrix_1.5-4.1     rmarkdown_2.16     reshape_0.8.8     
[57] rstudioapi_0.13    R6_2.5.1           git2r_0.31.0       compiler_4.1.2