\title{individual participant data (ipd) from five studies on uro-vaxom in urinary tract infections}
\description{individual participant data (ipd) of 601 patients from 5 studies comparing uro-vaxom versus placebo in recurrent urinary tract infections (uti) based on the numbers of recurrences experienced.}
\format{the data frame contains the following columns (one row per patient):
\bold{study}       \tab \code{factor}  \tab study identifier \cr
\bold{treatment}   \tab \code{factor}  \tab treatment (uro-vaxom or placebo) \cr
\bold{recurrences} \tab \code{numeric} \tab number of recurrences (relapses)
huber et al. (2000) jointly analyzed data from five randomized, placebo-controlled studies investigating the use of \emph{om-89} (uro-vaxom) in recurrent urinary tract infections (uti). treatment efficacy was evaluated based on the numbers of recurrences experienced by study participants.
the eventual analysis was carried out based on nonparametric wilcoxon-mann-whitney (wmw) tests applied for each study individually and then synthesizing the five resulting test statistic values. the wmw test statistics may be expressed in terms of \emph{common language effect sizes} (cles), that is, the estimated probability that a patient in the treatment group has a better outcome than a control patient.
huber, m., krauter, k., winkelmann, g., bauer, h. w., rahlfs, v. w., lauener, p. a., bleßmann, g. s. s., & bessler, w. g. (2000). immunostimulation by bacterial components: ii. efficacy studies and meta-analysis of the bacterial extract om-89. \emph{international journal of immunopharmacology}, \bold{22}(12), 1103--1111. \verb{https://doi.org/10.1016/s0192-0561(00)00070-9}
# compute wmw statistics for all 5 studies
# convert wmw statistics into estimated probability of superiority
prob <- wmw / (patients[,1]*patients[,2])
medicine, proportions, individual participant data)

\title{studies on deep-brain stimulation in patients with parkinson's disease}
\description{results from 46 studies examining the effects of deep-brain stimulation on motor skills of patients with parkinson's disease.}
\bold{study}      \tab \code{character}  \tab (first) author and year \cr
\bold{y1i}        \tab \code{numeric}    \tab observed mean difference at 3 months \cr
\bold{v1i}        \tab \code{numeric}    \tab sampling variance of the mean difference at 3 months \cr
\bold{y2i}        \tab \code{numeric}    \tab observed mean difference at 6 months \cr
\bold{v2i}        \tab \code{numeric}    \tab sampling variance of the mean difference at 6 months \cr
\bold{y3i}        \tab \code{numeric}    \tab observed mean difference at 12 months \cr
\bold{v3i}        \tab \code{numeric}    \tab sampling variance of the mean difference at 12 months \cr
\bold{y4i}        \tab \code{numeric}    \tab observed mean difference at the long-term follow-up \cr
\bold{v4i}        \tab \code{numeric}    \tab sampling variance of the mean difference at the long-term follow-up \cr
\bold{mdur}       \tab \code{numeric}    \tab mean disease duration (in years) \cr
\bold{mbase}      \tab \code{numeric}    \tab mean baseline updrs score
deep-brain stimulation (dbs), which is delivered through thin surgically implanted wires in specific areas of the brain and controlled by the patient, is meant to provide relief of the debilitating symptoms of parkinson's disease. the dataset includes the results from 46 studies examining the effects of dbs of the subthalamic nucleus on motor functioning, measured with the unified parkinson's disease rating scale (updrs). the effect size measure for this meta-analysis was the mean difference of the scores while the stimulator is active and the baseline scores (before implantation of the stimulator). since lower scores on the updrs indicate better functioning, negative numbers indicate improvements in motor skills. effects were generally measured at 3, 6, and 12 months after implantation of the stimulator, with some studies also including a further long-term follow-up. however, the number of measurements differed between studies - hence the missing data on some of the measurement occasions.
since the same patients were followed over time within a study, effect size estimates from multiple measurement occasions are likely to be correlated. a multivariate model accounting for the correlation in the effects can be used to meta-analyze these data. a difficulty with this approach is the lack of information about the correlation of the measurements over time in the individual studies. the approach taken by ishak et al. (2007) was to assume an autoregressive (ar1) structure for the estimates within the individual studies. in addition, the correlation in the true effects was modeled, again using an autoregressive structure.
ishak, k. j., platt, r. w., joseph, l., hanley, j. a., & caro, j. j. (2007). meta-analysis of longitudinal studies. \emph{clinical trials}, \bold{4}(5), 525--539. \verb{https://doi.org/10.1177/1740774507083567}
dat <- reshape(dat, direction="long", idvar="study", v.names=c("yi","vi"),
### remove missing measurement occasions from dat
### construct the full (block diagonal) v matrix with an ar(1) structure
### assuming an autocorrelation of 0.97 as estimated by ishak et al. (2007)
v <- vcalc(vi, cluster=study, time1=time, phi=0.97, data=dat)
with(dat, interaction.plot(time, study, yi, type="b", pch=19, lty="solid", xaxt="n",
legend=false, xlab="time point", ylab="mean difference", bty="l"))
### multivariate model with heteroscedastic ar(1) structure for the true effects
res <- rma.mv(yi, v, mods = ~ 0 + factor(time), random = ~ time | study,
medicine, raw mean differences, longitudinal models