bayesmeta (version 3.4)

BaetenEtAl2013: Ankylosing spondylitis example data

Description

Numbers of cases (patients) and events (responders) in the placebo control groups of eight studies.

Usage

data("BaetenEtAl2013")

Format

The data frame contains the following columns:

study	character	study label
year	numeric	publication year
events	numeric	number of responders
total	numeric	total number of patients

Details

A study was conducted in order to investigate a novel treatment in ankylosing spondylitis (Baeten et al., 2013). The primary endpoint related to treatment response. In order to formulate an informative prior distribution for the response rate to be expected in the control group of the new study, a systematic review of previous studies was consulted (McLeod et al., 2007), and, after a meta-analysis of the estimated response probabilities, the predictive distribution for the new study's response probability was derived. The predictive distribution here constitutes the meta-analytic-predictive (MAP) prior distribution (Schmidli et al., 2014). The data set contains the relevant data from the eight “historical” studies' placebo groups.

Note that the original analysis (Baeten et al., 2013) involved a binomial model, and the resulting posterior predictive distribution was eventually approximated by a mixture of beta distributions.

References

C. McLeod et al. Adalimumab, etanercept, and infliximab for the treatment of ankylosing spondylitis: a systematic review and economic evaluation. Health Technology Assessment, 11(28), 2007. tools:::Rd_expr_doi("10.3310/hta11280").

H. Schmidli, S. Gsteiger, S. Roychoudhury, A. O'Hagan, D. Spiegelhalter, B. Neuenschwander. Robust meta-analytic-predictive priors in clinical trials with historical control information. Biometrics, 70(4):1023-1032, 2014. tools:::Rd_expr_doi("10.1111/biom.12242").

See Also

uisd, ess.

Examples

# load data:
data("BaetenEtAl2013")

# show data:
BaetenEtAl2013

if (FALSE) {
# compute effect sizes (logarithmic odds) from the count data:
as <- escalc(xi=events, ni=total, slab=study,
             measure="PLO", data=BaetenEtAl2013)

# compute the unit information standard deviation (UISD):
uisd(as)

# perform meta-analysis
# (using uniform priors for effect and heterogeneity):
bm <- bayesmeta(as)

# show results (log-odds):
forestplot(bm, xlab="log-odds", zero=NA)
# show results (odds):
forestplot(bm, exponentiate=TRUE, xlab="odds", zero=NA)

# show posterior predictive distribution --
# in terms of log-odds:
bm$summary[,"theta"]
logodds <- bm$summary[c(2,5,6), "theta"]
logodds
# in terms of odds:
exp(logodds)
# in terms of probabilities:
(exp(logodds) / (exp(logodds) + 1))

# illustrate MAP prior density:
x <- seq(-3, 1, by=0.01)
plot(x, bm$dposterior(theta=x, predict=TRUE), type="l",
     xlab="log-odds (response)", ylab="posterior predictive density")
abline(h=0, v=0, col="grey")
}