Simulation Modules

The simulation module:

simulate: R(library(causeSims);
            snps <- readRDS("data/chr19_snpdata_hm3only.RDS");
            evd_list <- readRDS("data/evd_list_chr19_hm3.RDS");
            dat <- sum_stats(snps, evd_list,
                  n_copies = 30,
                  n1 = n1, n2=n2,
                  h1=h1, h2=h1,
                  neffect1 = neffect1, neffect2 = neffect2,
                  tau = tau, omega = omega, q = q,
                  cores = 4, ld_prune_pval_thresh = 0.01,
                  r2_thresh = 0.1))

     q: 0.1, 0.2, 0.3, 0.4, 0.5
     omega: 0.02, 0.05
     tau: 0
     n1: 12000, 40000
     n2: 12000, 40000
     neffect1: 1000
     neffect2: 1000
     h1: 0.25
     h2: 0.25
     $sim_params: c(q = q, omega = omega, tau = tau,  h1 = h1, h2 = h2, n1 = n1, n2 = n2, neffect1 = neffect1, neffect2 =neffect2)
     $dat: dat

The R code contained in R() is the guts of this module. A data object named dat is generated using the sum_stats function from the causeSims R pacakge. Below this, we specify parameters used to simulate the data. Most important are q, omega, and tau. q is the proportion of variants acting through \(U\) while omega and tau are standardized versions of \(\gamma\) and \(\eta\) in the paper. tau is the proportion of \(Y\) heritability explained by the causal effect of \(M\) on \(Y\) times the sign of \(\gamma\), \[ \tau = sign(\gamma)\frac{\gamma^2 h^2_{M}}{h^{2}_{Y}}, \] and omega is the proportion of \(Y\) heritability explained by \(U\), divided by \(q\) and multiplied by the sign of \(\eta\). \[ \omega = sign(\eta)\frac{\eta^2 h^2_{M}}{h^{2}_{Y}} \] This parameterization is sometimes more convenient for running simulations that using \(\eta\) and \(\gamma\). However, the sum_stats function will accept either omega and tau arguments or eta and gamma. Note that here we have specified that the function can use 4 cores. This should match the n_cpu parameter in the simulate section of the config file. The sum_stats function generates data both with and without LD. In this file we only analyze the “with LD” data but we will describe how to make modifications to analyze both or only the “no LD” data.

The gw_sig module is a helper module. This module computes the GCP (a parameter defined by LCV (O’Connor and Price 2019)) and computes the number of genome-wide significant variants. It also stores all the simulation parameters which makes it easier to extract them. Extracting parameters from the simulate module will require reading in the entire data set, objects created by the gw_sig module are smaller and faster to read.

gw_sig: R(library(causeSims);
           m_sig_nold <- with($(dat), sum(p_value_nold < thresh ));
           y_sig_nold <- with($(dat), sum(2*pnorm(-abs(beta_hat_2_nold/seb2)) < thresh ));
           m_sig <- with($(dat), sum(p_value < thresh & ld_prune==TRUE));

          params <- $(sim_params);
          tau <- as.numeric(params["tau"]);
          omega <- as.numeric(params["omega"]);
          q <- as.numeric(params["q"]);
          h1 <- as.numeric(params["h1"]);
          h2 <- as.numeric(params["h2"]);
          neffect1 <- as.numeric(params["neffect1"]);
          neffect2 <- as.numeric(params["neffect2"]);
          gamma <- sqrt(tau*sum(h2)/sum(h1))*sign(tau);
          eta <- sqrt(abs(omega)*sum(h2)/sum(h1))*sign(omega);

          #LCV parameters
          if(q == 0 & tau == 0){
            q.1 <- q.2 <- 0;
            gcp <- 0;
          }else if(q == 0){
            q.1 <- 1;
            q.2 <- 0;
            gcp <- 1;
          }else{
            q.1 <- sqrt(q);
            q.2 <- eta * sqrt(q) * sqrt(h1) / sqrt(h2);
            gcp = (log(q.2^2) - log(q.1^2)) / (log(q.2^2) + log(q.1^2));
          };
          gcp_mom <- gcp_moments($(dat), h1, h2)
          )
    thresh: 5e-8
    $m_sig: m_sig
    $m_sig_nold: m_sig_nold
    $y_sig_nold: y_sig_nold
    $q: q
    $omega: omega
    $tau: tau
    $gamma: gamma
    $eta: eta
    $h1: h1
    $h2: h2
    $n1: as.numeric(params["n1"])
    $n2: as.numeric(params["n2"])
    $neffect1: as.numeric(params["neffect1"])
    $neffect2: as.numeric(params["neffect2"])
    $lcv_q1: q.1
    $lcv_q2: q.2
    $lcv_gcp: gcp
    $lcv_gcp_mom: gcp_mom$gcp

CAUSE Modules

We have divided CAUSE analysis into parameter estimation and model fitting steps. This makes it easier to experiment with changes only to the parameter estimation step.

cause_params: R(library(causeSims);
                p1 <- cause_params_sims($(dat), null_wt = null_wt, no_ld=FALSE);
                )
    null_wt: 10
    $cause_params_ld: p1

cause: R(library(causeSims);
         library(cause);
         cause_res <- cause_sims($(dat), $(cause_params_ld), no_ld = FALSE);
         z <- -1*summary(cause_res)$z;
         p <- pnorm(-z);
         quants <- summary(cause_res)$quants)
    $cause_res: cause_res
    $sigma_g: cause_res$sigma_g
    $eta_med_2: quants[[1]][1,2]
    $q_med_2: quants[[1]][1,3]
    $eta_med_3: quants[[2]][1,2]
    $gamma_med_3: quants[[2]][1,1]
    $q_med_3: quants[[2]][1,3]
    $z: z
    $p: p

Both modules use wrapper functions from the causeSims package. These are very simple wrappers that make it easy to run CAUSE on the simulated data format. Note that here we use no_ld = FALSE in both modules. If you want to use the data that is simulated without LD instead you can change no_ld = TRUE. You could get results for both using the following set of modules.

cause_params: R(library(causeSims);
                p1 <- cause_params_sims($(dat), null_wt = null_wt, no_ld=FALSE);
                p2 <- cause_params_sims($(dat), null_wt = null_wt, no_ld=TRUE);
                )
    null_wt: 10
    $cause_params_ld: p1
    $cause_params_nold: p2

cause: R(library(causeSims);
         library(cause);
         if(no_ld==FALSE){
          cause_res <- cause_sims($(dat), $(cause_params_ld), no_ld = no_ld);
         else{
          cause_res <- cause_sims($(dat), $(cause_params_nold), no_ld = no_ld);
         }
         z <- -1*summary(cause_res)$z;
         p <- pnorm(-z);
         quants <- summary(cause_res)$quants)
    $no_ld: TRUE, FALSE
    $cause_res: cause_res
    $sigma_g: cause_res$sigma_g
    $eta_med_2: quants[[1]][1,2]
    $q_med_2: quants[[1]][1,3]
    $eta_med_3: quants[[2]][1,2]
    $gamma_med_3: quants[[2]][1,1]
    $q_med_3: quants[[2]][1,3]
    $z: z
    $p: p

Alternative MR Modules

There are many modules for alternative MR methods. Modules for IVW regression, Egger regression, MR-PRESSO, and the weighted median method are very similar and rely on wrappers from causeSims. We can just look at one of these.

ivw: R(library(causeSims);
       res <- ivw($(dat), p_val_thresh=thresh, no_ld = no_ld);
       )
    thresh: 5e-8
    no_ld: FALSE
    $z: res$z
    $p: res$p

To run on the data without LD change the no_ld parameter to no_ld: TRUE or no_ld: TRUE, FALSE to run both.

The GSMR module is a little more complicated

gsmr: R(library(causeSims);
        evd_list <- readRDS("data/evd_list_chr19_hm3.RDS");
        res <- gsmr_sims($(dat), evd_list, p_val_thresh  = 5e-8, no_ld = FALSE);
        if(!is.null(res)){
           z <- res$bxy/res$bxy_se;
           est <- res$bxy;
           p <- res$bxy_pval;
        }else{
           z <- est <- p <-  NA;
        }
      )
    thresh: 5e-8
    $z: z
    $p: p
    $est_gsmr: est
    $gsmr: res

GSMR requires the LD structure and sometimes returns errors. In this case the gsmr_sims wrapper returns NULL and we set results to missing. If no_ld = TRUE the LD data in evd_list is simply ignored.

LCV Module

Results from LCV are not compared with CAUSE in the paper because LCV is performing a different test than other MR methods. However, we have implemented wrappers and a module to run LCV.

LCV: R(library(causeSims);
       res <- try(lcv_sims($(dat),no_ld = no_ld, sig.thresh = thresh));
       if(class(res) == "try-error"){
            res <- list(pval.gcpzero.2tailed=NA, gcp.pm = NA, gcp.pse = NA);
        };
       )
    thresh: 30
    no_ld: FALSE
    $p: res$pval.gcpzero.2tailed
    $gcp_mean: res$gcp.pm
    $gcp_pse: res$gcp.pse
    $gcp_obj: res

When LCV returns errors, we set results to missing.