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

[Willems, R.P.J. (Roel)]

Dear Prof. Viechtbauer,

Thanks for your prompt reply. Your explanation was very helpful. However, to better clarify my previous question: We aim to pool cumulative proportions (No. of new events during the specified period / Size of population at start of period). We do not aim to pool incidence density (or incidence rate) or incidence rate ratios (IRRs) and we do not use the summed individual person-time for the population of study. 

For pooling the cumulative proportions, we do want to take into account the fact that studies used different time periods for which followed the baseline population at risk. To do so, we tried to use the mixed-Poisson model with a random effect for the different time periods (for example, cumulative proportion at 30 days, at 90 days, etc). This has been reported for incidence rate ratios, but have not found a way to do this for cumulative proportions (Bagos, Pantelis G and Nikolopoulos, Georgios K. "Mixed-Effects Poisson Regression Models for Meta-Analysis of Follow-Up Studies with Constant or Varying Durations" The International Journal of Biostatistics, vol. 5, no. 1, 2009. https://doi.org/10.2202/1557-4679.1168).

Our data already consist of a cumulative proportion with their respective exact 95% Poisson CI for each study.

Best,
Roel


-----Oorspronkelijk bericht-----
Van: Viechtbauer, Wolfgang (SP) <wolfgang.viechtbauer using maastrichtuniversity.nl> 
Verzonden: vrijdag 18 maart 2022 11:44
Aan: Willems, R.P.J. (Roel) <r.willems using amsterdamumc.nl>; 'r-sig-meta-analysis using r-project.org' <r-sig-meta-analysis using r-project.org>
Onderwerp: RE: Question regarding metarate calling the Poisson model for meta-analysis

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 |
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