Statistical Methods of Meta-Analysis for Count Data with Rare Events

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Typical effect measures in meta-analysis of count data are the risk ratio, the odds ratio and risk difference. Meta-analysis of effect measures of count data proceeds as follows. The effect measure is calculated for each component study (partly on the log-scale) accompanied by an estimate of the associated variance. It is then assumed that an approximate normality holds and the tools of meta-analysis are then applied as if these where actually arising from a normal distribution. This approach may be justifiable if both sizes, sample and event sizes, of the component studies are large. However, this becomes evidently flawed in the case of rare events, in the extreme case of no events at all, where some effect measures become undefined and all variance estimates undefined or meaningless. Introduction of smoothing constants will help to avoid undefined estimates but introduce bias instead. Hence, the main theme of the project is to use approaches that are appropriate for the count character of the data and where rare events including zero events are causing not only no problem but are an integral part of the event scale. The model classes considered are the mixed Poisson (for the risk ratio and risk difference) and the mixed logistic regression (for the odds ratio). Here, the study effect is treated as a normally distributed random effect, which is mixed with the appropriate count distribution, the Poisson (for the risk ratio and risk difference) and binomial (for the odds ratio). For the risk ratio and risk difference a particular interesting approach is considered. Using the fact that the conditional distribution of the counts in the experimental group, conditional on the margin of the events, is a binomial distribution, only the parameter of interest are contained as the baseline (control group) parameter get eliminated. Hence, inference can focus on the parameter of interest alone. In these models, the heterogeneity variance, which is the major parameter of interest, is provided as variance of the random effects distribution. This approach will be compared with conventional approaches such as DerSimonian-Laird, REML among others. As an alternative to the conventional chi-square heterogeneity test, a likelihood ratio test is investigated which tests the null hypothesis of homogeneity by setting the variance of the random effects distribution to zero. The mixed Poisson and logistic regression approach will be further generalized to allow inclusion of covariates on study level. In addition, the problem of missing values in one of the groups under comparison will be approached in the mixed effects modelling. Detailed simulation work will investigate and compare the various approaches and, finally, R-packages will be provided which contain the proposed methodology.