False positive and power results

The script extract_results_main.R will use the dscrutils package to extract results from the false positive and power analyses. If you are modifying the analysis and have changed the names of the output directories, you will need to change them in this file also. Depending on the changes you have made, you may need to make other modifications. Read more about dscrutils here and in the dscrutils documentation. This script will save R objects containing CAUSE, LCV, and other MR method results for both analyses. It will append the date so it won’t over-write the results downloaded by setup_sims(). Run it at the command line using

Rscript extract_results_main.R

or from inside R using source(extract_results_main.R). It will take several minutes to extract all of the results. If you would like to use your own files to plot, change the file names in the code below.

We first summarize results grouping by sample size and simulation setting. Here we are leaving out results of LCV but these are computed in the simulations and available (see plot_results_main.R for code).

library(tidyverse)

── Attaching packages ──────────────────────────────────────────────────────────────────────────────────────── tidyverse 1.2.1 ──

✔ ggplot2 3.2.0     ✔ purrr   0.3.2
✔ tibble  2.1.3     ✔ dplyr   0.8.3
✔ tidyr   0.8.3     ✔ stringr 1.4.0
✔ readr   1.3.1     ✔ forcats 0.4.0

── Conflicts ─────────────────────────────────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()

library(gridExtra)

Attaching package: 'gridExtra'

The following object is masked from 'package:dplyr':

    combine

library(pROC)

Type 'citation("pROC")' for a citation.

Attaching package: 'pROC'

The following objects are masked from 'package:stats':

    cov, smooth, var

library(jcolors)

causedf <- readRDS("sim_results/main_causedf.RDS")

mrdf <- readRDS("sim_results/main_mrdf.RDS")
                                     
######### Summaries
cause_summ <- causedf %>% 
              group_by(q, tau, omega,  n1, n2) %>%
              summarize(n_sig = sum(cause.p < 0.05, na.rm=T),
                        missing = sum(is.na(cause.p))) %>% 
              mutate(analysis = "cause")

mr_summ <- mrdf %>%
           group_by(q, tau, omega,  n1, n2, mr) %>%
           summarize(n_sig = sum(mr.p < 0.05, na.rm=T),
                     missing = sum(is.na(mr.p))) %>%
           rename(analysis = "mr")


res <- bind_rows(cause_summ, mr_summ) %>%
        ungroup() %>%
        mutate(label = fct_recode(analysis, "CAUSE"="cause",
                                     "Egger" = "egger", "GSMR"="gsmr",
                                     "IVW"="ivw", 
                                     "MR-PRESSO"="mrp", "Wtd. Median" = "wm"),
                 n1 = factor(paste0("N[M]==", n1)),
                 n2 = factor(paste0("N[Y]==", n2)))

Plotting power:

#colors
cc <- as.character(jcolors("default"))
cols <- c(cc[3], cc[1:2], cc[4:5],  "#D590DA")
#plot
pwr <- res %>%
       filter(q == 0) %>%
       ggplot(.) + 
          geom_line(aes(x=tau, y=n_sig/100, color=label)) +  
          geom_point(aes(x=tau, y=n_sig/100, color=label, shape=label)) +
          scale_color_manual(values=cols) + 
          scale_shape_manual(values= c(16, 3, 4, 0, 2, 6:8)) +
          geom_hline(yintercept=0.05, linetype=2) +
          xlab(expression("Percentage of Y heritability explained by M (" ~ tau ~ "=" ~ gamma^2 ~ h[M]^2/h[Y]^2 ~ ")")) +
          ylab("Percent Significant") + 
          theme_bw() + 
          theme(legend.title = element_blank(), 
                strip.text = element_text(size=14),
                axis.title = element_text(size=16),
                legend.text = element_text(size=12),
                legend.position = "bottom") +  
          guides(color=guide_legend(nrow=1),  
                 linetype=guide_legend(nrow=1),
                 shape=guide_legend(nrow=1) )  + 
          facet_wrap(~n1*n2, nrow=2, labeller = label_parsed)

Plotting false positives. The false positive simulations include two values of \(\eta\) (encoded through the omega parameter) though only the larger one is presented in the paper. Here we make plots for both. For convenience, in extracting results, we copy the results for \(q=0\).

z1 <-  filter(res, omega == 0 & tau == 0 & q == 0) %>% mutate(omega = 0.05)
z2 <-  filter(res, omega == 0 & tau == 0 & q == 0) %>% mutate(omega = 0.02)
res2 <- bind_rows(res, z1, z2) %>%
        filter(!(q == 0 & omega == 0 & tau == 0))

fp <- res2 %>%
      filter(tau == 0) %>%
      ggplot(.) +
        geom_line(aes(x=q, y=n_sig/100, color=label)) +
        geom_point(aes(x=q, y=n_sig/100, color=label, shape=label)) +
        geom_hline(yintercept=0.05, linetype=2) +
        scale_color_manual(values=cols) +
        scale_shape_manual(values= c(16, 3, 4, 0, 2, 6:8)) +
        geom_hline(yintercept=0.05, linetype=2) +
        xlab("Proportion of variants acting through U (q)") +
        ylab("Percent Significant") +
        theme_bw() +
        theme(legend.title = element_blank(),
            strip.text = element_text(size=14),
            axis.title = element_text(size=16),
            legend.text = element_text(size=12),
            legend.position = "bottom") +
        guides(color=guide_legend(nrow=1),
             linetype=guide_legend(nrow=1),
             shape=guide_legend(nrow=1) )  +
        facet_wrap(~omega*n1*n2, nrow=1, labeller=label_parsed)

ROC curves are a little more complicated to make. We want to evaluate how well each method is able to distinguish simulations with a causal effect of size \(\gamma = \sqrt{0.05}\) from simulations with a shared factor with an equal effect acconting for 30% of the trait \(M\) vairants. Both of these parameters can be modified. The first step is to combine the CAUSE and alternative MR results into a single data frame

x1 <- causedf %>%
      mutate(analysis = "cause", stat = -log10(cause.p)) %>%
      select(tag, q, omega, tau, n1, n2, analysis, stat)

x2 <- mrdf %>%
      mutate(stat = -log10(mr.p)) %>%
      rename(analysis = mr) %>%
      select(tag, q, omega, tau, n1, n2, analysis, stat)

full_results <- bind_rows(x1, x2)

full_results <- full_results %>% 
                mutate(label = fct_recode(analysis, "CAUSE"="cause",
                                     "Egger" = "egger", "GSMR"="gsmr",
                                     "IVW"="ivw",
                                     "MR-PRESSO"="mrp", "Wtd. Median" = "wm"))

Next we use the pROC package.

eff <- 0.05
q <- 0.3
n1s <- c(12000, 12000, 40000, 40000)
n2s <- c(12000, 40000, 12000, 40000)

methods <- with(full_results, unique(label)) %>%
            as.vector(.)

cc <- as.character(jcolors("default"))
cols <- c(cc[3], cc[1:2], cc[4:5],  "#D590DA")


roc_df <-lapply(seq_along(n1s), function(i){
                    my_n1 <- n1s[i]
                    my_n2 <- n2s[i]
                    rocs <- lapply(methods, function(m){
                       cat(m, " ")
                       xx <- filter(full_results, n1 == my_n1 & n2 == my_n2 & label == m &
                                 ( tau == eff | (omega == eff & q == my_q & tau == 0)))
                       xx$stat[is.na(xx$stat)] <- 0
                       with(xx, roc(predictor = stat, response = tau !=0)) %>%
                            with(., data.frame(thresh = thresholds, spec = specificities,
                                            sens = sensitivities, method = m,
                                            n1 = my_n1, n2 = my_n2,
                                            stringsAsFactors=F)) %>% 
                            return()

                })
                do.call(rbind, rocs)
            })
head(roc_df)

# A data frame with points to add to the curve
pw <- filter(res, tau == eff ) 
f <- filter(res, omega == eff2 & q == my_q & tau ==0)
df <- select(pw, label, n_sig, n1, n2) %>%
      rename(power = n_sig) %>%
      full_join(., f, c("label", "n1", "n2")) %>%
      rename(fp = n_sig) %>%
      select(label, power, fp, n1, n2) %>%
      filter(label %in% methods) %>%
      rename(method=label)

## Plotting!
plt <- roc_df %>% 
       arrange(sens) %>%
       ggplot(.) +
          geom_line(aes(x=1-spec, y=sens, col=method, group=method, linetype=method)) +
          geom_point(aes(x=fp/100, y = power/100, col=method, shape=method), size =4 , data=df) +
          scale_color_manual(values=cols) +
          scale_linetype_manual(values = rep(1, 6)) +
          scale_shape_manual(values = c(rep(16, 6))) +
          xlab("1 - Specificity (False Positive Rate)") + ylab("Sensitivity (Power)") +
          theme_bw() +
          theme(legend.title = element_blank(),
                strip.text = element_text(size=14),
                axis.title = element_text(size=16),
                legend.text = element_text(size=12),
                legend.position = "bottom") +
          guides(color=guide_legend(nrow=1),
                 linetype=guide_legend(nrow=1),
                 shape=guide_legend(nrow=1))  +
          facet_wrap(~n1*n2, ncol=4, labeller= label_parsed)

Prior robustness results

The sigma_g anlaysis is intended to evaluate how sensitive CAUSE is to changes in the prior on \(\gamma\) and \(\eta\). These parameters have the same \(N(0, \sigma_{\gamma, \eta})\) prior distribution. By default, \(\sigma_{\gamma \eta}\) is chosen guided by the data. These results dmeonstrate that, within a wide range, CAUSE is insensitive to the value of \(\sigma_{\gamma \eta}\).

The R script extract_sigma_g.R will use dscrutils to extract simulation results and store them in a data frame. Run it at the command line with

Rscript extract_sigma_g.R

or from inside an R session using source.

This code will append the date to the file it saves so it won’t save over the results downloaded by setup_sims(). If you want to use your own data frame, change the file name in the commands below.

causedf <- readRDS("sim_results/sg_causedf.RDS")
head(causedf)

  DSC simulate.output.file  tau     gamma q omega eta   h1   h2    n1
1   1 simulate/simulate_10 0.00 0.0000000 0     0   0 0.25 0.25 40000
2   1 simulate/simulate_10 0.00 0.0000000 0     0   0 0.25 0.25 40000
3   1 simulate/simulate_10 0.00 0.0000000 0     0   0 0.25 0.25 40000
4   1 simulate/simulate_11 0.05 0.2236068 0     0   0 0.25 0.25 40000
5   1 simulate/simulate_11 0.05 0.2236068 0     0   0 0.25 0.25 40000
6   1 simulate/simulate_11 0.05 0.2236068 0     0   0 0.25 0.25 40000
     n2 neffect1 neffect2 lcv_q1 lcv_q2 gcp gcp_mom m_sig_nold y_sig_nold
1 40000     1000     1000      0      0   0    0.00        101         96
2 40000     1000     1000      0      0   0    0.00        101         96
3 40000     1000     1000      0      0   0    0.00        101         96
4 40000     1000     1000      1      0   1    0.96         94         85
5 40000     1000     1000      1      0   1    0.96         94         85
6 40000     1000     1000      1      0   1    0.96         94         85
  m_sig     params
1   102    (0,0,0)
2   102    (0,0,0)
3   102    (0,0,0)
4   108 (0.05,0,0)
5   108 (0.05,0,0)
6   108 (0.05,0,0)
                                 cause_sigma_g.output.file quant   sigma_g
1 cause_sigma_g/simulate_10_cause_params_1_cause_sigma_g_1  0.51 8.9197112
2 cause_sigma_g/simulate_10_cause_params_1_cause_sigma_g_2  0.65 0.5803009
3 cause_sigma_g/simulate_10_cause_params_1_cause_sigma_g_3  0.80 0.2656855
4 cause_sigma_g/simulate_11_cause_params_1_cause_sigma_g_1  0.51 8.9197112
5 cause_sigma_g/simulate_11_cause_params_1_cause_sigma_g_2  0.65 0.5803009
6 cause_sigma_g/simulate_11_cause_params_1_cause_sigma_g_3  0.80 0.2656855
          z eta_sharing  q_sharing   eta_causal   q_causal gamma_causal
1 -5.688023 -0.06270989 0.02009531 -0.053846753 0.02294318 -0.002114384
2 -6.222519 -0.04002148 0.02456070 -0.032508692 0.02780765 -0.002286300
3 -5.770971 -0.01853399 0.03351503 -0.012154733 0.03793337 -0.002571933
4  4.926419  0.21590336 0.67297501 -0.008234885 0.03065362  0.176649144
5  4.940660  0.21546277 0.67362048 -0.005822829 0.03414573  0.176438987
6  4.871813  0.21381720 0.67599577 -0.001372277 0.04059740  0.175640524
             p
1 1.000000e+00
2 1.000000e+00
3 1.000000e+00
4 4.187512e-07
5 3.892923e-07
6 5.528927e-07

The results data frame contains simulation parameters and file information (columns 1-22), the CAUSE \(z\)-score (column 25) and \(p\)-value (column 31), and the posterior median for each simulation for parameters \(\eta\) and \(q\) in the sharing model and parameters \(\eta\), \(q\), and \(\gamma\) in the causal model. Each simulation was analyzed by CAUSE three times using different values of \(\sigma_{\gamma \eta}\) (column sigma_g). These are large, medium and small values which are chosen so that \(\sqrt{0.05}\) is the 51st, 65th and 80th quantile of the \(N(0, \sigma_{\gamma \eta})\) distribution respectively.

There are three sets of parameters used in simulations. Below we calculate the correlation in \(p\)-value and posterior median for each parameter in each setting across the three values of \(\sigma_{\gamma \eta}\). The following code only reports the minimum correlation for each parameter-simulation setting combination and the correlation between the medium and small values of \(\sigma_{\gamma \eta}\).

vars <- c("z", "p", "eta_sharing", "q_sharing",
          "eta_causal", "q_causal", "gamma_causal")

min_cor <- expand.grid(variable = vars,
                       params = unique(causedf$params), stringsAsFactors=F)
min_cor$min_cor <- NA
min_cor$cor_med_small <- NA
for(i in seq(nrow(min_cor))){
    v <- min_cor$variable[i]
    X <- select(causedf, simulate.output.file, params, quant, one_of(v)) %>%
         spread(quant, get(v))  %>%
         filter(params==min_cor$params[i]) %>%
         select(one_of(c("0.51", "0.65", "0.8")))

    min_cor$min_cor[i] <- min(cor(X))
    min_cor$cor_med_small[i] <- cor(X[,"0.65"], X[,"0.8"])

}
min_cor

       variable       params   min_cor cor_med_small
1             z      (0,0,0) 0.9086311     0.9463102
2             p      (0,0,0) 0.9940151     0.9963328
3   eta_sharing      (0,0,0) 0.9418110     0.9758594
4     q_sharing      (0,0,0) 0.9727896     0.9907447
5    eta_causal      (0,0,0) 0.9341944     0.9808693
6      q_causal      (0,0,0) 0.8259576     0.9291362
7  gamma_causal      (0,0,0) 0.9996609     0.9997962
8             z   (0.05,0,0) 0.9799585     0.9820971
9             p   (0.05,0,0) 0.9639080     0.9700564
10  eta_sharing   (0.05,0,0) 0.9994588     0.9996662
11    q_sharing   (0.05,0,0) 0.9999743     0.9999841
12   eta_causal   (0.05,0,0) 0.8727614     0.9539053
13     q_causal   (0.05,0,0) 0.5074016     0.7999716
14 gamma_causal   (0.05,0,0) 0.9999445     0.9999735
15            z (0,0.05,0.3) 0.9849564     0.9849564
16            p (0,0.05,0.3) 0.9943423     0.9956324
17  eta_sharing (0,0.05,0.3) 0.9453076     0.9745643
18    q_sharing (0,0.05,0.3) 0.9992086     0.9995995
19   eta_causal (0,0.05,0.3) 0.9482481     0.9802321
20     q_causal (0,0.05,0.3) 0.9499426     0.9863485
21 gamma_causal (0,0.05,0.3) 0.9997150     0.9998202

This code is also contained in summarize_sigma_g.R.

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.

Session information

sessionInfo()

R version 3.6.1 (2019-07-05)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 18.04.2 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/openblas/libblas.so.3
LAPACK: /usr/lib/x86_64-linux-gnu/libopenblasp-r0.2.20.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] jcolors_0.0.4   pROC_1.15.0     gridExtra_2.3   forcats_0.4.0  
 [5] stringr_1.4.0   dplyr_0.8.3     purrr_0.3.2     readr_1.3.1    
 [9] tidyr_0.8.3     tibble_2.1.3    ggplot2_3.2.0   tidyverse_1.2.1

loaded via a namespace (and not attached):
 [1] tidyselect_0.2.5     xfun_0.8             haven_2.1.1         
 [4] lattice_0.20-38      colorspace_1.4-1     generics_0.0.2      
 [7] vctrs_0.2.0          htmltools_0.3.6      yaml_2.2.0          
[10] rlang_0.4.0          pillar_1.4.2         glue_1.3.1          
[13] withr_2.1.2          modelr_0.1.4         readxl_1.3.1        
[16] plyr_1.8.4           munsell_0.5.0        gtable_0.3.0        
[19] workflowr_1.4.0.9000 cellranger_1.1.0     rvest_0.3.4         
[22] evaluate_0.14        knitr_1.23           highr_0.8           
[25] broom_0.5.2          Rcpp_1.0.1           scales_1.0.0        
[28] backports_1.1.4      jsonlite_1.6         fs_1.3.1            
[31] hms_0.5.0            digest_0.6.20        stringi_1.4.3       
[34] grid_3.6.1           rprojroot_1.3-2      cli_1.1.0           
[37] tools_3.6.1          magrittr_1.5         lazyeval_0.2.2      
[40] crayon_1.3.4         whisker_0.3-2        pkgconfig_2.0.2     
[43] zeallot_0.1.0        xml2_1.2.0           lubridate_1.7.4     
[46] assertthat_0.2.1     rmarkdown_1.13       httr_1.4.0          
[49] rstudioapi_0.10      R6_2.4.0             nlme_3.1-140        
[52] git2r_0.26.1         compiler_3.6.1