susieR summary statistics problem

Last updated: 2018-11-03

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We show the problem using simulated data N3finemapping in susieR package.

We observed in a summary statistics setting where we get summary stats from full data but later put a smaller n for sample size into the computation. Then the ``good’’ result (also from good initialization) did not give the largest elbo. Rather a bad result (from a random initialization) did.

library(susieR)
data(N3finemapping)
attach(N3finemapping)
b <- data$true_coef[,1]
plot(b, pch=16, ylab='effect size', main='true effect size')

The summary statistics come from per-variable univariate simple regression. The results are \(\hat{\beta}\) and \(SE(\hat{\beta})\) from which the p-values (from t-distribution) and \(z\)-scores can be derived.

p_values = 2 * pt(-abs(sumstats[1,,1] / sumstats[2,,1]), df = nrow(data$X) - 2)
z_scores = abs(qnorm(p_values/2)) * sign(sumstats[1,,1])
susie_plot(z_scores, y = "z", b=b)

For this example the correlation matrix can be computed directly from data provide,

R <- cor(data$X)

The susie_z function converts the z scores to t statistics based on the provided sample size, n.

fitted = susie_z(z = z_scores, R = R, n = nrow(data$X), L =10, 
                 scaled_prior_variance = 0.1, estimate_residual_variance = TRUE)
susie_plot(fitted, y='PIP', b=b)

par(mfrow=c(2,3))
Ls = c(3, 5, 10, 15, 20, 21)
for(l in Ls){
  fitted_n = susie_z(z = z_scores, R = R, n = 150, L=l,
                 scaled_prior_variance = 0.1, estimate_residual_variance = TRUE)
  susie_plot(fitted_n, y='PIP', b=b, main = paste0('L = ', l, ' elbo = ',
                                                   susie_get_objective(fitted_n)))
}

par(mfrow=c(1,1))

s.init = susie_init_coef(which(b!=0), b[which(b!=0)], ncol(data$X))
fitted_z <- susie_z(z = z_scores, 
                    R = R, n = 150, L = 10, 
                    scaled_prior_variance = 0.1, s_init=s.init,
                    estimate_residual_variance = TRUE)
susie_plot(fitted_z, y="PIP", b=b, main = paste0('L = 10 elbo = ',
                                                   susie_get_objective(fitted_z)))

sessionInfo()

R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS  10.14

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.5/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_0.6.1.0385

loaded via a namespace (and not attached):
 [1] workflowr_1.1.1   Rcpp_0.12.19      lattice_0.20-35  
 [4] digest_0.6.18     rprojroot_1.3-2   R.methodsS3_1.7.1
 [7] grid_3.5.1        backports_1.1.2   magrittr_1.5     
[10] git2r_0.23.0      evaluate_0.12     stringi_1.2.4    
[13] whisker_0.3-2     R.oo_1.22.0       R.utils_2.7.0    
[16] Matrix_1.2-14     rmarkdown_1.10    tools_3.5.1      
[19] stringr_1.3.1     yaml_2.2.0        compiler_3.5.1   
[22] htmltools_0.3.6   knitr_1.20        expm_0.999-3     

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