GWAS for fitness in Drosophila

Inspecting the effect of adaptive shrinkage on the SNP effect size estimates

Relationship between raw $p$ -values and the local false sign rate

Conclusion

Session information

Last updated: 2018-10-04

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library(dplyr)
library(readr)
library(ggplot2)
library(gridExtra)
library(tidyr)

db <- DBI::dbConnect(RSQLite::SQLite(), "data/derived/annotations.sqlite3")

# Results for all 1,613,615 SNPs, even those that are in 100% LD with others (these are grouped up by the SNP_clump column)
all_snps <- tbl(db, "univariate_lmm_results")

# All SNPs and SNP groups that are in <100% LD with one another (n = 1,201,969)
SNP_clumps <- all_snps %>% select(-SNP) %>% distinct() %>% collect(n=Inf)

Inspecting the effect of adaptive shrinkage on the SNP effect size estimates

The plots reveal that the R package mashr, which implemented multivariate adaptive shrinkage, was effective at shrinking the effect size estimates towards zero. The amount of shrinkage applied was stronger when applying mashr using data-driven covariance matrices, as opposed to ‘canonical’ covariance matrices that were selected a priori by us.

hex_plot <- function(x, y, xlab, ylab){
    ggplot(SNP_clumps, aes_string(x, y)) + 
    geom_abline(linetype = 2) + 
    geom_vline(xintercept = 0, linetype = 3) +
    geom_hline(yintercept = 0, linetype = 3) +
    stat_binhex(bins = 200, colour = "#FFFFFF00") + 
    scale_fill_distiller(palette = "Purples") + 
    coord_cartesian(xlim = c(-1,1), ylim = c(-1,1)) + 
    theme_minimal() + xlab(xlab) + ylab(ylab) +
    theme(legend.position = "none")
}
grid.arrange(
  hex_plot("beta_female_early_raw", "beta_female_early_mashr_canonical", "Raw estimate of SNP effect size from GEMMA", "Corrected estimate from mashr (canonical)"),
  hex_plot("beta_female_early_raw", "beta_female_early_mashr_ED", "Raw estimate of SNP effect size from GEMMA", "Corrected estimate from mashr (data-driven)"),
  hex_plot("beta_female_early_mashr_canonical", "beta_female_early_mashr_ED", "Corrected estimate from mashr (canonical)", "Corrected estimate from mashr (data-driven)"), 
  ncol = 3)

Relationship between raw $p$ -values and the local false sign rate

The local false sign rate (defined as the probability that a SNP’s true effect is non-zero and has the same sign as the effect size estimate) was correlated with the raw p-value (as expected). Note that the false sign rate is sometime ‘more significant’ than the p-value; one likely reason for this is that the local false sign rate uses the information provided by the correlations among SNP effects on our four fitness traits, while the $p$ -value ignores this information. Another reason is that the local false sign rate was (noisily) estimated using a Markov chain, in a Bayesian model that incorporates priors, while the p-value is estimated by maximum likelihood and has comes from a frequentist model lacking priors.

As for the effect sizes, the local false sign rates provided by the data-driven approach are almost always less significant than those provided by the canonical approach.

hex_plot2 <- function(p, xlab, ylab){
    p + 
    geom_abline(linetype = 2) + 
    stat_binhex(bins = 200, colour = "#FFFFFF00") + 
    scale_fill_distiller(palette = "Blues") + 
    scale_x_continuous(expand = c(0,0)) + scale_y_continuous(expand = c(0,0)) +
    coord_cartesian(xlim = c(0, 8), ylim = c(0, 8)) + 
    theme_minimal() + xlab(xlab) + ylab(ylab) +
    theme(legend.position = "none")
}

grid.arrange(
  SNP_clumps %>% ggplot(aes(-log10(pvalue_female_early_raw), -log10(LFSR_female_early_mashr_canonical))) %>% hex_plot2("-log10 raw p-value from GEMMA", "-log10 local false sign rate (canonical)"),
  SNP_clumps %>% ggplot(aes(-log10(pvalue_female_early_raw), -log10(LFSR_female_early_mashr_ED))) %>% hex_plot2("-log10 raw p-value from GEMMA", "-log10 local false sign rate (data-driven)"),
  SNP_clumps %>% ggplot(aes(-log10(LFSR_female_early_mashr_canonical), -log10(LFSR_female_early_mashr_ED))) %>% hex_plot2("-log10 local false sign rate (canonical)", "-log10 local false sign rate (data-driven)"),
  ncol = 3)

Conclusion

Based on these plots, we elected to focus on the results generated by the data-driven mashr analysis, as opposed to the canonical mashr analysis. This is more conservative, because the effect sizes and local false sign rates are more moderate in the data-driven analysis. Also, using the data-driven approach yields estimates that are independent of our prior expectations about the possible covariance structures that might exist in the data, and is therefore robust to the possibility that our expectations are wrong.

Session information

sessionInfo()

R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.6

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_AU.UTF-8/en_AU.UTF-8/en_AU.UTF-8/C/en_AU.UTF-8/en_AU.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] hexbin_1.27.2 tidyr_0.8.1   gridExtra_2.3 ggplot2_3.0.0 readr_1.1.1  
[6] dplyr_0.7.6  

loaded via a namespace (and not attached):
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 [4] compiler_3.5.1     pillar_1.3.0       git2r_0.23.0      
 [7] plyr_1.8.4         workflowr_1.1.1    bindr_0.1.1       
[10] R.methodsS3_1.7.1  R.utils_2.7.0      tools_3.5.1       
[13] bit_1.1-14         digest_0.6.15      lattice_0.20-35   
[16] memoise_1.1.0      RSQLite_2.1.1      evaluate_0.11     
[19] tibble_1.4.2       gtable_0.2.0       pkgconfig_2.0.1   
[22] rlang_0.2.2        DBI_1.0.0          yaml_2.2.0        
[25] bindrcpp_0.2.2     withr_2.1.2        stringr_1.3.1     
[28] knitr_1.20         hms_0.4.2          bit64_0.9-7       
[31] rprojroot_1.3-2    grid_3.5.1         tidyselect_0.2.4  
[34] glue_1.3.0         R6_2.2.2           rmarkdown_1.10    
[37] blob_1.1.1         purrr_0.2.5        magrittr_1.5      
[40] whisker_0.3-2      backports_1.1.2    scales_1.0.0      
[43] htmltools_0.3.6    assertthat_0.2.0   colorspace_1.3-2  
[46] labeling_0.3       stringi_1.2.4      lazyeval_0.2.1    
[49] munsell_0.5.0      crayon_1.3.4       R.oo_1.22.0

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GWAS for fitness in Drosophila

Inspecting the effect of adaptive shrinkage on the SNP effect size estimates

Relationship between raw pp-values and the local false sign rate

Conclusion

Session information

Relationship between raw $p$ -values and the local false sign rate