Refine SuSiE model

In this vignette, we demonstrate a procedure that helps SuSiE get out of local optimum.

We simulate phenotype using UK Biobank genotypes from 50,000 individuals. There are 1001 SNPs. It is simulated to have exactly 2 non-zero effects at 234, 287.

library(susieR)
library(curl)
data_file <- tempfile(fileext = ".RData")
data_url <- paste0("https://raw.githubusercontent.com/stephenslab/susieR/",
                   "master/inst/datafiles/FinemappingConvergence1k.RData")
curl_download(data_url,data_file)
load(data_file)
b <- FinemappingConvergence$true_coef
susie_plot(FinemappingConvergence$z, y = "z", b=b)

The strongest marginal association is a non-effect SNP.

Since the sample size is large, we use sufficient statistics (\(X^\intercal X, X^\intercal y, y^\intercal y\) and sample size \(n\)) to fit susie model. It identifies 2 Credible Sets, one of them is false positive. This is because susieR get stuck around a local minimum.

fitted <- with(FinemappingConvergence,
               susie_suff_stat(XtX = XtX, Xty = Xty, yty = yty, n = n))
susie_plot(fitted, y="PIP", b=b, main=paste0("ELBO = ", round(susie_get_objective(fitted),2)))

Our refine procedure to get out of local optimum is

fit a susie model, \(s\) (suppose it has \(K\) CSs).
for CS in \(s\), set SNPs in CS to have prior weight 0, fit susie model –> we have K susie models: \(t_1, \cdots, t_K\).
for each \(k = 1, \cdots, K\), fit susie with initialization at \(t_k\) (\(\alpha, \mu, \mu^2\)) –> \(s_k\)
if \(\max_k \text{elbo}(s_k) > \text{elbo}(s)\), set \(s = s_{kmax}\) where \(kmax = \arg_k \max \text{elbo}(s_k)\) and go to step 2; if no, break.

We fit susie model with above procedure by setting refine = TRUE.

fitted_refine <- with(FinemappingConvergence,
                      susie_suff_stat(XtX = XtX, Xty = Xty, yty = yty,
                                      n = n, refine=TRUE))
# WARNING: XtX is not symmetric; forcing XtX to be symmetric by replacing XtX with (XtX + t(XtX))/2
# WARNING: XtX is not symmetric; forcing XtX to be symmetric by replacing XtX with (XtX + t(XtX))/2
# WARNING: XtX is not symmetric; forcing XtX to be symmetric by replacing XtX with (XtX + t(XtX))/2
# WARNING: XtX is not symmetric; forcing XtX to be symmetric by replacing XtX with (XtX + t(XtX))/2
# WARNING: XtX is not symmetric; forcing XtX to be symmetric by replacing XtX with (XtX + t(XtX))/2
# WARNING: XtX is not symmetric; forcing XtX to be symmetric by replacing XtX with (XtX + t(XtX))/2
# WARNING: XtX is not symmetric; forcing XtX to be symmetric by replacing XtX with (XtX + t(XtX))/2
# WARNING: XtX is not symmetric; forcing XtX to be symmetric by replacing XtX with (XtX + t(XtX))/2
# WARNING: XtX is not symmetric; forcing XtX to be symmetric by replacing XtX with (XtX + t(XtX))/2
# WARNING: XtX is not symmetric; forcing XtX to be symmetric by replacing XtX with (XtX + t(XtX))/2
susie_plot(fitted_refine, y="PIP", b=b, main=paste0("ELBO = ", round(susie_get_objective(fitted_refine),2)))

With the refine procedure, it identifies 2 CSs with the true signals, and the achieved evidence lower bound (ELBO) is higher.

Session information

Here are some details about the computing environment, including the versions of R, and the R packages, used to generate these results.

sessionInfo()
# R version 3.6.2 (2019-12-12)
# Platform: x86_64-apple-darwin15.6.0 (64-bit)
# Running under: macOS Catalina 10.15.7
# 
# Matrix products: default
# BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
# LAPACK: /Library/Frameworks/R.framework/Versions/3.6/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] curl_4.3       susieR_0.12.10
# 
# loaded via a namespace (and not attached):
#  [1] tidyselect_1.1.1   xfun_0.29          bslib_0.3.1        purrr_0.3.4       
#  [5] lattice_0.20-38    colorspace_1.4-1   vctrs_0.3.8        generics_0.0.2    
#  [9] htmltools_0.5.2    yaml_2.2.0         utf8_1.1.4         rlang_0.4.11      
# [13] mixsqp_0.3-46      pkgdown_2.0.2      jquerylib_0.1.4    pillar_1.6.2      
# [17] glue_1.4.2         DBI_1.1.0          RcppZiggurat_0.1.5 matrixStats_0.61.0
# [21] lifecycle_1.0.0    plyr_1.8.5         stringr_1.4.0      munsell_0.5.0     
# [25] gtable_0.3.0       ragg_0.3.1         memoise_1.1.0      evaluate_0.14     
# [29] knitr_1.37         fastmap_1.1.0      parallel_3.6.2     irlba_2.3.3       
# [33] fansi_0.4.0        Rfast_2.0.3        highr_0.8          Rcpp_1.0.7        
# [37] scales_1.1.0       backports_1.1.5    desc_1.2.0         jsonlite_1.7.2    
# [41] systemfonts_1.0.2  fs_1.5.2           ggplot2_3.3.5      digest_0.6.23     
# [45] stringi_1.4.3      dplyr_1.0.7        grid_3.6.2         rprojroot_1.3-2   
# [49] tools_3.6.2        magrittr_2.0.1     sass_0.4.0         tibble_3.1.3      
# [53] crayon_1.4.1       pkgconfig_2.0.3    ellipsis_0.3.2     Matrix_1.2-18     
# [57] assertthat_0.2.1   rmarkdown_2.11     reshape_0.8.8      R6_2.4.1          
# [61] compiler_3.6.2

Yuxin Zou

2022-06-13

Session information