Last updated: 2023-06-12

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Introduction

The goal of this analysis is to benchmark the newly developed mr.mash.rss (aka mr.mash with summary statistics) against already existing methods in the task of predicting phenotypes from genotypes using only summary data. To do so, we used real genotypes from the array data of the UK Biobank. We randomly sampled 105,000 nominally unrelated (\(r_A\) < 0.025 between any pair) individuals of European ancestry (i.e., Caucasian and white British fields). After retaining variants with minor allele frequency (MAF) > 0.01, minor allele count (MAC) > 5 genotype missing rate < 0.1 and Hardy-Weinberg Equilibrium (HWE) test p-value > \(1 *10^{-10}\), our data consisted of 595,071 genetic variants (i.e., our predictors). Missing genotypes were imputed with the mean genotype for the respective genetic variant.

The linkage disequilibrium (LD) matrices were computed using 146,288 nominally unrelated (\(r_A\) < 0.025 between any pair) individuals of European ancestry (i.e., Caucasian and white British fields), that did not overlap with the 105,000 individuals used for the rest of the analyses.

For each simulation replicate, we randomly sampled 5,000 (out of the 105,000) individuals to be the test set. The test set was only used to evaluate prediction accuracy. All the other steps were carried out on the training set of 100,000 individuals.

We simulated 5 traits (i.e., our responses) by randomly sampling 5,000 variants (out of the total of 595,071) to be causal, with different effect sharing structures across traits (see below). The genetic effects explain 50% of the total per-trait variance. The residuals are uncorrelated across traits.

Summary statistics (i.e., effect size and its standard error) were obtained by univariate simple linear regression of each trait on each variant, one at a time. Traits and variants were not standardized.

Three different methods were fitted:

  • LDpred2 per-chromosome with the auto option, 500 iterations (after 500 burn-in iterations), \(h^2\) initialized as 0.5/22 and \(p\) initialized using the same grid as in the original paper.
  • LDpred2 genome-wide with the auto option, 500 iterations (after 500 burn-in iterations), \(h^2\) initialized as 0.5/22 (WRONG) and \(p\) initialized using the same grid as in the original paper.
  • mr.mash.rss per-chromosome, with only data-driven covariance matrices computed as described in the mr.mash paper, updating the (full rank) residual covariance and the mixture weights, without standardizing the variables.

Equal effects scenario

###Load libraries
library(ggplot2)
library(cowplot)

repz <- 1:20
prefix <- "output/prediction_accuracy/ukb_caucasian_white_british_unrel_100000"
scenarioz <- "equal_effects_indep_resid"
methodz <- c("mr_mash_rss", "ldpred2_auto", "ldpred2_auto_gwide")
metric <- "r2"
traitz <- 1:5

i <- 0

n_col <- 6
n_row <- length(repz) * length(scenarioz) * length(methodz) * length(traitz)
res <- as.data.frame(matrix(NA, ncol=n_col, nrow=n_row))
colnames(res) <- c("rep", "scenario", "method", "trait", "metric", "score")



for(sce in scenarioz){
  for(met in methodz){
    for(repp in repz){
      dat <- readRDS(paste0(prefix, "_", sce, "_", met, "_pred_acc_", repp, ".rds"))
      
      for(trait in traitz){
        i <- i + 1
        
        res[i, 1] <- repp
        res[i, 2] <- sce
        res[i, 3] <- met
        res[i, 4] <- trait
        res[i, 5] <- metric
        res[i, 6] <- dat$r2[trait]
      }
    }
  }
}

res <- transform(res, scenario=as.factor(scenario),
                      method=as.factor(method),
                      trait=as.factor(trait))

p_methods_shared <- ggplot(res, aes(x = trait, y = score, fill = method)) +
  geom_boxplot(color = "black", outlier.size = 1, width = 0.85) +
  stat_summary(fun=mean, geom="point", shape=23,
               position = position_dodge2(width = 0.87,   
                                          preserve = "single")) +
  ylim(0.3, 0.51) +
  scale_fill_manual(values = c("pink", "red", "green"))+ #, labels = c("g-lasso", "smt-lasso", "e-net")) +
  labs(x = "Trait", y = expression(italic(R)^2), title = "Equal effects", fill="Method") +
  geom_hline(yintercept=0.5, linetype="dotted", linewidth=1, color = "black") +
  theme_cowplot(font_size = 16) +
  theme(plot.title = element_text(hjust = 0.5, size=14))

print(p_methods_shared)

Version Author Date
886b637 fmorgante 2023-06-12 

sessionInfo()
R version 4.1.2 (2021-11-01)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Rocky Linux 8.5 (Green Obsidian)

Matrix products: default
BLAS/LAPACK: /opt/ohpc/pub/libs/gnu9/openblas/0.3.7/lib/libopenblasp-r0.3.7.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] cowplot_1.1.1 ggplot2_3.4.1

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.10      highr_0.10       pillar_1.9.0     compiler_4.1.2  
 [5] bslib_0.4.2      later_1.3.0      jquerylib_0.1.4  git2r_0.31.0    
 [9] workflowr_1.7.0  tools_4.1.2      digest_0.6.31    gtable_0.3.3    
[13] jsonlite_1.8.4   evaluate_0.20    lifecycle_1.0.3  tibble_3.2.1    
[17] pkgconfig_2.0.3  rlang_1.1.0      cli_3.6.1        rstudioapi_0.14 
[21] yaml_2.3.7       xfun_0.37        fastmap_1.1.1    withr_2.5.0     
[25] dplyr_1.1.1      stringr_1.5.0    knitr_1.42       generics_0.1.3  
[29] fs_1.6.1         vctrs_0.6.1      sass_0.4.5       tidyselect_1.2.0
[33] rprojroot_2.0.3  grid_4.1.2       glue_1.6.2       R6_2.5.1        
[37] fansi_1.0.4      rmarkdown_2.20   farver_2.1.1     magrittr_2.0.3  
[41] whisker_0.4.1    scales_1.2.1     promises_1.2.0.1 htmltools_0.5.4 
[45] colorspace_2.1-0 httpuv_1.6.9     labeling_0.4.2   utf8_1.2.3      
[49] stringi_1.7.12   munsell_0.5.0    cachem_1.0.7