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analysis.R
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analysis.R
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## This file processes the results of the simulation study and computes
## and graphs the relevant performance metrics.
rm(list=ls())
# setwd("C:/Users/Antonio/Desktop/population_adjustment_simstudy")
load(file="survival_settings.RData")
source("functions.R") # load functions to compute performance measures and for plotting
# TRUE VALUE OF TARGET ESTIMAND IS ZERO
Delta.AB <- 0
# container of means and variances for all replicates in each scenario
maic.means.list <- vector(mode="list", scenarios)
maic.variances.list <- vector(mode="list", scenarios)
stc.means.list <- vector(mode="list", scenarios)
stc.variances.list <- vector(mode="list", scenarios)
bucher.means.list <- vector(mode="list", scenarios)
bucher.variances.list <- vector(mode="list", scenarios)
# average treatment effect container
maic.ate <- rep(NA, scenarios)
stc.ate <- rep(NA, scenarios)
bucher.ate <- rep(NA, scenarios)
maic.ate.mcse <- rep(NA, scenarios) # monte carlo standard error
stc.ate.mcse <- rep(NA, scenarios)
bucher.ate.mcse <- rep(NA, scenarios)
# lower bound of confidence interval container
maic.lci <- vector(mode="list", scenarios)
stc.lci <- vector(mode="list", scenarios)
bucher.lci <- vector(mode="list", scenarios)
maic.lci.mean <- rep(NA, scenarios)
stc.lci.mean <- rep(NA, scenarios)
bucher.lci.mean <- rep(NA, scenarios)
maic.lci.mcse <- rep(NA, scenarios)
stc.lci.mcse <- rep(NA, scenarios)
bucher.lci.mcse <- rep(NA, scenarios)
# upper bound of confidence interval container
maic.uci <- vector(mode="list", scenarios)
stc.uci <- vector(mode="list", scenarios)
bucher.uci <- vector(mode="list", scenarios)
maic.uci.mean <- rep(NA, scenarios)
stc.uci.mean <- rep(NA, scenarios)
bucher.uci.mean <- rep(NA, scenarios)
maic.uci.mcse <- rep(NA, scenarios)
stc.uci.mcse <- rep(NA, scenarios)
bucher.uci.mcse <- rep(NA, scenarios)
# Confidence interval widths
maic.ciwidth <- vector(mode="list", scenarios)
stc.ciwidth <- vector(mode="list", scenarios)
bucher.ciwidth <- vector(mode="list", scenarios)
# Bias containers
maic.bias <- rep(NA, scenarios)
stc.bias <- rep(NA, scenarios)
bucher.bias <- rep(NA, scenarios)
maic.bias.mcse <- rep(NA, scenarios)
stc.bias.mcse <- rep(NA, scenarios)
bucher.bias.mcse <- rep(NA, scenarios)
# mean absolute error (MAE) containers
maic.abs.err <- vector(mode="list", scenarios)
stc.abs.err <- vector(mode="list", scenarios)
bucher.abs.err <- vector(mode="list", scenarios)
maic.mae <- rep(NA, scenarios)
stc.mae <- rep(NA, scenarios)
bucher.mae <- rep(NA, scenarios)
maic.mae.mcse <- rep(NA, scenarios)
stc.mae.mcse <- rep(NA, scenarios)
bucher.mae.mcse <- rep(NA, scenarios)
# mean square error (MSE) containers
maic.mse <- rep(NA, scenarios)
stc.mse <- rep(NA, scenarios)
bucher.mse <- rep(NA, scenarios)
maic.mse.mcse <- rep(NA, scenarios)
stc.mse.mcse <- rep(NA, scenarios)
bucher.mse.mcse <- rep(NA, scenarios)
# variability ratio containers
maic.vr <- rep(NA, scenarios)
stc.vr <- rep(NA, scenarios)
bucher.vr <- rep(NA, scenarios)
maic.vr.mcse <- rep(NA, scenarios)
stc.vr.mcse <- rep(NA, scenarios)
bucher.vr.mcse <- rep(NA, scenarios)
# empirical standard error (EmpSE) containers
maic.empse <- rep(NA, scenarios)
stc.empse <- rep(NA, scenarios)
bucher.empse <- rep(NA, scenarios)
maic.empse.mcse <- rep(NA, scenarios)
stc.empse.mcse <- rep(NA, scenarios)
bucher.empse.mcse <- rep(NA, scenarios)
# coverage rate (%) of 95% confidence intervals
maic.cov <- rep(NA, scenarios)
stc.cov <- rep(NA, scenarios)
bucher.cov <- rep(NA, scenarios)
maic.cov.mcse <- rep(NA, scenarios)
stc.cov.mcse <- rep(NA, scenarios)
bucher.cov.mcse <- rep(NA, scenarios)
# % of replicates worse than Bucher for each scenario
maic.error.worse.than <- rep(NA,scenarios)
maic.error.worse.than.mcse <- rep(NA,scenarios)
stc.error.worse.than <- rep(NA,scenarios)
stc.error.worse.than.mcse <- rep(NA,scenarios)
# standardized biases
maic.std.bias <- rep(NA,scenarios)
stc.std.bias <- rep(NA,scenarios)
bucher.std.bias <- rep(NA,scenarios)
# approximate effective sample sizes
maic.aess.mean <- rep(NA,scenarios)
maic.aess.mcse <- rep(NA,scenarios)
# number of replicates for which MAIC weighted regression has separability issues
maic.separability.list <- rep(NA, scenarios)
# assume MAIC analysis stage has separability issues if abs(treatment effect) > max.effect
max.effect <- 10
# number of replicates for which STC does not converge
stc.notconverges.list <- rep(NA, scenarios)
# assume that STC has not converged if variance greater than this number
max.variance <- 5
# table storing parameter settings and performance measures for each scenario
scenarios.df <- data.frame()
for (i in 1:scenarios) {
file.id <- paste0("N_AC", pc$N_AC[i], "b_X", round(pc$b_X[i], digits=2),
"b_EM", round(pc$b_EM[i], digits=2),
"meanX_AC", pc$meanX_AC[i], "corX", pc$corX[i])
# MAIC
load(paste0("Results/MAIC/means_", file.id, ".RData"))
load(paste0("Results/MAIC/variances_", file.id, ".RData"))
# number of replicates for which MAIC weighted regression has separability issues
maic.separability.list[i] <- sum(abs(means)>max.effect)
# discard these replicates (1 of 162000 in this sim. study)
maic.no.sep <- abs(means)<max.effect
means <- means[maic.no.sep]
variances <- variances[maic.no.sep]
### MATCHING-ADJUSTED INDIRECT COMPARISON
maic.means.list[[i]] <- means
maic.variances.list[[i]] <- variances
maic.bias[i] <- bias(maic.means.list[[i]], Delta.AB)
maic.bias.mcse[i] <- bias.mcse(maic.means.list[[i]])
maic.mae[i] <- mae(maic.means.list[[i]], Delta.AB)
maic.abs.err[[i]] <- maic.means.list[[i]] - (Delta.AB)
maic.mae.mcse[i] <- mcse.estimate(maic.abs.err[[i]])
maic.mse[i] <- mse(maic.means.list[[i]], Delta.AB)
maic.mse.mcse[i] <- mse.mcse(maic.means.list[[i]], Delta.AB)
maic.ate[i] <- mean(maic.means.list[[i]])
maic.ate.mcse[i] <- mcse.estimate(maic.means.list[[i]])
# construct confidence interval using normal distribution
maic.lci[[i]] <- maic.means.list[[i]] + qnorm(0.025)*sqrt(maic.variances.list[[i]])
maic.uci[[i]] <- maic.means.list[[i]] + qnorm(0.975)*sqrt(maic.variances.list[[i]])
maic.ciwidth[[i]] <- maic.uci[[i]] - maic.lci[[i]]
maic.lci.mean[i] <- mean(maic.lci[[i]])
maic.lci.mcse[i] <- mcse.estimate(maic.lci[[i]])
maic.uci.mean[i] <- mean(maic.uci[[i]])
maic.uci.mcse[i] <- mcse.estimate(maic.uci[[i]])
maic.cov[i] <- coverage(maic.lci[[i]], maic.uci[[i]], Delta.AB)
maic.cov.mcse[i] <- coverage.mcse(maic.cov[i], length(maic.lci[[i]]))
maic.empse[i] <- empse(maic.means.list[[i]])
maic.empse.mcse[i] <- empse.mcse(maic.empse[i], length(maic.means.list[[i]]))
maic.vr[i] <- var.ratio(maic.means.list[[i]], sqrt(maic.variances.list[[i]]))
maic.vr.mcse[i] <- var.ratio.mcse(avg.se=mean(sqrt(maic.variances.list[[i]])),
emp.se=maic.empse[i],
var.avg.se=mcse.estimate(sqrt(maic.variances.list[[i]]))^2,
var.emp.se=maic.empse.mcse[i]^2)
maic.std.bias[i] <- (maic.bias[i]*100)/maic.empse[i]
load(paste0("Results/MAIC/aess_", file.id, ".RData"))
maic.aess.mean[i] <- mean(approx.ess.maic)
maic.aess.mcse[i] <- mcse.estimate(approx.ess.maic)
### SIMULATED TREATMENT COMPARISON ("plug-in" approach)
load(paste0("Results/STC/means_", file.id, ".RData"))
load(paste0("Results/STC/variances_", file.id, ".RData"))
stc.notconverges.list[i] <- sum(variances>max.variance)
# discard replicates for which STC did not converge (0 of 162000 in this sim. study)
stc.converges <- variances<max.variance
means <- means[stc.converges]
variances <- variances[stc.converges]
stc.means.list[[i]] <- means
stc.variances.list[[i]] <- variances
stc.bias[i] <- bias(stc.means.list[[i]], Delta.AB)
stc.bias.mcse[i] <- bias.mcse(stc.means.list[[i]])
stc.mae[i] <- mae(stc.means.list[[i]], Delta.AB)
stc.mae.mcse[i] <- mcse.estimate(stc.means.list[[i]])
stc.abs.err[[i]] <- stc.means.list[[i]] - (Delta.AB)
stc.mae.mcse[i] <- mcse.estimate(stc.abs.err[[i]])
stc.mse[i] <- mse(stc.means.list[[i]], Delta.AB)
stc.mse.mcse[i] <- mse.mcse(stc.means.list[[i]], Delta.AB)
stc.ate[i] <- mean(stc.means.list[[i]])
stc.ate.mcse[i] <- mcse.estimate(stc.means.list[[i]])
stc.lci[[i]] <- stc.means.list[[i]] + qnorm(0.025)*sqrt(stc.variances.list[[i]])
stc.uci[[i]] <- stc.means.list[[i]] + qnorm(0.975)*sqrt(stc.variances.list[[i]])
stc.ciwidth[[i]] <- stc.uci[[i]] - stc.lci[[i]]
stc.lci.mean[i] <- mean(stc.lci[[i]])
stc.lci.mcse[i] <- mcse.estimate(stc.lci[[i]])
stc.uci.mean[i] <- mean(stc.uci[[i]])
stc.uci.mcse[i] <- mcse.estimate(stc.uci[[i]])
stc.cov[i] <- coverage(stc.lci[[i]], stc.uci[[i]], Delta.AB)
stc.cov.mcse[i] <- coverage.mcse(stc.cov[i], length(stc.lci[[i]]))
stc.empse[i] <- empse(stc.means.list[[i]])
stc.empse.mcse[i] <- empse.mcse(stc.empse[i], length(stc.means.list[[i]]))
stc.vr[i] <- var.ratio(stc.means.list[[i]], sqrt(stc.variances.list[[i]]))
stc.vr.mcse[i] <- var.ratio.mcse(avg.se=mean(sqrt(stc.variances.list[[i]])),
emp.se=stc.empse[i],
var.avg.se=mcse.estimate(sqrt(stc.variances.list[[i]]))^2,
var.emp.se=stc.empse.mcse[i]^2)
stc.std.bias[i] <- (stc.bias[i]*100)/stc.empse[i]
### BUCHER METHOD (STANDARD INDIRECT COMPARISON)
load(paste0("Results/Bucher/means_", file.id, ".RData"))
load(paste0("Results/Bucher/variances_", file.id, ".RData"))
bucher.means.list[[i]] <- means
bucher.variances.list[[i]] <- variances
bucher.bias[i] <- bias(bucher.means.list[[i]], Delta.AB)
bucher.bias.mcse[i] <- bias.mcse(bucher.means.list[[i]])
bucher.mae[i] <- mae(bucher.means.list[[i]], Delta.AB)
bucher.abs.err[[i]] <- bucher.means.list[[i]] - (Delta.AB)
bucher.mae.mcse[i] <- mcse.estimate(bucher.abs.err[[i]])
bucher.mse[i] <- mse(bucher.means.list[[i]], Delta.AB)
bucher.mse.mcse[i] <- mse.mcse(bucher.means.list[[i]], Delta.AB)
bucher.ate[i] <- mean(bucher.means.list[[i]])
bucher.ate.mcse[i] <- mcse.estimate(bucher.means.list[[i]])
bucher.lci[[i]] <- bucher.means.list[[i]] + qnorm(0.025)*sqrt(bucher.variances.list[[i]])
bucher.uci[[i]] <- bucher.means.list[[i]] + qnorm(0.975)*sqrt(bucher.variances.list[[i]])
bucher.ciwidth[[i]] <- bucher.uci[[i]] - bucher.lci[[i]]
bucher.lci.mean[i] <- mean(bucher.lci[[i]])
bucher.lci.mcse[i] <- mcse.estimate(bucher.lci[[i]])
bucher.uci.mean[i] <- mean(bucher.uci[[i]])
bucher.uci.mcse[i] <- mcse.estimate(bucher.uci[[i]])
bucher.cov[i] <- coverage(bucher.lci[[i]], bucher.uci[[i]], Delta.AB)
bucher.cov.mcse[i] <- coverage.mcse(bucher.cov[i], length(bucher.lci[[i]]))
bucher.empse[i] <- empse(bucher.means.list[[i]])
bucher.empse.mcse[i] <- empse.mcse(bucher.empse[i], replicates)
bucher.vr[i] <- var.ratio(bucher.means.list[[i]], sqrt(bucher.variances.list[[i]]))
bucher.vr.mcse[i] <- var.ratio.mcse(avg.se=mean(sqrt(bucher.variances.list[[i]])),
emp.se=bucher.empse[i],
var.avg.se=mcse.estimate(sqrt(bucher.variances.list[[i]]))^2,
var.emp.se=bucher.empse.mcse[i]^2)
bucher.std.bias[i] <- (bucher.bias[i]*100)/bucher.empse[i]
truth <- Delta.AB # true baseline A vs. B treatment effect
maic.error.worse.than[i] <- sum(abs(bucher.means.list[[i]][maic.no.sep]-truth)<abs(maic.means.list[[i]]-truth))/sum(maic.no.sep)
maic.error.worse.than.mcse[i] <- coverage.mcse(maic.error.worse.than[i], sum(maic.no.sep))
stc.error.worse.than[i] <- sum(abs(bucher.means.list[[i]][stc.converges]-truth)<abs(stc.means.list[[i]]-truth))/sum(stc.converges)
stc.error.worse.than.mcse[i] <- coverage.mcse(stc.error.worse.than[i], sum(stc.converges))
tmp.scenarios <- cbind(i, pc$N_AC[i], pc$b_X[i], pc$b_EM[i], pc$meanX_AC[i], pc$corX[i])
maic.tmp.metrics <- cbind(maic.ate[i], maic.ate.mcse[i], maic.lci.mean[i],
maic.lci.mcse[i], maic.uci.mean[i], maic.uci.mcse[i],
maic.bias[i], maic.bias.mcse[i], maic.mse[i], maic.mse.mcse[i],
maic.mae[i], maic.mae.mcse[i], maic.cov[i], maic.cov.mcse[i],
maic.empse[i], maic.empse.mcse[i], maic.vr[i], maic.vr.mcse[i],
maic.error.worse.than[i], maic.error.worse.than.mcse[i],
maic.std.bias[i], maic.aess.mean[i], maic.aess.mcse[i])
stc.tmp.metrics <- cbind(stc.ate[i], stc.ate.mcse[i], stc.lci.mean[i],
stc.lci.mcse[i], stc.uci.mean[i], stc.uci.mcse[i],
stc.bias[i], stc.bias.mcse[i], stc.mse[i], stc.mse.mcse[i],
stc.mae[i], stc.mae.mcse[i], stc.cov[i], stc.cov.mcse[i],
stc.empse[i], stc.empse.mcse[i], stc.vr[i], stc.vr.mcse[i],
stc.error.worse.than[i], stc.error.worse.than.mcse[i],
stc.std.bias[i], stc.notconverges.list[i])
bucher.tmp.metrics <- cbind(bucher.ate[i], bucher.ate.mcse[i], bucher.lci.mean[i],
bucher.lci.mcse[i], bucher.uci.mean[i], bucher.uci.mcse[i],
bucher.bias[i], bucher.bias.mcse[i], bucher.mse[i], bucher.mse.mcse[i],
bucher.mae[i], bucher.mae.mcse[i], bucher.cov[i], bucher.cov.mcse[i],
bucher.empse[i], bucher.empse.mcse[i], bucher.vr[i], bucher.vr.mcse[i],
bucher.std.bias[i])
tmp.scenarios<- cbind(tmp.scenarios, maic.tmp.metrics, stc.tmp.metrics, bucher.tmp.metrics)
scenarios.df <- rbind(scenarios.df, tmp.scenarios)
}
colnames(scenarios.df) <- c("Scenario", "N_AC", "b_X","b_EM","meanX_AC", "corX",
"maic.ate", "maic.ate.mcse", "maic.lci.mean",
"maic.lci.mcse", "maic.uci.mean", "maic.uci.mcse",
"maic.bias", "maic.bias.mcse", "maic.mse", "maic.mse.mcse",
"maic.mae", "maic.mae.mcse", "maic.cov", "maic.cov.mcse",
"maic.empse", "maic.empse.mcse", "maic.vr", "maic.vr.mcse",
"maic.error.worse.than", "maic.error.worse.than.mcse",
"maic.std.bias", "maic.aess.mean", "maic.aess.mcse",
"stc.ate", "stc.ate.mcse",
"stc.lci.mean", "stc.lci.mcse", "stc.uci.mean", "stc.uci.mcse",
"stc.bias", "stc.bias.mcse", "stc.mse", "stc.mse.mcse",
"stc.mae", "stc.mae.mcse", "stc.cov", "stc.cov.mcse",
"stc.empse", "stc.empse.mcse", "stc.vr", "stc.vr.mcse",
"stc.error.worse.than", "stc.error.worse.than.mcse",
"stc.std.bias","stc.no.convergence",
"bucher.ate", "bucher.ate.mcse", "bucher.lci.mean",
"bucher.lci.mcse", "bucher.uci.mean", "bucher.uci.mcse",
"bucher.bias", "bucher.bias.mcse", "bucher.mse", "bucher.mse.mcse",
"bucher.mae", "bucher.mae.mcse", "bucher.cov", "bucher.cov.mcse",
"bucher.empse", "bucher.empse.mcse", "bucher.vr",
"bucher.vr.mcse", "bucher.std.bias")
write.csv(scenarios.df, "Analysis/scenarios.csv", row.names = FALSE)
scenarios.df <- read.csv(file="Analysis/scenarios.csv", header=TRUE, sep=",")
scenarios.df$b_EM <- round(scenarios.df$b_EM, 2)
scenarios.df$b_X <- round(scenarios.df$b_X, 2)
# reorder simulation results in order to be presented in nested loop plot (FOR BIAS).
# consider re-ordering on a case-by-case basis for each plot
# (function is by Rücker, G., Schwarzer, G. Presenting simulation results in a nested loop plot.
# BMC Med Res Methodol 14, 129 (2014) doi:10.1186/1471-2288-14-129)
nldata <- nestedloop(scenarios.df,
varnames=c("b_EM","meanX_AC","b_X","N_AC","corX"),
varlabels=c("Effect-modifying interaction", "Covariate overlap",
"Prognostic variable effect", "Subjects in trial with patient-level data",
"Covariate correlation"),
sign=c(1, 1, 1, 1, 1))
pd.bias <- nldata # object to be used in nested loop plot
# use labels instead of numeric values for the following factors
pd.bias$meanX_AC <- factor(pd.bias$meanX_AC, levels=c(0.15,0.3,0.45),
labels=c("poor","moderate","strong"))
pd.bias$corX <- factor(pd.bias$corX, levels=c(0,0.35),labels=c("none","moderate"))
pd.bias$b_EM <- factor(pd.bias$b_EM,levels=c(0.40,0.69,1.11), labels=c("moderate","strong",
"very strong"))
pd.bias$b_X <- factor(pd.bias$b_X, levels=c(0.40,0.69,1.11), labels=c("moderate","strong",
"very strong"))
# reorder simulation results in nested loop plot presentation order (FOR MSE)
nldata <- nestedloop(scenarios.df,
varnames=c("b_EM","N_AC","meanX_AC","b_X","corX"),
varlabels=
c("Effect-modifiying interaction",
"Subjects in trial with patient-level data", "Covariate overlap",
"Prognostic variable effect",
"Covariate correlation"),
sign=c(1, 1, 1, 1, 1))
pd.mse <- nldata
pd.mse$meanX_AC <- factor(pd.mse$meanX_AC,levels=c(0.15,0.3,0.45),
labels=c("poor","moderate","strong"))
pd.mse$corX <- factor(pd.mse$corX, levels=c(0,0.35),labels=c("none","moderate"))
pd.mse$b_EM <- factor(pd.mse$b_EM,levels=c(0.40,0.69,1.11),labels=c("moderate","strong",
"very strong"))
pd.mse$b_X <- factor(pd.mse$b_X,levels=c(0.40,0.69,1.11),labels=c("moderate","strong",
"very strong"))
# reorder simulation results in nested loop plot presentation order (for empirical standard error)
nldata <- nestedloop(scenarios.df,
varnames=c("N_AC","b_EM","meanX_AC","b_X","corX"),
varlabels=
c("Subjects in trial with patient-level data",
"Effect-modifiying interaction",
"Covariate overlap",
"Prognostic variable effect",
"Covariate correlation"),
sign=c(1, 1, 1, 1, 1))
pd.ese <- nldata
pd.ese$meanX_AC <- factor(pd.ese$meanX_AC,levels=c(0.15,0.3,0.45),
labels=c("poor","moderate","strong"))
pd.ese$corX <- factor(pd.ese$corX, levels=c(0,0.35),labels=c("none","moderate"))
pd.ese$b_EM <- factor(pd.ese$b_EM,levels=c(0.40,0.69,1.11),labels=c("moderate","strong",
"very strong"))
pd.ese$b_X <- factor(pd.ese$b_X,levels=c(0.40,0.69,1.11),labels=c("moderate","strong",
"very strong"))
# reorder simulation results in nested loop plot presentation order (for coverage)
nldata <- nestedloop(scenarios.df,
varnames=c("meanX_AC","b_EM","N_AC","b_X","corX"),
varlabels=
c("Covariate overlap", "Effect-modifiying interaction",
"Subjects in trial with patient-level data",
"Prognostic variable effect",
"Covariate correlation"),
sign=c(1, 1, 1, 1, 1))
pd.cover <- nldata
pd.cover$meanX_AC <- factor(pd.cover$meanX_AC,levels=c(0.15,0.3,0.45),
labels=c("poor","moderate","strong"))
pd.cover$corX <- factor(pd.cover$corX, levels=c(0,0.35),labels=c("none","moderate"))
pd.cover$b_EM <- factor(pd.cover$b_EM,levels=c(0.40,0.69,1.11),labels=c("moderate","strong",
"very strong"))
pd.cover$b_X <- factor(pd.cover$b_X,levels=c(0.40,0.69,1.11),labels=c("moderate","strong",
"very strong"))
# reorder simulation results in nested loop plot presentation order (FOR % reduction in ESS)
nldata <- nestedloop(scenarios.df,
varnames=c("meanX_AC","corX","b_EM","N_AC","b_X"),
varlabels=
c("Covariate overlap", "Covariate correlation",
"Effect-modifiying interaction",
"Subjects in trial with patient-level data",
"Prognostic variable effect"),
sign=c(1, 1, 1, 1, 1))
pd.aess <- nldata
pd.aess$meanX_AC <- factor(pd.aess$meanX_AC,levels=c(0.15,0.3,0.45),
labels=c("poor","moderate","strong"))
pd.aess$corX <- factor(pd.aess$corX, levels=c(0,0.35),labels=c("none","moderate"))
pd.aess$b_EM <- factor(pd.aess$b_EM,levels=c(0.40,0.69,1.11),labels=c("moderate","strong",
"very strong"))
pd.aess$b_X <- factor(pd.aess$b_X,levels=c(0.40,0.69,1.11),labels=c("moderate","strong",
"very strong"))
### MAIN MANUSCRIPT PLOTS ###
### Nested loop plot for MSE (TIFF)
tiff("Analysis/mse.tiff", res=800, width=18, height=15, units='in')
par(pty="m")
plot(pd.mse$maic.mse,
type="n",
ylim=c(0,0.6), bty="n",
xlab="Scenario",
ylab="Mean square error (MSE)",
las=1, xaxt="n",
cex.axis=1.5, cex.lab=1.5)
lines(pd.mse, col=c("#BBBBBB", "#CCCCCC", "#DDDDDD", "#EEEEEE"))
lines(pd.mse, which="r", ymin.refline=0.45, ymax.refline=0.6, cex.ref=1.5)
lines(pd.mse$maic.mse, col="red", lty=2,type="s", lwd=2.5)
lines(pd.mse$stc.mse, col="green", lty=5, type="s", lwd=2.5)
lines(pd.mse$bucher.mse, col="blue", lty=4, type="s", lwd=2.5)
legend("left",lwd=c(2.5,2.5,2.5),col=c("red","green","blue"), lty=c(2,5,4),
cex=1.5,bty="n",c("MAIC", "STC","Bucher"))
dev.off()
### Nested loop plot for MSE (PDF)
pdf("Analysis/mse.pdf", width=18,height=15,pointsize=20)
par(pty="m")
plot(pd.mse$maic.mse,
type="n",
ylim=c(0,0.6), bty="n",
xlab="Scenario",
ylab="Mean square error (MSE)",
las=1, xaxt="n",
cex.axis=1.15, cex.lab=1.15)
lines(pd.mse, col=c("#BBBBBB", "#CCCCCC", "#DDDDDD", "#EEEEEE"))
lines(pd.mse, which="r", ymin.refline=0.45, ymax.refline=0.6, cex.ref=0.9)
lines(pd.mse$maic.mse, col="red", lty=2,type="s", lwd=2.5)
lines(pd.mse$stc.mse, col="green", lty=5, type="s", lwd=2.5)
lines(pd.mse$bucher.mse, col="blue", lty=4, type="s", lwd=2.5)
legend("left",lwd=c(2.5,2.5,2.5),col=c("red","green","blue"), lty=c(2,5,4),
cex=1.15,bty="n",c("MAIC", "STC","Bucher"))
dev.off()
### Nested loop plot for empirical standard error (TIFF)
tiff("Analysis/EmpSE.tiff", res=800, width=18, height=15, units='in')
par(pty="m")
plot(pd.ese$maic.empse, type="n",ylim=c(0, 0.6), bty="n", xlab="Scenario",
ylab="Empirical standard error (ESE)",las=1, xaxt="n",
cex.axis=1.5, cex.lab=1.5)
lines(pd.ese, col=c("#BBBBBB", "#CCCCCC", "#DDDDDD", "#EEEEEE"))
lines(pd.ese, which="r", ymin.refline=0.45, ymax.refline=0.6, cex.ref=1.5)
lines(pd.ese$maic.empse, col="red", lty=2,type="s",lwd=2.5)
lines(pd.ese$stc.empse, col="green", lty=5, type="s", lwd=2.5)
lines(pd.ese$bucher.empse, col="blue", lty=4, type="s", lwd=2.5)
legend("bottom", lwd=c(2.5,2.5,2.5), col=c("red","green","blue"), lty=c(2,5,4),
cex=1.5, bty="n", c("MAIC", "STC", "Bucher"))
dev.off()
### Nested loop plot for empirical standard error (PDF)
pdf("Analysis/EmpSE.pdf",width=18, height=15,pointsize=20)
par(pty="m")
plot(pd.ese$maic.empse, type="n",ylim=c(0, 0.6), bty="n", xlab="Scenario",
ylab="Empirical standard error (ESE)",las=1, xaxt="n",
cex.axis=1.15, cex.lab=1.15)
lines(pd.ese, col=c("#BBBBBB", "#CCCCCC", "#DDDDDD", "#EEEEEE"))
lines(pd.ese, which="r", ymin.refline=0.45, ymax.refline=0.6, cex.ref=0.9)
lines(pd.ese$maic.empse, col="red", lty=2,type="s",lwd=2.5)
lines(pd.ese$stc.empse, col="green", lty=5, type="s", lwd=2.5)
lines(pd.ese$bucher.empse, col="blue", lty=4, type="s", lwd=2.5)
legend("bottom", lwd=c(2.5,2.5,2.5), col=c("red","green","blue"), lty=c(2,5,4),
cex=1.15, bty="n", c("MAIC", "STC", "Bucher"))
dev.off()
### Nested loop plot for coverage (TIFF)
tiff("Analysis/coverage.tiff", res=800, width=18, height=15, units='in')
par(pty="m")
plot(pd.cover$maic.cov*100, type="n", ylim=c(20, 100), bty="n", xlab="Scenario",
ylab="Coverage of 95% confidence intervals (%)", las=1, xaxt="n",
cex.axis=1.5, cex.lab=1.5)
abline(h=95, col="grey") # nominal
lines(pd.cover, col=c("#BBBBBB", "#CCCCCC", "#DDDDDD", "#EEEEEE"))
lines(pd.cover, which="r", ymin.refline=20, ymax.refline=40, cex.ref=1.5)
lines(pd.cover$maic.cov*100, col="red", lty=2,type="s", lwd=2.5)
lines(pd.cover$stc.cov*100, col="green", lty=5, type="s", lwd=2.5)
lines(pd.cover$bucher.cov*100, col="blue", lty=4, type="s", lwd=2.5)
legend("right", lwd=c(2.5,2.5,2.5), col=c("red","green", "blue"),
lty=c(2,5,4), cex=1.5, bty="n",c("MAIC", "STC", "Bucher"))
dev.off()
### Nested loop plot for coverage (PDF)
pdf("Analysis/coverage.pdf", width=18,height=15,pointsize=20)
par(pty="m")
plot(pd.bias$maic.cov*100, type="n", ylim=c(20, 100), bty="n", xlab="Scenario",
ylab="Coverage of 95% confidence intervals (%)", las=1, xaxt="n",
cex.axis=1.15, cex.lab=1.15)
abline(h=95, col="grey") # nominal
lines(pd.cover, col=c("#BBBBBB", "#CCCCCC", "#DDDDDD", "#EEEEEE"))
lines(pd.cover, which="r", ymin.refline=20, ymax.refline=40, cex.ref=0.9)
lines(pd.cover$maic.cov*100, col="red", lty=2,type="s", lwd=2.5)
lines(pd.cover$stc.cov*100, col="green", lty=5, type="s", lwd=2.5)
lines(pd.cover$bucher.cov*100, col="blue", lty=4, type="s", lwd=2.5)
legend("right", lwd=c(2.5,2.5,2.5), col=c("red","green", "blue"),
lty=c(2,5,4), cex=1.15, bty="n",c("MAIC", "STC", "Bucher"))
dev.off()
### Nested loop plot for variability ratio (TIFF)
tiff("Analysis/variability_ratio.tiff", res=800, width=18, height=15, units='in')
par(pty="m")
plot(pd.cover$maic.vr, type="n", ylim=c(0.8,1.2), bty="n", xlab="Scenario", ylab="Variability ratio",
las=1, xaxt="n", cex.axis=1.5, cex.lab=1.5)
abline(h=1, col="grey") # unbiased variance
lines(pd.cover, col=c("#BBBBBB", "#CCCCCC", "#DDDDDD", "#EEEEEE"))
lines(pd.cover, which="r", ymin.refline=1.1, ymax.refline=1.2, cex.ref=1.5)
lines(pd.cover$maic.vr, col="red", lty=2,type="s",lwd=2.5)
lines(pd.cover$stc.vr, col="green", lty=5, type="s", lwd=2.5)
lines(pd.cover$bucher.vr, col="blue", lty=4, type="s", lwd=2.5)
legend("bottom", lwd=c(2.5,2.5,2.5), col=c("red","green","blue"),lty=c(2,5,4),
cex=1.5, bty="n", c("MAIC", "STC", "Bucher"))
dev.off()
### Nested loop plot for variability ratio (PDF)
pdf("Analysis/variability_ratio.pdf", width=18,height=15,pointsize=20)
par(pty="m")
plot(pd.cover$maic.vr, type="n", ylim=c(0.8,1.2), bty="n", xlab="Scenario", ylab="Variability ratio",
las=1, xaxt="n", cex.axis=1.15, cex.lab=1.15)
abline(h=1, col="grey") # unbiased variance
lines(pd.cover, col=c("#BBBBBB", "#CCCCCC", "#DDDDDD", "#EEEEEE"))
lines(pd.cover, which="r", ymin.refline=1.1, ymax.refline=1.2, cex.ref=0.9)
lines(pd.cover$maic.vr, col="red", lty=2,type="s",lwd=2.5)
lines(pd.cover$stc.vr, col="green", lty=5, type="s", lwd=2.5)
lines(pd.cover$bucher.vr, col="blue", lty=4, type="s", lwd=2.5)
legend("bottom", lwd=c(2.5,2.5,2.5), col=c("red","green","blue"),lty=c(2,5,4),
cex=1.15, bty="n", c("MAIC", "STC", "Bucher"))
dev.off()
### Nested loop plot for bias (TIFF)
tiff("Analysis/bias.tiff", res=800, width=18, height=15, units='in')
par(pty="m")
plot(pd.bias$maic.bias, type="n", ylim=c(-1,0.6), bty="n", xlab="Scenario", ylab="Bias",
las=1, xaxt="n", cex.axis=1.5, cex.lab=1.5)
abline(h=0, col="grey") # no bias
lines(pd.bias, col=c("#BBBBBB", "#CCCCCC", "#DDDDDD", "#EEEEEE")) # add vertical lines
lines(pd.bias, which="r",ymin.refline=0.2, ymax.refline=0.6, cex.ref=1.5) # add reference lines
lines(pd.bias$maic.bias, col="red", lty=2,type="s", lwd=2.5) # performance measures
lines(pd.bias$stc.bias, col="green", lty=5, type="s", lwd=2.5)
lines(pd.bias$bucher.bias, col="blue", lty=4, type="s", lwd=2.5)
legend("bottom",lwd=c(2.5,2.5,2.5),col=c("red","green", "blue"),
lty=c(2,5,4),cex=1.5,bty="n", c("MAIC", "STC", "Bucher")) # legend
dev.off()
### Nested loop plot for bias (PDF)
pdf("Analysis/bias.pdf", width=18, height=15, pointsize=20)
par(pty="m")
plot(pd.bias$maic.bias, type="n", ylim=c(-1,0.6), bty="n", xlab="Scenario", ylab="Bias",
las=1, xaxt="n", cex.axis=1.15, cex.lab=1.15)
abline(h=0, col="grey") # no bias
lines(pd.bias, col=c("#BBBBBB", "#CCCCCC", "#DDDDDD", "#EEEEEE")) # add vertical lines
lines(pd.bias, which="r",ymin.refline=0.2, ymax.refline=0.6, cex.ref=0.9) # add reference lines
lines(pd.bias$maic.bias, col="red", lty=2,type="s", lwd=2.5) # performance measures
lines(pd.bias$stc.bias, col="green", lty=5, type="s", lwd=2.5)
lines(pd.bias$bucher.bias, col="blue", lty=4, type="s", lwd=2.5)
legend("bottom",lwd=c(2.5,2.5,2.5),col=c("red","green", "blue"),
lty=c(2,5,4),cex=1.15,bty="n", c("MAIC", "STC", "Bucher")) # legend
dev.off()
#### SUPPLEMENTARY MATERIAL PLOTS ####
### Nested loop plot for MAE
pdf("Analysis/Supplementary_Material/mae.pdf", width=18, height=15, pointsize=20)
par(pty="m")
plot(pd.mse$maic.mae,type="n",ylim=c(0, 0.9),bty="n",xlab="Scenario",
ylab="Mean absolute error (MAE)",las=1, xaxt="n", cex.axis=1.15, cex.lab=1.15)
lines(pd.mse, col=c("#BBBBBB", "#CCCCCC", "#DDDDDD", "#EEEEEE"))
lines(pd.mse, which="r",ymin.refline=0.675, ymax.refline=0.9,cex.ref=0.9)
lines(pd.mse$maic.mae, col="red", lty=2,type="s", lwd=2.5)
lines(pd.mse$stc.mae, col="green", lty=5, type="s", lwd=2.5)
lines(pd.mse$bucher.mae, col="blue", lty=4, type="s", lwd=2.5)
legend("left",lwd=c(2.5,2.5,2.5),col=c("red","green","blue"),lty=c(2,5,4),
cex=1.15,bty="n",c("MAIC", "STC", "Bucher"))
dev.off()
### Nested loop plot of standardized biases
pdf("Analysis/Supplementary_Material/std_biases.pdf", width=18,height=15,pointsize=20)
par(pty="m")
plot(pd.bias$maic.std.bias, ylim=c(-460,350), bty="n", xlab="Scenario", ylab="Standardized percentage bias",
las=1, xaxt="n",cex.axis=1.15, cex.lab=1.15)
abline(h=0, col="grey") # no bias
lines(pd.bias, col=c("#BBBBBB", "#CCCCCC", "#DDDDDD", "#EEEEEE"))
lines(pd.bias, which="r", ymin.refline=147.5, ymax.refline=350, cex.ref=0.9)
lines(pd.bias$maic.std.bias, col="red", lty=2,type="s", lwd=2.5)
lines(pd.bias$stc.std.bias, col="green", lty=5, type="s", lwd=2.5)
lines(pd.bias$bucher.std.bias, col="blue", lty=4, type="s", lwd=2.5)
legend("bottomleft",lwd=c(2.5,2.5,2.5), col=c("red","green","blue"), lty=c(2,5,4),
cex=1.15, bty="n", c("MAIC", "STC", "Bucher"))
dev.off()
### Nested loop plot of confidence interval width
pdf("Analysis/Supplementary_Material/CI_width.pdf", width=18,height=15,pointsize=20)
par(pty="m")
plot(pd.mse$maic.uci.mean-pd.mse$maic.lci.mean, type="n", ylim=c(0, 2), bty="n", xlab="Scenario",
ylab="95% confidence interval width", las=1, xaxt="n",cex.axis=1.15, cex.lab=1.15)
lines(pd.mse, col=c("#BBBBBB", "#CCCCCC", "#DDDDDD", "#EEEEEE"))
lines(pd.mse, which="r", ymin.refline=1.5, ymax.refline=2, cex.ref=0.9)
lines(pd.mse$maic.uci.mean-pd.mse$maic.lci.mean, col="red", lty=2,type="s", lwd=2.5)
lines(pd.mse$stc.uci.mean-pd.mse$stc.lci.mean, col="green", lty=5, type="s", lwd=2.5)
lines(pd.mse$bucher.uci.mean-pd.mse$bucher.lci.mean, col="blue", lty=4, type="s", lwd=2.5)
legend("bottom", lwd=c(2.5,2.5,2.5), col=c("red","green","blue"), lty=c(2,5,4),
cex=1.15, bty="n", c("MAIC", "STC", "Bucher"))
dev.off()
### Nested loop plot of % replicates worse than Bucher
pdf("Analysis/Supplementary_Material/worse_than_bucher.pdf", width=18,height=15,pointsize=20)
par(pty="m")
plot(pd.cover$maic.error.worse.than*100, type="n", ylim=c(0, 100), bty="n", xlab="Scenario",
ylab="% of point estimates worse than Bucher", las=1, xaxt="n",cex.axis=1.15, cex.lab=1.15)
lines(pd.cover, col=c("#BBBBBB", "#CCCCCC", "#DDDDDD", "#EEEEEE"))
lines(pd.cover, which="r", ymin.refline=75, ymax.refline=100, cex.ref=0.9)
lines(pd.cover$maic.error.worse.than*100, col="red", lty=2,type="s", lwd=2.5)
lines(pd.cover$stc.error.worse.than*100, col="green", lty=5, type="s", lwd=2.5)
legend("bottom", lwd=c(2.5, 2.5), col=c("red","green","blue"), lty=c(2,5),
cex=1.15, bty="n", c("MAIC", "STC"))
dev.off()
### Nested loop plot of MAIC % reduction in effective sample size
pdf("Analysis/Supplementary_Material/maic_percentage_reduction_ess.pdf", width=18,height=15,pointsize=20)
par(pty="m")
plot((pd.aess$N_AC-pd.aess$maic.aess.mean)*100/pd.aess$N_AC, type="n", ylim=c(0,110),
bty="n", xlab="Scenario", ylab="% reduction in effective sample size", las=1, xaxt="n",
cex.axis=1.15, cex.lab=1.15)
lines(pd.aess, col=c("#BBBBBB", "#CCCCCC", "#DDDDDD", "#EEEEEE"))
lines(pd.aess, which="r", ymin.refline=85, ymax.refline=110, cex.ref=0.9)
lines((pd.aess$N_AC-pd.aess$maic.aess.mean)*100/pd.aess$N_AC, col="red", lty=2,type="s", lwd=2.5)
legend("bottom", lwd=c(2.5), col=c("red"), lty=c(2), cex=1.15, bty="n", c("MAIC"))
dev.off()
# Plot of bias converging over a simulation scenario (simulation scenario 1)
maic.rolling.bias.1 <- cumsum(maic.means.list[[1]])/(1:replicates) # moving averages
stc.rolling.bias.1 <- cumsum(stc.means.list[[1]])/(1:replicates)
bucher.rolling.bias.1 <- cumsum(bucher.means.list[[1]])/(1:replicates)
pdf("Analysis/Supplementary_material/rolling_bias_convergence.pdf", width=18, height=15, pointsize=20)
plot(maic.rolling.bias.1, xlab="Simulation number", ylab="Rolling bias", col="red",
type="l",ylim=c(-0.4,0.1), lwd=2, lty=2, cex.axis=1.15, cex.lab=1.15)
abline(h=0, col="grey") # no bias
lines(stc.rolling.bias.1, col="green", lwd=2, lty=5)
lines(bucher.rolling.bias.1, col="blue", lwd=2, lty=4)
legend("bottom", legend = c("MAIC", "STC", "Bucher"),
col = c("red", "green","blue"), bty = "n",
pt.cex = 2, cex = 1.2, text.col = "black", horiz = F , inset = c(0.1, 0.1),
lwd=c(2,2,2), lty=c(2,5,4))
dev.off()