Last updated: 2020-10-23

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Knit directory: mr_mash_test/

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Unstaged changes:
    Modified:   dsc/midway2.yml

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These are the previous versions of the repository in which changes were made to the R Markdown (analysis/results_mvreg_all_genes_prior_GTExrealX_indepV_B_1causalrespr10.Rmd) and HTML (docs/results_mvreg_all_genes_prior_GTExrealX_indepV_B_1causalrespr10.html) files. If you’ve configured a remote Git repository (see ?wflow_git_remote), click on the hyperlinks in the table below to view the files as they were in that past version.

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Rmd fbf086e fmorgante 2020-10-22 Add new scenarios + fix bug
html 82e4357 fmorgante 2020-10-22 Build site.
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Rmd 34c5598 fmorgante 2020-10-22 Add low PVE scenario
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Rmd 547efa4 fmorgante 2020-10-22 Fix a few things
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Rmd 9fe619a fmorgante 2020-10-22 Add new results

###Set options
options(stringsAsFactors=FALSE)

###Load libraries
library(dscrutils)
library(ggplot2)
library(cowplot)
library(scales)

###Function to convert dscquery output from list to data.frame suitable for plotting
convert_dsc_to_dataframe_gtex <- function(dsc){
  ###Data.frame to store the results after convertion
  dsc_df <- data.frame()
  
  ###Get length of list elements 
  n_elem <- length(dsc$DSC)
  
  ###Loop through the dsc list
  for(i in 1:n_elem){
    ##Prepare vectors making up the final data frame
    r_scalar <- dsc$simulate.r[i]
    p_causal <- rep(dsc$simulate.p_causal[i], times=r_scalar)
    r <- rep(dsc$simulate.r[i], times=r_scalar)
    response <- 1:r_scalar
    pve <- rep(dsc$simulate.pve[i], times=r_scalar)
    simulate <- rep(dsc$simulate[i], times=r_scalar)
    fit <- rep(dsc$fit[i], times=r_scalar)
    score <- rep(dsc$score[i], times=r_scalar)
    score.err <- dsc$score.err[[i]]
    timing <- rep(dsc$fit.time[i], times=r_scalar)
    
    ##Build the data frame
    df <- data.frame(p_num_caus=p_causal, r=r, response=response, pve=pve,  
                     scenario=simulate, method=fit, score_metric=score, score_value=score.err, time=timing)
    dsc_df <- rbind(dsc_df, df)
  }
  
  ###Get number of genes
  n_methods <- length(unique(dsc_out$fit))
  n_metrics <- length(unique(dsc_out$score))
  n_genes <- n_elem/n_methods/n_metrics
  
  ###Compute replicates
  reptot <- rep(rep(1:n_genes, each=dsc$simulate.r[1]), n_methods*n_metrics)
   
  dsc_df <- data.frame(rep=reptot, dsc_df)
  
  return(dsc_df)
}

###Function to compute rmse (relative to mr_mash_em_can)
compute_rrmse <- function(dsc_plot, log10_scale=FALSE){
  dsc_plot <- transform(dsc_plot, experiment=paste(rep, response, scenario, sep="-"))
  t <- 0
  for (i in unique(dsc_plot$experiment)) {
    t <- t+1
    rmse_data  <- dsc_plot[which(dsc_plot$experiment == i & dsc_plot$score_metric=="scaled_rmse"), ]
    mse_mr_mash_consec_em <- rmse_data[which(rmse_data$method=="mr_mash_em_can"), "score_value"]
    if(!log10_scale)
      rmse_data$score_value <- rmse_data$score_value/mse_mr_mash_consec_em
    else
      rmse_data$score_value <- log10(rmse_data$score_value/mse_mr_mash_consec_em)
    rmse_data$score_metric <- "scaled_rrmse"
    if(t>1){
      rmse_data_tot <- rbind(rmse_data_tot, rmse_data)
    } else if(t==1){
      rmse_data_tot <- rmse_data
    }
  }
  
  rmse_data_tot$experiment <- NULL
  
  return(rmse_data_tot)
}

###Set some quantities used in the following plots
colors <- c("cyan", "skyblue", "dodgerblue", "mediumblue", "limegreen", "green", "gold", "orange", "red", "firebrick", "darkmagenta", "mediumpurple")

PVE=0.2

###Load the dsc results
dsc_out <- dscquery("output/mvreg_all_genes_prior_GTExrealX_indepV_B_1causalrespr10", 
                    c("simulate.p_causal", "simulate.r", "simulate.r_causal", "simulate.pve", "simulate.B_cor", "simulate.w", 
                      "simulate.B_scale", "simulate.V_cor", "simulate", "fit", "score", "score.err", "fit.time"), 
                    groups="fit: mr_mash_em_can, mr_mash_em_data, mr_mash_em_dataAndcan, mr_mash_em_dataAndcan_dropcomp, mlasso, mtlasso, enet",
                    verbose=FALSE)

###Obtain simulation parameters
prop_testset <- 0.2
p_causal <- unique(dsc_out$simulate.p_causal)
r <- unique(dsc_out$simulate.r)
r_causal <- eval(parse(text=unique(dsc_out$simulate.r_causal)))
pve <- unique(dsc_out$simulate.pve)
w <- eval(parse(text=unique(dsc_out$simulate.w)))
B_cor <- eval(parse(text=unique(dsc_out$simulate.B_cor)))
B_scale <- eval(parse(text=unique(dsc_out$simulate.B_scale)))
V_cor <- unique(dsc_out$simulate.V_cor)

###Remove list elements that are not useful anymore
dsc_out$simulate.r_causal <- NULL
dsc_out$simulate.w <- NULL
dsc_out$simulate.B_cor <- NULL
dsc_out$simulate.B_scale <- NULL
dsc_out$simulate.V_cor <- NULL

Simulation set up

The results below are based on simulations with GTEx v8 cis-genotypes for 838 samples, with 5 causal variants, 10 responses with a per-response proportion of variance explained (PVE) of 0.2. Causal effects, B, were drawn from MVN(0, Sigma), Sigma is such that it achieves a correlation between responses of 0. Response 1 has causal effects while the remaining nine responses do not have any causal effect. The responses, Y, were drawn from MN(XB, I, V), where V is such that it achieves a correlation between responses of 0 and a scale defined by PVE, in the case of cuasal responses. Non causal responses are from N(0, 1).

2000 genes were simulated and univariate summary statistics were obtained by simple linear regression in the training data (80% of the data. The indexes of the training-test individuals were the same for all the datasets). These regression coefficients and standard errors were used as input in the mash pipeline (from Gao) to compute data-driven covariance matrices (up to the ED step included). In particular, the top variable per gene was used to define a “strong” set and 4 random variables per gene were used to define a “random” set. Covariance matrices were estimated using flash, PCA (including the top 3 PCs), and the empirical covariance matrix.

The first 50 genes were used for the prediction analysis. mr.mash was fitted to the training data, updating V (imposing a diagonal structure) and updating the prior weights using EM updates. The mixture prior consisted of components defined by:

  • canonical matrices corresponding to different settings of effect sharing/specificity (i.e., singletons, independent, low heterogeneity, medium heterogeneity, high heterogeneity, shared) plus the spike.

  • data-driven matrices estimated as described above plus the spike.

  • both canonical and data-driven matrices plus the spike.

  • both canonical and data-driven matrices plus the spike, dropping components with \(w_0 < 1e-8\).

The covariances matrices were scaled by a grid of values computed from the univariate summary statistics as in the mash paper. The posterior mean of the regression coefficients were initialized to the estimates of the group-LASSO. The mixture weights were initialized with the proportion of zero-coefficients from the group-LASSO estimate as the weight on the spike and the proportion of non-zero-coefficients split equally among the remaining components.Convergence was declared when the maximum difference in the ELBO between two successive iterations was smaller than 1e-2.

Then, responses were predicted on the test data (20% of the data).

Here, we evaluate the accuracy of prediction assessed by \(r^2\) and bias (slope) from the regression of the true response on the predicted response, and the relative root mean square error (rRMSE) scaled by the standard deviation of the true responses in the test data. The boxplots are across the 50 genes.

mr.mash vs other methods

Here, we compare mr.mash to the multivariate versions of LASSO as implemented in glmnet. The form of the penalty id the following: \(\lambda[(1-\alpha)/2 ||\mathbf{\beta}_j||^2_2 + \alpha ||\mathbf{\beta}_j||_2]\). \(\lambda\) is chosen by cross-validation in the training set. We also compare to the UTMOST implementation by Abhishek, and the response-by-response elastic net. All the methods were using 1 thread.

###Convert from list to data.frame for plotting
dsc_plots <- convert_dsc_to_dataframe_gtex(dsc_out)

###Compute rmse score (relative to mr_mash_consec_em) and add it to the data
rrmse_dat <- compute_rrmse(dsc_plots)
dsc_plots <- rbind(dsc_plots, rrmse_dat)

###Remove mse from scores and keep only methods wanted
dsc_plots <- dsc_plots[which(dsc_plots$score_metric!="scaled_rmse" ), ]

###Create factor version of method
dsc_plots$method_fac <- factor(dsc_plots$method, levels=c("mr_mash_em_can", "mr_mash_em_data",
                                                          "mr_mash_em_dataAndcan", "mr_mash_em_dataAndcan_dropcomp", 
                                                          "mlasso", "mtlasso", "enet"),
                                                labels=c("mr_mash_can", "mr_mash_data", "mr_mash_both", 
                                                         "mr_mash_both_drop", "mlasso", "mtlasso", "enet"))

###Create factor version of response
dsc_plots$response_fac <- as.factor(dsc_plots$response)

###Create plots
p_rrmse <- ggplot(dsc_plots[which(dsc_plots$score_metric=="scaled_rrmse"), ], aes_string(x = "response_fac", y = "score_value", fill = "method_fac")) +
  geom_boxplot(color = "black", outlier.size = 1, width = 0.85) +
  scale_fill_manual(values = colors) +
  labs(x = "Response", y = "Error", title = "rRMSE", fill="Method") +
  geom_hline(yintercept=1, linetype="dotted", size=1) +
  theme_cowplot(font_size = 20) +
  theme(plot.title = element_text(hjust = 0.5))

print(p_rrmse)

Version Author Date
fd99070 fmorgante 2020-10-22
1f6cf75 fmorgante 2020-10-22

Let’s now remove outliers from the plots to make things a little clearer.

p_rrmse_noout <- ggplot(dsc_plots[which(dsc_plots$score_metric=="scaled_rrmse"), ], aes_string(x = "response_fac", y = "score_value", fill = "method_fac")) +
  Ipaper::geom_boxplot2(color = "black",width.errorbar = 0, width = 0.85) +
  scale_fill_manual(values = colors) +
  labs(x = "Response", y = "Error", title = "rRMSE", fill="Method") +
  geom_hline(yintercept=1, linetype="dotted", size=1) +
  theme_cowplot(font_size = 20) +
  theme(plot.title = element_text(hjust = 0.5))

print(p_rrmse_noout)

Version Author Date
fd99070 fmorgante 2020-10-22
1f6cf75 fmorgante 2020-10-22

Here, we look at the elapsed time (\(log_2\) seconds) of each method. Note that the mr.mash run time does not include the run time of group-LASSO (but should be considered since we used it to initialize mr.mash).

dsc_plots_time <- dsc_plots[which(dsc_plots$response==1 & dsc_plots$score_metric=="scaled_rrmse"), 
                          -which(colnames(dsc_plots) %in% c("score_metric", "score_value", "response"))]

p_time <- ggplot(dsc_plots_time, aes_string(x = "method_fac", y = "time", fill = "method_fac")) +
  geom_boxplot(color = "black", outlier.size = 1, width = 0.85) +
  scale_fill_manual(values = colors) +
  scale_y_continuous(trans="log2", breaks = trans_breaks("log2", function(x) 2^x),
                     labels = trans_format("log2", math_format(2^.x))) +
  labs(x = "", y = "Elapsed time (seconds) in log2 scale", title = "Run time", fill="Method") +
  theme_cowplot(font_size = 20) +
  theme(axis.line.x = element_blank(), axis.text.x = element_blank(), axis.ticks.x = element_blank(),
        plot.title = element_text(hjust = 0.5))

print(p_time)

Version Author Date
fd99070 fmorgante 2020-10-22
1f6cf75 fmorgante 2020-10-22

PVE=0.05

###Load the dsc results
dsc_out <- dscquery("output/mvreg_all_genes_prior_GTExrealX_indepV_B_1causalrespr10_lowPVE", 
                    c("simulate.p_causal", "simulate.r", "simulate.r_causal", "simulate.pve", "simulate.B_cor", "simulate.w", 
                      "simulate.B_scale", "simulate.V_cor", "simulate", "fit", "score", "score.err", "fit.time"), 
                    groups="fit: mr_mash_em_can, mr_mash_em_data, mr_mash_em_dataAndcan, mr_mash_em_dataAndcan_dropcomp, mlasso, mtlasso, enet",
                    verbose=FALSE)

###Obtain simulation parameters
prop_testset <- 0.2
p_causal <- unique(dsc_out$simulate.p_causal)
r <- unique(dsc_out$simulate.r)
r_causal <- eval(parse(text=unique(dsc_out$simulate.r_causal)))
pve <- unique(dsc_out$simulate.pve)
w <- eval(parse(text=unique(dsc_out$simulate.w)))
B_cor <- eval(parse(text=unique(dsc_out$simulate.B_cor)))
B_scale <- eval(parse(text=unique(dsc_out$simulate.B_scale)))
V_cor <- unique(dsc_out$simulate.V_cor)

###Remove list elements that are not useful anymore
dsc_out$simulate.r_causal <- NULL
dsc_out$simulate.w <- NULL
dsc_out$simulate.B_cor <- NULL
dsc_out$simulate.B_scale <- NULL
dsc_out$simulate.V_cor <- NULL

In this section the set up is exactly the same but with PVE=0.05.

mr.mash vs other methods

###Convert from list to data.frame for plotting
dsc_plots <- convert_dsc_to_dataframe_gtex(dsc_out)

###Compute rmse score (relative to mr_mash_consec_em) and add it to the data
rrmse_dat <- compute_rrmse(dsc_plots)
dsc_plots <- rbind(dsc_plots, rrmse_dat)

###Remove mse from scores and keep only methods wanted
dsc_plots <- dsc_plots[which(dsc_plots$score_metric!="scaled_rmse" ), ]

###Create factor version of method
dsc_plots$method_fac <- factor(dsc_plots$method, levels=c("mr_mash_em_can", "mr_mash_em_data",
                                                          "mr_mash_em_dataAndcan", "mr_mash_em_dataAndcan_dropcomp", 
                                                          "mlasso", "mtlasso", "enet"),
                                                labels=c("mr_mash_can", "mr_mash_data", "mr_mash_both", 
                                                         "mr_mash_both_drop", "mlasso", "mtlasso", "enet"))

###Create factor version of response
dsc_plots$response_fac <- as.factor(dsc_plots$response)

###Create plots
p_rrmse <- ggplot(dsc_plots[which(dsc_plots$score_metric=="scaled_rrmse"), ], aes_string(x = "response_fac", y = "score_value", fill = "method_fac")) +
  geom_boxplot(color = "black", outlier.size = 1, width = 0.85) +
  scale_fill_manual(values = colors) +
  labs(x = "Response", y = "Error", title = "rRMSE", fill="Method") +
  geom_hline(yintercept=1, linetype="dotted", size=1) +
  theme_cowplot(font_size = 20) +
  theme(plot.title = element_text(hjust = 0.5))

print(p_rrmse)

Version Author Date
b1d88f3 fmorgante 2020-10-22

Let’s now remove outliers from the plots to make things a little clearer.

p_rrmse_noout <- ggplot(dsc_plots[which(dsc_plots$score_metric=="scaled_rrmse"), ], aes_string(x = "response_fac", y = "score_value", fill = "method_fac")) +
  Ipaper::geom_boxplot2(color = "black",width.errorbar = 0, width = 0.85) +
  scale_fill_manual(values = colors) +
  labs(x = "Response", y = "Error", title = "rRMSE", fill="Method") +
  geom_hline(yintercept=1, linetype="dotted", size=1) +
  theme_cowplot(font_size = 20) +
  theme(plot.title = element_text(hjust = 0.5))

print(p_rrmse_noout)

Version Author Date
b1d88f3 fmorgante 2020-10-22

Here, we look at the elapsed time (\(log_2\) seconds) of each method. Note that the mr.mash run time does not include the run time of group-LASSO (but should be considered since we used it to initialize mr.mash).

dsc_plots_time <- dsc_plots[which(dsc_plots$response==1 & dsc_plots$score_metric=="scaled_rrmse"), 
                          -which(colnames(dsc_plots) %in% c("score_metric", "score_value", "response"))]

p_time <- ggplot(dsc_plots_time, aes_string(x = "method_fac", y = "time", fill = "method_fac")) +
  geom_boxplot(color = "black", outlier.size = 1, width = 0.85) +
  scale_fill_manual(values = colors) +
  scale_y_continuous(trans="log2", breaks = trans_breaks("log2", function(x) 2^x),
                     labels = trans_format("log2", math_format(2^.x))) +
  labs(x = "", y = "Elapsed time (seconds) in log2 scale", title = "Run time", fill="Method") +
  theme_cowplot(font_size = 20) +
  theme(axis.line.x = element_blank(), axis.text.x = element_blank(), axis.ticks.x = element_blank(),
        plot.title = element_text(hjust = 0.5))

print(p_time)

Version Author Date
b1d88f3 fmorgante 2020-10-22

sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Scientific Linux 7.4 (Nitrogen)

Matrix products: default
BLAS/LAPACK: /software/openblas-0.2.19-el7-x86_64/lib/libopenblas_haswellp-r0.2.19.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

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

other attached packages:
[1] devtools_2.1.0  usethis_1.5.1   magrittr_1.5    scales_1.1.1   
[5] cowplot_1.0.0   ggplot2_3.3.2   dscrutils_0.4.2

loaded via a namespace (and not attached):
 [1] pkgload_1.1.0      jsonlite_1.6       foreach_1.4.4     
 [4] Ipaper_0.1.5       assertthat_0.2.1   sp_1.3-1          
 [7] cellranger_1.1.0   yaml_2.2.1         remotes_2.1.0     
[10] progress_1.2.2     sessioninfo_1.1.1  pillar_1.4.6      
[13] backports_1.1.10   lattice_0.20-38    glue_1.4.2        
[16] reticulate_1.10    digest_0.6.25      RColorBrewer_1.1-2
[19] promises_1.0.1     colorspace_1.4-1   htmltools_0.3.6   
[22] httpuv_1.4.5       Matrix_1.2-15      plyr_1.8.6        
[25] clipr_0.4.1        pkgconfig_2.0.3    purrr_0.3.3       
[28] processx_3.4.4     whisker_0.3-2      openxlsx_4.1.0    
[31] later_0.7.5        git2r_0.26.1       tibble_3.0.4      
[34] farver_2.0.3       ellipsis_0.3.1     withr_2.3.0       
[37] repr_0.17          cli_2.1.0          crayon_1.3.4      
[40] readxl_1.1.0       memoise_1.1.0      evaluate_0.14     
[43] ps_1.4.0           fs_1.3.1           fansi_0.4.1       
[46] doParallel_1.0.14  xml2_1.2.0         pkgbuild_1.1.0    
[49] tools_3.5.1        data.table_1.12.8  prettyunits_1.1.1 
[52] hms_0.5.3          matrixStats_0.57.0 lifecycle_0.2.0   
[55] stringr_1.4.0      munsell_0.5.0      zip_1.0.0         
[58] callr_3.5.1        compiler_3.5.1     rlang_0.4.8       
[61] grid_3.5.1         rstudioapi_0.11    iterators_1.0.10  
[64] base64enc_0.1-3    labeling_0.3       rmarkdown_1.10    
[67] boot_1.3-20        testthat_2.3.2     gtable_0.3.0      
[70] codetools_0.2-15   reshape2_1.4.4     R6_2.4.1          
[73] lubridate_1.7.4    knitr_1.20         dplyr_0.8.0.1     
[76] workflowr_1.6.2    rprojroot_1.3-2    desc_1.2.0        
[79] stringi_1.4.6      parallel_3.5.1     IRdisplay_0.6.1   
[82] Rcpp_1.0.5         vctrs_0.3.4        tidyselect_0.2.5