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master_script.R
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master_script.R
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# *******************************************************************
# ***** Analysis scripts accompanying 'Bayesian multivariate *****
# ***** meta-regression: A tutorial'
# ***** Author: Amy Mulick, LSHTM *****
# ***** February 2024 *****
# ***** *****
# *******************************************************************
rm(list=ls())
#### Load packages, data & scripts
library("rjags")
library("mixmeta")
load(file="../data/ecz_sev_MVMA_data.RData")
d <- ecz_sev_MVMA_data
source("../scripts/JAGS_scripts.R")
###########################################
###### prepare data for Bayesian analysis ######
###########################################
# ensure correct order of dataset
d <- d[order(d$outcome,d$exposure,d$study),]
# JAGS input parameters
jdat <- list(N=length(table(d$study)),
M=length(table(d$exposure)),
P=length(table(d$outcome)),
a.tau=0.005)
jdat$logor=array(d$logor, dim = c(jdat$N, jdat$M, jdat$P))
jdat$se=array(d$se, dim = c(jdat$N, jdat$M, jdat$P))
jdat$exposure=array(as.numeric(as.factor(d$exposure)), dim=c(jdat$N, jdat$M, jdat$P))
# matrix of hyperprior limits
hp.scale <- matrix(c(0.001, 0.25, 0.001, 0.1, 10, 2, 1000, 4, 100, 2, 1/100, 1/2),
nrow = 6, byrow = T)
# parameters to collect in output
to.collect <- c("b","tau2")
###########################################
###### Bayesian analyses ######
###########################################
# models with random seeds set for each chain for reproducible results
for (y in 1:dim(hp.scale)[1]) { #loop over different hyperpriors
for (z in 1:dim(hp.scale)[2]){ #loop over different limits
jdat$a.tau <- hp.scale[y, z]
set.seed(1000399)
jmod <- jags.model(textConnection(get(paste0("jcode.", y))), data=jdat,
n.chains=2, n.adapt=1000,
inits=list(list(.RNG.name = "base::Wichmann-Hill",
.RNG.seed = 123456),
list(.RNG.name = "base::Wichmann-Hill",
.RNG.seed = 7890)))
update(jmod,5000)
nam <- paste("jpos", y, z, sep=".")
assign(nam, coda.samples(jmod, to.collect, n.iter=100000, thin=5))
}
}
rm(nam)
###########################################
###### graphs ######
###########################################
# diagnostic plots
for (y in 1:dim(hp.scale)[1]) { #loop over different hyperpriors
for (z in 1:dim(hp.scale)[2]){ #loop over different limits
jpos <- get(paste("jpos", y, z, sep="."))
tit <- paste("Bayesian model, hyperprior", y,
ifelse(z==1, "(vague)", "(lightly informative)"))
# transform to analysis scale if relevant. HP1&2 were precision,
# 3&4 variance (no transformation needed), 5&6 SD
for (i in 1:length(jpos)) {
if (y==1 | y==2) jpos[[i]][, grep("tau2\\[", colnames(jpos[[i]]))] <-
apply(jpos[[i]][, grep("tau2\\[", colnames(jpos[[i]]))], 1:2, function(x) 1/x)
if (y==5 | y==6) jpos[[i]][, grep("tau2\\[", colnames(jpos[[i]]))] <-
apply(jpos[[i]][, grep("tau2\\[", colnames(jpos[[i]]))], 1:2, function(x) sqrt(x))
}
par(mfrow=c(4,3), mar=c(1,2,4,1), oma=c(0,0,2,0))
traceplot(jpos)
title(main=tit, outer=T)
gelman.plot(jpos, auto.layout = F, ylim=c(1, 1.5))
title(main=tit, outer=T)
}
}
# Figure 1
{
par(mfrow=c(1,1), mar=c(4,2,3,1))
plot(NULL, axes = F, xlab = "", ylab = "Relative Risk", ylim = log(c(0.5, 5)),
xlim = c(0,3.1), main = "Observed effects of eczema on CVD, by severity")
abline(h=0)
axis(1, at = 0:3, labels = c("None", levels(d$exposure)))
axis(2, at = log(c(0.5,0.8,1,2,5)), labels = c(0.5,0.8,1,2,5), las = 2)
c <- 2
for (i in levels(d$outcome)){
for (j in levels(d$study)) {
d.t <- d[d$outcome==i & d$study==j, ]
d.t$exposure <- as.numeric(d.t$exposure)
lines(c(0, d.t$exposure + (c-3)/80), c(0, d.t$logor),
lwd=2, type = "b", col=c)
segments(d.t$exposure + (c-3)/60, d.t$logor - 1.96*d.t$se,
d.t$exposure + (c-3)/60, d.t$logor + 1.96*d.t$se,
lwd=2, col=c)
}
c <- c+1
}
legend("topleft",levels(d$outcome),col=2:7,lty=1,ncol=2,pch=1, lwd=2)
rm(d.t, c)
}
# Figure 2
{ # create dataset
d.t <- data.frame()
for (y in 1:dim(hp.scale)[1]) { #loop over different hyperpriors
for (z in 1:dim(hp.scale)[2]){ #loop over different limits
m <- summary(get(paste("jpos", y, z, sep=".")))
dd <- data.frame(cbind(m[["statistics"]], m[["quantiles"]]))
dd$pr <- y
dd$v.i <- z
d.t <- rbind(d.t, dd)
}
}
rm(dd, m)
d.t$desc <- paste0("HP ", d.t$pr, ifelse(d.t$v.i==1, ": vague", ": lightly inf."))
titles <- levels(d$outcome)
# graph labels
par(mfcol = c(2,7), mar=c(4,2,2,1), oma=c(1,1,1,3))
plot(NA, axes=F, xlim=log(c(0.75, 2)), ylim=c(1,13), xlab = "", ylab = "")
mtext(d.t$desc[grep("b\\[1.", rownames(d.t))], side=2,
at=0.2+12:1, las=2, adj=0, line=-5, cex=0.9)
plot(NA, axes=F, xlim=log(c(0.75, 2)), ylim=c(1,13), xlab = "", ylab = "")
mtext(d.t$desc[grep("b\\[1.", rownames(d.t))], side=2,
at=0.2+12:1, las=2, adj=0, line=-5, cex=0.9)
#graph results
for (y in 1:length(titles)) {
e <- paste0("b\\[", y, ".")
f <- paste0("tau2\\[", y, ".")
b <- d.t[grep(e, rownames(d.t)), ]
t <- d.t[grep(f, rownames(d.t)), ]
b$CrI <- paste0(format(exp(b$X50.), digits=3), " (",
format(exp(b$X2.5.), digits=2, nsmall=2),", ",
format(exp(b$X97.5.), digits=2, nsmall=2),")")
t$CrI <- paste0(format(sqrt(t$X50.), digits=3), " (",
format(sqrt(t$X2.5.), digits=2, nsmall=2),", ",
format(sqrt(t$X97.5.), digits=2, nsmall=2),")")
# betas
plot(NA, axes=F, xlim=log(c(0.75, 2)), ylim=c(1,13), main=titles[y],
xlab = "Hazard ratio", ylab = "")
axis(1, at=log(c(0.75, 1, 1.5, 2)), labels=paste(c(0.75, 1, 1.5, 2)))
abline(v=0)
text(log(2.6), 0.2+c(12.6,12:1), c("Median (95% CrI)", b[, "CrI"]), adj=1,
font=c(2, rep(1,12)), cex=c(1, rep(0.95,12)), xpd=NA)
points(b[, "X50."], 12:1, pch = 15)
segments(b[, "X2.5."], 12:1, b[, "X97.5."], 12:1)
# taus
plot(NA, axes=F, xlim=sqrt(c(0, 4)), ylim=c(1,13),
xlab = "Between-study SD \n(units in log(HR))", ylab = "")
axis(1, at=sqrt(c(0, 0.25, 1, 4)), labels=paste(sqrt(c(0, 0.25, 1, 4))))
text(sqrt(6), 0.2+c(12.6,12:1), c("Median (95% CrI)", t[, "CrI"]), adj=1,
font=c(2, rep(1,12)), cex=c(1, rep(0.95,12)), xpd=NA)
points(sqrt(t[, "X50."]), 12:1, pch = 15)
segments(sqrt(t[, "X2.5."]), 12:1, sqrt(t[, "X97.5."]), 12:1)
}
#save best estimates & delete unnecessary objects
b.res <- d.t[d.t$pr==3 & d.t$v.i==2, c("X50.", "X2.5.", "X97.5.")]
b.res <- b.res[grep("b\\[", rownames(b.res)),]
rm(d.t, b, t, e, f)
}
# Figure 3
{
m <- list()
j=1
for (i in levels(d$outcome)) {
m[[j]] <- mixmeta(logor ~ as.numeric(exposure) - 1, se, random = ~ 1|study,
data=d[d$outcome == i,])[c("coefficients", "vcov")]
j <- j+1
}
d.t <- data.frame(effect=unlist(m)[grep("exposure", names(unlist(m)))],
se=sqrt(unlist(m)[grep("vcov", names(unlist(m)))]))
d.t$lb <- d.t$effect - 1.96*d.t$se
d.t$ub <- d.t$effect + 1.96*d.t$se
d.t$CI <- paste0(format(exp(d.t$effect), digits = 3), " (",
format(exp(d.t$lb), digits = 2), ", ",
format(exp(d.t$ub), digits = 3), ")")
d.t$outcome <- levels(d$outcome)
b.res$CrI <- paste0(format(exp(b.res[, "X50."]), digits=3), " (",
format(exp(b.res[, "X2.5."]), digits=3), ", ",
format(exp(b.res[, "X97.5."]), digits=3), ")")
par(mfrow=c(1,1), mar=c(4,1,2,1), oma=c(1,1,1,1))
plot(NA, axes=F, xlim=log(c(0.75, 2)), ylim=c(0,6),
main= "Frequentist vs. Bayesian comparison", xlab = "Hazard ratio", ylab = "")
axis(1, at=log(c(0.75, 1, 1.5, 2)), labels=paste(c(0.75, 1, 1.5, 2)))
abline(v=0)
text(log(2), 6:1, d.t[, "CI"], adj=1)
mtext(d.t[, "outcome"] , side=2, at=6:1, las=2, adj=0, line=2)
mtext("--> More severe eczema increases risk", side=1, at=log(1.01), cex=0.75, adj=0)
points(d.t[, "effect"], 6:1, pch = 15)
segments(d.t[, "lb"], 6:1, d.t[, "ub"], 6:1, )
points(b.res[, "X50."], 6:1-0.25, pch = 15, col="gray")
segments(b.res[, "X2.5."], 6:1-0.25, b.res[, "X97.5."], 6:1-0.25, col="gray")
text(log(2), 6:1-0.25, b.res$CrI, adj=1, col="gray")
rm(d.t, m)
}
###########################################
###### multivariate frequentist attempt ######
###########################################
d <- d[order(d$outcome, d$study, d$exposure),]
dd <- reshape(d[, c("study", "outcome", "exposure", "logor", "se")],
idvar = c("study","exposure"), timevar = "outcome", direction = "wide")
model <- mixmeta(as.matrix(dd[, grep("logor", names(dd))]) ~ as.numeric(dd$exposure) -1,
S=as.matrix(dd[, grep("se[.]", names(dd))]),
random= ~ 1|dd$study, bscov = "diag")