[R-meta] Question regarding metarate calling the Poisson model for meta-analysis

[Viechtbauer, Wolfgang (SP)]

Dear Roel,

I can't quite follow exactly what you are tying to do or have done.

"We wanted to use the random effects, to account for different cumulative time periods of follow-up." This sounds like you want some kind of model that includes multiple random effects, at multiple levels (e.g., a random effect at the estimate level (for overdispersion) and a random effect at some higher level to account for clustering / a multilevel structure). rma.glmm() is not set up for that. In this case, you can just use glmer() from lme4 directly.

"The pooled results however, showed confidence limits that differed significantly when we compared these to exact Poisson 95% CIs that we calculated separately." Are you talking about CIs for the individual rates or for the pooled result? If you already have an exact CI for the pooled result, then why bother with metarate(), rma.glmm(), or glmer()? But if you are talking about the individual rates: The CIs are constructed are typically Wald-type CIs (possibly on a transformed scale and then back-transformed). So these can differ from exact CIs computed directly based on a Poisson distribution. For example:

summary(escalc(measure="IR", xi=10, ti=500))[c("ci.lb", "ci.ub")]
summary(escalc(measure="IRLN", xi=10, ti=500), transf=exp)[c("ci.lb", "ci.ub")]
summary(escalc(measure="IRS", xi=10, ti=500), transf=\(x) x^2)[c("ci.lb", "ci.ub")]

And comparing those against the exact CI:

round(c(poisson.test(10, 500)$conf.int), 4)

Note that these CIs are typically just used in a forest plot for visualization of the individual studies/estimates. They are not used in the actual meta-analysis. So even though the CIs may not be 'exact', they do convey approximately the uncertainty in the different estimates and how these uncertainties differ from each other.

If you prefer to show exact CIs in a forest plot, you can do that as follows:

dat <- dat.nielweise2008
dat <- escalc(measure="IRLN", xi=x1i, ti=t1i, data=dat, slab=paste0(authors, ", ", year))

res <- rma(yi, vi, data=dat)

par(mfrow=c(1,2))

forest(res, refline=NA, transf=exp, digits=3, psize=1, header=TRUE)

# compute the 'exact' CIs
cis <- tapply(dat, dat$study, FUN = \(x) poisson.test(x$x1i, x$t1i)$conf.int)
cis <- do.call(rbind, cis)

# set up the forest plot using the exact CIs for the individual rates
dat <- escalc(measure="IR", xi=x1i, ti=t1i, data=dat, slab=paste0(authors, ", ", year))
forest(dat$yi, ci.lb=cis[,1], ci.ub=cis[,2], refline=NA, digits=3, psize=1, header=TRUE, ylim=c(-1.5,res$k+3))
abline(h=0)

# add the estimate from the model
pred <- predict(res, transf=exp)
addpoly(pred$pred, ci.lb=pred$ci.lb, ci.ub=pred$ci.ub, row=-1)

I put the two forest plots side-by-side to illustrate how they differ. Note that one cannot construct the forest plot on some transformed scale such that the CIs will be symmetric when using the exact CIs, so you will end up with these skewed-looking CIs, as opposed to:

forest(res, refline=NA, atransf=exp, digits=3, psize=1, header=TRUE)

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Willems, R.P.J. (Roel)
>Sent: Friday, 18 March, 2022 9:23
>To: 'r-sig-meta-analysis using r-project.org'
>Subject: [R-meta] Question regarding metarate calling the Poisson model for meta-
>analysis
>
>Dear all,
>
>We are conducting a systematic review and meta-analysis to determine the risk of
>infection in previously-colonized patients with multidrug-resistant
>microorganisms. Using metarate, we have tried to call the random intercept
>Poisson regression model (Stijnen et al., 2010) from the R package metafor in
>order to pool cumulative incidence (proportions). We wanted to use the random
>effects, to account for different cumulative time periods of follow-up. The
>pooled results however, showed confidence limits that differed significantly when
>we compared these to exact Poisson 95% CIs that we calculated separately. Is it
>possible to use your R package to perform meta-analyses using the Poisson-based
>approach, with a random effect for follow-up time to account for variations in
>cumulative time period per individual study. We aimed to yield point estimates
>and 95% CIs for the cumulative incidence (not using any risk ratios or comparator
>groups).
>
>We would like to inquire whether it is possible to conduct the intended meta-
>analysis using this package? Otherwise, could you inform us on a good alternative
>approach?
>
>Best,
>Roel
>
>R.P.J. Willems MD
>Medical Microbiology and Infection Prevention AII | Location AMC |
>L1-247 | Meibergdreef 9, 1105 HZ Amsterdam
>E: r.willems using amsterdamumc.nl<mailto:r.willems using amsterdamumc.nl>
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