dat.viechtbauer2021: Studies to Illustrate Model Checking Methods
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dat.viechtbauer2021 R Documentation
Studies to Illustrate Model Checking Methods
Description
Results from 20 hypothetical randomized clinical trials examining the effectiveness of a medication for treating some disease.
Usage
dat.viechtbauer2021
Format
The data frame contains the following columns:
trial numeric trial number
nTi numeric number of patients in the treatment group
nCi numeric number of patients in the control group
xTi numeric number of patients in the treatment group with remission
xCi numeric number of patients in the control group with remission
dose numeric dosage of the medication provided to patients in the treatment group (in milligrams per day)
Details
The dataset was constructed for the purposes of illustrating the model checking and diagnostic methods described in Viechtbauer (2021). The code below provides the results for many of the analyses and plots discussed in the book chapter.
Concepts
medicine, odds ratios, outliers, model checks
Author(s)
Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org
Source
Viechtbauer, W. (2021). Model checking in meta-analysis. In C. H. Schmid, T. Stijnen, & I. R. White (Eds.), Handbook of meta-analysis (pp. 219-254). Boca Raton, FL: CRC Press. https://doi.org/10.1201/9781315119403
Examples
### copy data into 'dat' and examine data
dat <- dat.viechtbauer2021
dat
## Not run:
### load metafor package
library(metafor)
### calculate log odds ratios and corresponding sampling variances
dat <- escalc(measure="OR", ai=xTi, n1i=nTi, ci=xCi, n2i=nCi, add=1/2, to="all", data=dat)
dat
### number of studies
k <- nrow(dat)
### fit models
res.CE <- rma(yi, vi, data=dat, method="CE") # same as method="EE"
res.CE
res.RE <- rma(yi, vi, data=dat, method="DL")
res.RE
res.MR <- rma(yi, vi, mods = ~ dose, data=dat, method="FE")
res.MR
res.ME <- rma(yi, vi, mods = ~ dose, data=dat, method="DL")
res.ME
### forest and bubble plot
par(mar=c(5,4,1,2))
forest(dat$yi, dat$vi, psize=0.8, efac=0, xlim=c(-4,6), ylim=c(-3,23),
cex=1, width=c(5,5,5), xlab="Log Odds Ratio (LnOR)")
addpoly(res.CE, row=-1.5, mlab="CE Model")
addpoly(res.RE, row=-2.5, mlab="RE Model")
text(-4, 22, "Trial", pos=4, font=2)
text( 6, 22, "LnOR [95% CI]", pos=2, font=2)
abline(h=0)
tmp <- regplot(res.ME, xlim=c(0,250), ylim=c(-1,1.5), predlim=c(0,250), shade=FALSE, digits=1,
xlab="Dosage (mg per day)", psize="seinv", plim=c(NA,5), bty="l", las=1,
lty=c("solid", "dashed"), label=TRUE, labsize=0.8, offset=c(1,0.7))
res.sub <- rma(yi, vi, mods = ~ dose, data=dat, method="DL", subset=-6)
abline(res.sub, lty="dotted")
points(tmp$xi, tmp$yi, pch=21, cex=tmp$psize, col="black", bg="darkgray")
par(mar=c(5,4,4,2))
### number of standardized deleted residuals larger than +-1.96 in each model
sum(abs(rstudent(res.CE)$z) >= qnorm(.975))
sum(abs(rstudent(res.MR)$z) >= qnorm(.975))
sum(abs(rstudent(res.RE)$z) >= qnorm(.975))
sum(abs(rstudent(res.ME)$z) >= qnorm(.975))
### plot of the standardized deleted residuals for the RE and ME models
plot(NA, NA, xlim=c(1,20), ylim=c(-4,4), xlab="Study", ylab="Standardized (Deleted) Residual",
xaxt="n", main="Random-Effects Model", las=1)
axis(side=1, at=1:20)
abline(h=c(-1.96,1.96), lty="dotted")
abline(h=0)
points(1:20, rstandard(res.RE)$z, type="o", pch=19, col="gray70")
points(1:20, rstudent(res.RE)$z, type="o", pch=19)
legend("top", pch=19, col=c("gray70","black"), lty="solid",
legend=c("Standardized Residuals","Standardized Deleted Residuals"), bty="n")
plot(NA, NA, xlim=c(1,20), ylim=c(-4,4), xlab="Study", ylab="Standardized (Deleted) Residual",
xaxt="n", main="Mixed-Effects Model", las=1)
axis(side=1, at=1:20)
abline(h=c(-1.96,1.96), lty="dotted")
abline(h=0)
points(1:20, rstandard(res.ME)$z, type="o", pch=19, col="gray70")
points(1:20, rstudent(res.ME)$z, type="o", pch=19)
legend("top", pch=19, col=c("gray70","black"), lty="solid",
legend=c("Standardized Residuals","Standardized Deleted Residuals"), bty="n")
### Baujat plots
baujat(res.CE, main="Common-Effects Model", xlab="Squared Pearson Residual", ylim=c(0,5), las=1)
baujat(res.ME, main="Mixed-Effects Model", ylim=c(0,2), las=1)
### GOSH plots (skipped because this takes quite some time to run)
if (FALSE) {
res.GOSH.CE <- gosh(res.CE, subsets=10^7)
plot(res.GOSH.CE, cex=0.2, out=6, xlim=c(-0.25,1.25), breaks=c(200,100))
res.GOSH.ME <- gosh(res.ME, subsets=10^7)
plot(res.GOSH.ME, het="tau2", out=6, breaks=50, adjust=0.6, las=1)
}
### plot of treatment dosage against the standardized residuals
plot(dat$dose, rstandard(res.ME)$z, pch=19, xlab="Dosage (mg per day)",
ylab="Standardized Residual", xlim=c(0,250), ylim=c(-2.5,2.5), las=1)
abline(h=c(-1.96,1.96), lty="dotted", lwd=2)
abline(h=0)
title("Standardized Residual Plot")
text(dat$dose[6], rstandard(res.ME)$z[6], "6", pos=4, offset=0.4)
### quadratic polynomial model
rma(yi, vi, mods = ~ dose + I(dose^2), data=dat, method="DL")
### lack-of-fit model
resLOF <- rma(yi, vi, mods = ~ dose + factor(dose), data=dat, method="DL", btt=3:9)
resLOF
### scatter plot to illustrate the lack-of-fit model
regplot(res.ME, xlim=c(0,250), ylim=c(-1.0,1.5), xlab="Dosage (mg per day)", ci=FALSE,
predlim=c(0,250), psize=1, pch=19, col="gray60", digits=1, lwd=1, bty="l", las=1)
dosages <- sort(unique(dat$dose))
lines(dosages, fitted(resLOF)[match(dosages, dat$dose)], type="o", pch=19, cex=2, lwd=2)
points(dat$dose, dat$yi, pch=19, col="gray60")
legend("bottomright", legend=c("Linear Model", "Lack-of-Fit Model"), pch=c(NA,19), col="black",
lty="solid", lwd=c(1,2), pt.cex=c(1,2), seg.len=4, bty="n")
### checking normality of the standardized deleted residuals
qqnorm(res.ME, type="rstudent", main="Standardized Deleted Residuals", pch=19, label="out",
lwd=2, pos=24, ylim=c(-4,3), lty=c("solid", "dotted"), las=1)
### checking normality of the random effects
sav <- qqnorm(ranef(res.ME)$pred, main="BLUPs of the Random Effects", cex=1, pch=19,
xlim=c(-2.2,2.2), ylim=c(-0.6,0.6), las=1)
abline(a=0, b=sd(ranef(res.ME)$pred), lwd=2)
text(sav$x[6], sav$y[6], "6", pos=4, offset=0.4)
### hat values for the CE and RE models
plot(NA, NA, xlim=c(1,20), ylim=c(0,0.21), xaxt="n", las=1, xlab="Study", ylab="Hat Value")
axis(1, 1:20, cex.axis=1)
points(hatvalues(res.CE), type="o", pch=19, col="gray70")
points(hatvalues(res.RE), type="o", pch=19)
abline(h=1/20, lty="dotted", lwd=2)
title("Hat Values for the CE/RE Models")
legend("topright", pch=19, col=c("gray70","black"), lty="solid",
legend=c("Common-Effects Model", "Random-Effects Model"), bty="n")
### heatmap of the hat matrix for the ME model
cols <- colorRampPalette(c("blue", "white", "red"))(101)
h <- hatvalues(res.ME, type="matrix")
image(1:nrow(h), 1:ncol(h), t(h[nrow(h):1,]), axes=FALSE,
xlab="Influence of the Observed Effect of Study ...", ylab="On the Fitted Value of Study ...",
col=cols, zlim=c(-max(abs(h)),max(abs(h))))
axis(1, 1:20, tick=FALSE)
axis(2, 1:20, labels=20:1, las=1, tick=FALSE)
abline(h=seq(0.5,20.5,by=1), col="white")
abline(v=seq(0.5,20.5,by=1), col="white")
points(1:20, 20:1, pch=19, cex=0.4)
title("Heatmap for the Mixed-Effects Model")
### plot of leverages versus standardized residuals for the ME model
plot(hatvalues(res.ME), rstudent(res.ME)$z, pch=19, cex=0.2+3*sqrt(cooks.distance(res.ME)),
las=1, xlab="Leverage (Hat Value)", ylab="Standardized Deleted Residual",
xlim=c(0,0.35), ylim=c(-3.5,2.5))
abline(h=c(-1.96,1.96), lty="dotted", lwd=2)
abline(h=0, lwd=2)
ids <- c(3,6,9)
text(hatvalues(res.ME)[ids] + c(0,0.013,0.010), rstudent(res.ME)$z[ids] - c(0.18,0,0), ids)
title("Leverage vs. Standardized Deleted Residuals")
### plot of the Cook's distances for the ME model
plot(1:20, cooks.distance(res.ME), ylim=c(0,1.6), type="o", pch=19, las=1, xaxt="n", yaxt="n",
xlab="Study", ylab="Cook's Distance")
axis(1, 1:20, cex.axis=1)
axis(2, seq(0,1.6,by=0.4), las=1)
title("Cook's Distances")
### plot of the leave-one-out estimates of tau^2 for the ME model
x <- influence(res.ME)
plot(1:20, x$inf$tau2.del, ylim=c(0,0.15), type="o", pch=19, las=1, xaxt="n", xlab="Study",
ylab=expression(paste("Estimate of ", tau^2, " without the ", italic(i), "th study")))
abline(h=res.ME$tau2, lty="dashed")
axis(1, 1:20)
title("Residual Heterogeneity Estimates")
### plot of the covariance ratios for the ME model
plot(1:20, x$inf$cov.r, ylim=c(0,2.0), type="o", pch=19, las=1, xaxt="n",
xlab="Study", ylab="Covariance Ratio")
abline(h=1, lty="dashed")
axis(1, 1:20)
title("Covariance Ratios")
### fit mixed-effects model without studies 3 and/or 6
rma(yi, vi, mods = ~ dose, data=dat, method="DL", subset=-3)
rma(yi, vi, mods = ~ dose, data=dat, method="DL", subset=-6)
rma(yi, vi, mods = ~ dose, data=dat, method="DL", subset=-c(3,6))
## End(Not run)
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| dat.viechtbauer2021 | R Documentation |
Studies to Illustrate Model Checking Methods
Description
Results from 20 hypothetical randomized clinical trials examining the effectiveness of a medication for treating some disease.
Usage
dat.viechtbauer2021
Format
The data frame contains the following columns:
| trial | numeric | trial number |
| nTi | numeric | number of patients in the treatment group |
| nCi | numeric | number of patients in the control group |
| xTi | numeric | number of patients in the treatment group with remission |
| xCi | numeric | number of patients in the control group with remission |
| dose | numeric | dosage of the medication provided to patients in the treatment group (in milligrams per day) |
Details
The dataset was constructed for the purposes of illustrating the model checking and diagnostic methods described in Viechtbauer (2021). The code below provides the results for many of the analyses and plots discussed in the book chapter.
Concepts
medicine, odds ratios, outliers, model checks
Author(s)
Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org
Source
Viechtbauer, W. (2021). Model checking in meta-analysis. In C. H. Schmid, T. Stijnen, & I. R. White (Eds.), Handbook of meta-analysis (pp. 219-254). Boca Raton, FL: CRC Press. https://doi.org/10.1201/9781315119403
Examples
### copy data into 'dat' and examine data
dat <- dat.viechtbauer2021
dat
## Not run:
### load metafor package
library(metafor)
### calculate log odds ratios and corresponding sampling variances
dat <- escalc(measure="OR", ai=xTi, n1i=nTi, ci=xCi, n2i=nCi, add=1/2, to="all", data=dat)
dat
### number of studies
k <- nrow(dat)
### fit models
res.CE <- rma(yi, vi, data=dat, method="CE") # same as method="EE"
res.CE
res.RE <- rma(yi, vi, data=dat, method="DL")
res.RE
res.MR <- rma(yi, vi, mods = ~ dose, data=dat, method="FE")
res.MR
res.ME <- rma(yi, vi, mods = ~ dose, data=dat, method="DL")
res.ME
### forest and bubble plot
par(mar=c(5,4,1,2))
forest(dat$yi, dat$vi, psize=0.8, efac=0, xlim=c(-4,6), ylim=c(-3,23),
cex=1, width=c(5,5,5), xlab="Log Odds Ratio (LnOR)")
addpoly(res.CE, row=-1.5, mlab="CE Model")
addpoly(res.RE, row=-2.5, mlab="RE Model")
text(-4, 22, "Trial", pos=4, font=2)
text( 6, 22, "LnOR [95% CI]", pos=2, font=2)
abline(h=0)
tmp <- regplot(res.ME, xlim=c(0,250), ylim=c(-1,1.5), predlim=c(0,250), shade=FALSE, digits=1,
xlab="Dosage (mg per day)", psize="seinv", plim=c(NA,5), bty="l", las=1,
lty=c("solid", "dashed"), label=TRUE, labsize=0.8, offset=c(1,0.7))
res.sub <- rma(yi, vi, mods = ~ dose, data=dat, method="DL", subset=-6)
abline(res.sub, lty="dotted")
points(tmp$xi, tmp$yi, pch=21, cex=tmp$psize, col="black", bg="darkgray")
par(mar=c(5,4,4,2))
### number of standardized deleted residuals larger than +-1.96 in each model
sum(abs(rstudent(res.CE)$z) >= qnorm(.975))
sum(abs(rstudent(res.MR)$z) >= qnorm(.975))
sum(abs(rstudent(res.RE)$z) >= qnorm(.975))
sum(abs(rstudent(res.ME)$z) >= qnorm(.975))
### plot of the standardized deleted residuals for the RE and ME models
plot(NA, NA, xlim=c(1,20), ylim=c(-4,4), xlab="Study", ylab="Standardized (Deleted) Residual",
xaxt="n", main="Random-Effects Model", las=1)
axis(side=1, at=1:20)
abline(h=c(-1.96,1.96), lty="dotted")
abline(h=0)
points(1:20, rstandard(res.RE)$z, type="o", pch=19, col="gray70")
points(1:20, rstudent(res.RE)$z, type="o", pch=19)
legend("top", pch=19, col=c("gray70","black"), lty="solid",
legend=c("Standardized Residuals","Standardized Deleted Residuals"), bty="n")
plot(NA, NA, xlim=c(1,20), ylim=c(-4,4), xlab="Study", ylab="Standardized (Deleted) Residual",
xaxt="n", main="Mixed-Effects Model", las=1)
axis(side=1, at=1:20)
abline(h=c(-1.96,1.96), lty="dotted")
abline(h=0)
points(1:20, rstandard(res.ME)$z, type="o", pch=19, col="gray70")
points(1:20, rstudent(res.ME)$z, type="o", pch=19)
legend("top", pch=19, col=c("gray70","black"), lty="solid",
legend=c("Standardized Residuals","Standardized Deleted Residuals"), bty="n")
### Baujat plots
baujat(res.CE, main="Common-Effects Model", xlab="Squared Pearson Residual", ylim=c(0,5), las=1)
baujat(res.ME, main="Mixed-Effects Model", ylim=c(0,2), las=1)
### GOSH plots (skipped because this takes quite some time to run)
if (FALSE) {
res.GOSH.CE <- gosh(res.CE, subsets=10^7)
plot(res.GOSH.CE, cex=0.2, out=6, xlim=c(-0.25,1.25), breaks=c(200,100))
res.GOSH.ME <- gosh(res.ME, subsets=10^7)
plot(res.GOSH.ME, het="tau2", out=6, breaks=50, adjust=0.6, las=1)
}
### plot of treatment dosage against the standardized residuals
plot(dat$dose, rstandard(res.ME)$z, pch=19, xlab="Dosage (mg per day)",
ylab="Standardized Residual", xlim=c(0,250), ylim=c(-2.5,2.5), las=1)
abline(h=c(-1.96,1.96), lty="dotted", lwd=2)
abline(h=0)
title("Standardized Residual Plot")
text(dat$dose[6], rstandard(res.ME)$z[6], "6", pos=4, offset=0.4)
### quadratic polynomial model
rma(yi, vi, mods = ~ dose + I(dose^2), data=dat, method="DL")
### lack-of-fit model
resLOF <- rma(yi, vi, mods = ~ dose + factor(dose), data=dat, method="DL", btt=3:9)
resLOF
### scatter plot to illustrate the lack-of-fit model
regplot(res.ME, xlim=c(0,250), ylim=c(-1.0,1.5), xlab="Dosage (mg per day)", ci=FALSE,
predlim=c(0,250), psize=1, pch=19, col="gray60", digits=1, lwd=1, bty="l", las=1)
dosages <- sort(unique(dat$dose))
lines(dosages, fitted(resLOF)[match(dosages, dat$dose)], type="o", pch=19, cex=2, lwd=2)
points(dat$dose, dat$yi, pch=19, col="gray60")
legend("bottomright", legend=c("Linear Model", "Lack-of-Fit Model"), pch=c(NA,19), col="black",
lty="solid", lwd=c(1,2), pt.cex=c(1,2), seg.len=4, bty="n")
### checking normality of the standardized deleted residuals
qqnorm(res.ME, type="rstudent", main="Standardized Deleted Residuals", pch=19, label="out",
lwd=2, pos=24, ylim=c(-4,3), lty=c("solid", "dotted"), las=1)
### checking normality of the random effects
sav <- qqnorm(ranef(res.ME)$pred, main="BLUPs of the Random Effects", cex=1, pch=19,
xlim=c(-2.2,2.2), ylim=c(-0.6,0.6), las=1)
abline(a=0, b=sd(ranef(res.ME)$pred), lwd=2)
text(sav$x[6], sav$y[6], "6", pos=4, offset=0.4)
### hat values for the CE and RE models
plot(NA, NA, xlim=c(1,20), ylim=c(0,0.21), xaxt="n", las=1, xlab="Study", ylab="Hat Value")
axis(1, 1:20, cex.axis=1)
points(hatvalues(res.CE), type="o", pch=19, col="gray70")
points(hatvalues(res.RE), type="o", pch=19)
abline(h=1/20, lty="dotted", lwd=2)
title("Hat Values for the CE/RE Models")
legend("topright", pch=19, col=c("gray70","black"), lty="solid",
legend=c("Common-Effects Model", "Random-Effects Model"), bty="n")
### heatmap of the hat matrix for the ME model
cols <- colorRampPalette(c("blue", "white", "red"))(101)
h <- hatvalues(res.ME, type="matrix")
image(1:nrow(h), 1:ncol(h), t(h[nrow(h):1,]), axes=FALSE,
xlab="Influence of the Observed Effect of Study ...", ylab="On the Fitted Value of Study ...",
col=cols, zlim=c(-max(abs(h)),max(abs(h))))
axis(1, 1:20, tick=FALSE)
axis(2, 1:20, labels=20:1, las=1, tick=FALSE)
abline(h=seq(0.5,20.5,by=1), col="white")
abline(v=seq(0.5,20.5,by=1), col="white")
points(1:20, 20:1, pch=19, cex=0.4)
title("Heatmap for the Mixed-Effects Model")
### plot of leverages versus standardized residuals for the ME model
plot(hatvalues(res.ME), rstudent(res.ME)$z, pch=19, cex=0.2+3*sqrt(cooks.distance(res.ME)),
las=1, xlab="Leverage (Hat Value)", ylab="Standardized Deleted Residual",
xlim=c(0,0.35), ylim=c(-3.5,2.5))
abline(h=c(-1.96,1.96), lty="dotted", lwd=2)
abline(h=0, lwd=2)
ids <- c(3,6,9)
text(hatvalues(res.ME)[ids] + c(0,0.013,0.010), rstudent(res.ME)$z[ids] - c(0.18,0,0), ids)
title("Leverage vs. Standardized Deleted Residuals")
### plot of the Cook's distances for the ME model
plot(1:20, cooks.distance(res.ME), ylim=c(0,1.6), type="o", pch=19, las=1, xaxt="n", yaxt="n",
xlab="Study", ylab="Cook's Distance")
axis(1, 1:20, cex.axis=1)
axis(2, seq(0,1.6,by=0.4), las=1)
title("Cook's Distances")
### plot of the leave-one-out estimates of tau^2 for the ME model
x <- influence(res.ME)
plot(1:20, x$inf$tau2.del, ylim=c(0,0.15), type="o", pch=19, las=1, xaxt="n", xlab="Study",
ylab=expression(paste("Estimate of ", tau^2, " without the ", italic(i), "th study")))
abline(h=res.ME$tau2, lty="dashed")
axis(1, 1:20)
title("Residual Heterogeneity Estimates")
### plot of the covariance ratios for the ME model
plot(1:20, x$inf$cov.r, ylim=c(0,2.0), type="o", pch=19, las=1, xaxt="n",
xlab="Study", ylab="Covariance Ratio")
abline(h=1, lty="dashed")
axis(1, 1:20)
title("Covariance Ratios")
### fit mixed-effects model without studies 3 and/or 6
rma(yi, vi, mods = ~ dose, data=dat, method="DL", subset=-3)
rma(yi, vi, mods = ~ dose, data=dat, method="DL", subset=-6)
rma(yi, vi, mods = ~ dose, data=dat, method="DL", subset=-c(3,6))
## End(Not run)
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