susieR summary statistics problem 2

Last updated: 2018-11-03

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

We fit the susie model using sample size n = 150. The t statistics derived from z scores with sample size 150 are similar to the true t statistics (n = 574), but the susie results are different.

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.

t_stat = sumstats[1,,1] / sumstats[2,,1]
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)

fitted_t = susie_bhat(bhat = t_stat, shat = 1, R = R, n = 150, L=10,
                 scaled_prior_variance = 0.1, estimate_residual_variance = TRUE)
susie_plot(fitted_t, y='PIP', b=b, main = paste0('L = 10 elbo = ',
                                                   susie_get_objective(fitted_t)))

fitted_z = susie_z(z = z_scores, R = R, n = 150, L=10,
                 scaled_prior_variance = 0.1, estimate_residual_variance = TRUE)
susie_plot(fitted_z, y='PIP', b=b, main = paste0('L = 10 elbo = ',
                                                   susie_get_objective(fitted_z)))

n = 150
new_t = qt(pnorm(-abs(z_scores)), df = n-2) # all negative
new_t[which(z_scores > 0)] = -1 * new_t[which(z_scores > 0)]

mean(abs(new_t - t_stat))

[1] 0.01987562

boxplot(cbind(z_scores, t_stat, new_t))

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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