Last updated: 2021-03-06

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We observe the convergence problem for SuSiE in simulation. We illustrate 2 data here.

library(susieR)
dat = readRDS('data/susie_convergence_problem.rds')

Data 1

The region contains 1001 SNPs. There are two causals at 234, 287.

d1 = dat$d1
b = d1$true_coef
idx = which(b!=0)

par(mfrow=c(1,2))
plot(d1$z, pch = 16, xlab = 'SNPs', ylab = 'z')
points(idx, d1$z[idx], col='red', pch = 16)
log10p = -log10(pnorm(-abs(d1$z))*2)
plot(log10p, pch = 16, xlab = 'SNPs', ylab = '-log10 p value')
points(idx, log10p[idx], col='red', pch = 16)

Version Author Date
9c68be0 zouyuxin 2021-03-06

The SNP with strongest marginal association is 236. The correlation between causal SNPs and top SNP is

d1$ld[c(234, 236, 287), c(234, 236, 287)]
          V234        V236        V287
[1,] 1.0000000  0.56423775  0.53418375
[2,] 0.5642378  1.00000000 -0.03744934
[3,] 0.5341837 -0.03744934  1.00000000

Using L = 3, the susie model gives 3 CSs. (I used susie_suff_stat, which gives the same result as susie.)

f1 = susie_suff_stat(XtX = d1$XtX, Xty = d1$Xty, yty = d1$yty, n = d1$n, L=3, track_fit = T)
susie_plot(f1, y='PIP', b=b, add_legend = T, main=paste0('ELBO: ', round(susie_get_objective(f1), 4)))

Version Author Date
9c68be0 zouyuxin 2021-03-06 
summary(f1)

Variables in credible sets:

 variable variable_prob cs
      233     1.0000000  3
      236     1.0000000  1
      291     0.8150868  2
      287     0.1849131  2

Credible sets summary:

 cs cs_log10bf cs_avg_r2 cs_min_r2 variable
  1   30.80784 1.0000000 1.0000000      236
  3   31.30944 1.0000000 1.0000000      233
  2   61.20570 0.9989095 0.9978195  287,291

The SNPs in CS1 and CS3 are partially correlated with SNP 234. The correlation between them is

d1$ld[c(233, 234, 236), c(233, 234, 236)]
           V233      V234       V236
[1,]  1.0000000 0.5996649 -0.2407775
[2,]  0.5996649 1.0000000  0.5642378
[3,] -0.2407775 0.5642378  1.0000000
susie_plot_iteration(f1, L=3, 'assets/susie_convergence_problem/susie_convergence_problem_d1_f1', pos=c(233, 234, 236, 287, 291))
variable 1 2 3 4 5
SNP 233 234 236 287 291

Using L = 2, we find the correct CSs, and the ELBO is larger.

f2 = susie_suff_stat(XtX = d1$XtX, Xty = d1$Xty, yty = d1$yty, n = d1$n, L=2, track_fit = T)
susie_plot(f2, y='PIP', b=b, add_legend = T, main=paste0('ELBO: ', round(susie_get_objective(f2), 3)))

Version Author Date
9c68be0 zouyuxin 2021-03-06 
susie_plot_iteration(f2, L=2, 'assets/susie_convergence_problem/susie_convergence_problem_d1_f2', pos=c(233, 234, 236, 287, 291))

Data 2

The region contains 1001 SNPs. There are three causals at 252, 340, 375.

d2 = dat$d2
b = d2$true_coef
idx = which(b!=0)

par(mfrow=c(1,2))
plot(d2$z, pch = 16, xlab = 'SNPs', ylab = 'z')
points(idx, d2$z[idx], col='red', pch = 16)
log10p = -log10(pnorm(-abs(d2$z))*2)
plot(log10p, pch = 16, xlab = 'SNPs', ylab = '-log10 p value')
points(idx, log10p[idx], col='red', pch = 16)

Version Author Date
9c68be0 zouyuxin 2021-03-06

The SNP with strongest marginal association is 222. The correlation between causal SNPs and top SNP is

d2$ld[c(222, idx), c(222, idx)]
          V222       V252        V340        V375
[1,] 1.0000000  0.5508992  0.55055773  0.79251604
[2,] 0.5508992  1.0000000  0.99949772 -0.01428270
[3,] 0.5505577  0.9994977  1.00000000 -0.01412418
[4,] 0.7925160 -0.0142827 -0.01412418  1.00000000

Using L = 10, the susie model gives 1 CS.

f3 = susie_suff_stat(XtX = d2$XtX, Xty = d2$Xty, yty = d2$yty, n = d2$n, L=10, track_fit = T)
susie_plot(f3, y='PIP', b=b, add_legend = T, main=paste0('ELBO: ', round(susie_get_objective(f3), 4)))

Version Author Date
9c68be0 zouyuxin 2021-03-06

It identifies the top SNP.

susie_plot_iteration(f3, L=10, 'assets/susie_convergence_problem/susie_convergence_problem_d2_f3', pos=c(222, idx))

Using L = 3, it converges to the same solution as L = 10.

f4 = susie_suff_stat(XtX = d2$XtX, Xty = d2$Xty, yty = d2$yty, n = d2$n, L=3, track_fit = T,
                     estimate_residual_variance = T, estimate_prior_variance = T)
susie_plot(f4, y='PIP', b=b, add_legend = T, main=paste0('ELBO: ', round(susie_get_objective(f4), 4)))

Version Author Date
9c68be0 zouyuxin 2021-03-06

We initialize at the truth,

beta_val = b[idx]
sinit = susieR::susie_init_coef(idx, beta_val, length(b))
finittrue = susie_suff_stat(XtX = d2$XtX, Xty = d2$Xty, yty = d2$yty, n = d2$n, track_fit = T, s_init = sinit,
                            estimate_residual_variance = T,estimate_prior_variance = TRUE, max_iter = 200)
susie_plot(finittrue, y='PIP', b=b, add_legend = T, main=paste0('ELBO: ', round(susie_get_objective(finittrue), 4)))

Version Author Date
9c68be0 zouyuxin 2021-03-06 

sessionInfo()
R version 4.0.3 (2020-10-10)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Big Sur 10.16

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.0/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] susieR_0.10.0   workflowr_1.6.2

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.6       plyr_1.8.6       pillar_1.4.7     compiler_4.0.3  
 [5] later_1.1.0.1    git2r_0.27.1     tools_4.0.3      digest_0.6.27   
 [9] evaluate_0.14    lifecycle_1.0.0  tibble_3.0.6     gtable_0.3.0    
[13] lattice_0.20-41  pkgconfig_2.0.3  rlang_0.4.10     Matrix_1.2-18   
[17] yaml_2.2.1       xfun_0.19        stringr_1.4.0    dplyr_1.0.2     
[21] knitr_1.30       generics_0.1.0   fs_1.5.0         vctrs_0.3.6     
[25] tidyselect_1.1.0 rprojroot_2.0.2  grid_4.0.3       reshape_0.8.8   
[29] glue_1.4.2       R6_2.5.0         rmarkdown_2.5    purrr_0.3.4     
[33] ggplot2_3.3.3    magrittr_2.0.1   whisker_0.4      scales_1.1.1    
[37] promises_1.1.1   ellipsis_0.3.1   htmltools_0.5.0  colorspace_2.0-0
[41] httpuv_1.5.4     stringi_1.5.3    munsell_0.5.0    crayon_1.4.1