Documentation

Funnel plots are a graphical representation of the observed intervention effects, plotted on the x-axis, against each study’s size or precision, plotted on the y-axis. This type of plot forms a funnel shape in the absence of bias. The funnel shape occurs because as the study size increases, the precision of each study’s effect estimates also increases; larger studies thus have a lower standard error and are closer to the true effect estimate. Smaller studies may have more widely spread effect estimates due to their higher variability, which scatter at the base of the funnel plot.

Each study is represented by a dot of equal size and plotted according to the observed outcome and corresponding standard error. The solid vertical line indicates the average effect size among the included studies and the dotted diagonal lines forming the funnel shape serve as the 95% CI for the aggregated studies.

# Funnel plot

nstudy=10
se=y=NULL
set.seed(1234)
  for (istudy in 1:nstudy) {
  se=c(se, runif(1, 0.1, 0.4))
  y=c(y, rnorm(1, sd=se))
}

random = rma(y, sei=se)
funnel(random)

The contour enhanced funnel plot depicts the same information from the included studies as the simple funnel plot, but has additional shaded areas which represent different confidence intervals. In the example, the white region of the funnel corresponds with the 90% CI, the white and light gray regions correspond with the 95% CI, and the white, light gray, and dark gray regions correspond with the 99% CI, though these levels of confidence may be adjusted in the R code.

# Contour enhanced funnel plot

nstudy=10
se=y=NULL
set.seed(1234)
  for (istudy in 1:nstudy) {
  se=c(se, runif(1, 0.1, 0.4))
  y=c(y, rnorm(1, sd=se))
}

random = rma(y, sei=se)
funnel(random, 
  level=c(90, 95, 99), 
  shade=c("white", "gray", "darkgray"), 
  refline=0
)

Network meta-analysis compares multiple interventions simultaneously by analyzing studies making different comparisons in the same analysis.

data(Senn2013)

# Generation of an object of class 'netmeta' with reference
# treatment 'plac'
#
net1 <- netmeta(TE, seTE, treat1, treat2, studlab,
                data = Senn2013, sm = "MD", reference = "plac")

# Network graph with default settings
#
netgraph(net1)

The SROC, or summary receiver operating characteristic, curve relates the between-study heterogeneity and the sensitivity and specificity of diagnostic test studies, where specificity is measured on the x-axis while sensitivity is measured on the y-axis. A regular ROC curve plots the relationship between the false positive rate, or when specificity is 1, and the true positive rate, when sensitivity is 1.

The SROC curve plots the specificity and sensitivity from each study in the ROC space to observe the threshold effect in diagnostic studies. The specificity-sensitivity pairs from each study are represented by dots, whose size depends on the size of the study. The line passing through these points, or the SROC curve, is the line of best fit while the dotted 45 degree line is an indicator for the case of complete randomness. The more the dots gravitate toward the top left corner, the better is the sensitivity or true positive rate.

The cross-hair plots show the individual studies in ROC space with paired confidence intervals representing sensitivity and specificity.

library(mada)
data("AuditC")
rs <- rowSums(AuditC)
weights <- 4 * rs / max(rs)
crosshair(AuditC, xlim = c(0,0.6), ylim = c(0.4,1),col = 1:14, lwd = weights)

This PPV & NPV plot jointly display the positive predictive value and the negative predictive value. In this figure, the solid curves are the PPV and NPV; the dotted curves represent the 95% confidence interval. The vertical dashed line is usually used to present a specific prevalence.

####### plots function
ppv.npv.plot.func <- function(fit, title, prev_ttp){
###### prevalence
prev<-c(0, seq(0.0005, 0.9995, 0.0005), 1)

# mmeta method results
mu0 = fit$coefficients[1] # sensitivity
nu0 = fit$coefficients[3] # specificity
covt = fit$vcov[c(1,3), c(1,3)]

# ppv
ppv <- prev * expit(mu0) / (prev * expit(mu0) + (1-prev)*(1-expit(nu0))) 

# npv
npv <- (1-prev) * expit(nu0) / ((1-prev) * expit(nu0) + prev*(1-expit(mu0))) 

# LRP <-mu0-log(1+exp(mu0))-nu0+log(1+exp(nu0))
temp <-matrix(c(1-exp(mu0)/(1+exp(mu0)), -1+exp(nu0)/(1+exp(nu0))), nrow=1)
std.logLRP<-sqrt(temp%*%covt[1:2, 1:2]%*%t(temp))
ppvCI.upper <- expit(logit(ppv)+qnorm(0.975)*as.numeric(std.logLRP))
ppvCI.lower <- expit(logit(ppv)-qnorm(0.975)*as.numeric(std.logLRP))

temp<-matrix(c(-exp(mu0)/(1+exp(mu0)), -exp(nu0)/(1+exp(nu0))), nrow=1)
std.logLRN <- sqrt(temp%*%covt[1:2, 1:2]%*%t(temp))
npvCI.upper <- expit(logit(npv)+qnorm(0.975)*as.numeric(std.logLRN))
npvCI.lower <- expit(logit(npv)-qnorm(0.975)*as.numeric(std.logLRN))

###### values at prev_ttp
index = which(round(prev,4) == prev_ttp)
### ppv
ppv_list = round(c(ppv[index],
ppvCI.lower[index],
ppvCI.upper[index]),2)
### npv
npv_list = round(c(npv[index],
npvCI.lower[index],
npvCI.upper[index]),2)

###### plot
plot(prev,ppv, type="l", xlab="Prevalence", ylab="Predictive Values",
xlim=c(0, 1), ylim=c(0, 1), xaxs="r", yaxs="r", lwd=1,cex=0.8, col = "red")
lines(prev, npv, lty=1, col = "blue")
lines(prev, ppvCI.upper, lty=3, col = "red")
lines(prev, ppvCI.lower, lty=3, col = "red")
lines(prev, npvCI.upper, lty=3, col = "blue")
lines(prev, npvCI.lower, lty=3, col = "blue")
text(0.15, 0.92, "NPV", col = "blue")
text(0.15, 0.20, "PPV", col = "red")
abline(v=prev_ttp, lty=2, lwd=2) 
axis(side = 1, at = prev_ttp)
title(title)
text(0.55, 0.32, paste("When prevalence is 0.35 \nPPV = ",
ppv_list[1]," (",ppv_list[2],",",ppv_list[3],")",
"\nNPV = ", 
npv_list[1]," (",npv_list[2],",",npv_list[3],")", 
sep = ""))
#### specific values
dt_ppv = rbind(prev, ppv, ppvCI.lower, ppvCI.upper)
dt_npv = rbind(prev, npv, npvCI.lower, npvCI.upper)
# list = round(seq(0.09, 1, by = 0.05),4)
list = round(seq(0.10, 0.90, by = 0.10),4)
prev_round = round(prev, 4)
dt_ppv_list = round(dt_ppv[,prev_round %in% list],2)
dt_npv_list = round(dt_npv[,prev_round %in% list],2)


return(list(ppv_list = ppv_list,
npv_list = npv_list,
dt_ppv_list = dt_ppv_list,
dt_npv_list = dt_npv_list))
}

This plot is used to present the estimated sensitivity or specificity with summary points and corresponding confidence region.

A Visualization Tool for Bivariate Meta-Analysis