Exact inference for the random-effect model for meta-analyses with rare events

Meta-analysis allows for the aggregation of results from multiple studies to improve statistical inference for the parameter of interest. In recent years, random-effect meta-analysis has been employed to synthesize estimates of incidence rates of adverse events across heterogeneous clinical trials to evaluate treatment safety. However, the validity of existing approaches relies on asymptotic approximation as the number of studies becomes large. In practice, a limited number of trials are typically available for analysis. Moreover, adverse events are typically rare; thus, study-specific incidence rate estimates may be unstable or undefined. In this paper, we present a method for construction of an exact confidence interval for the location parameter of the beta-binomial model through inversion of exact tests. The coverage level of the proposed confidence interval is guaranteed to achieve at least the nominal level, regardless of the number of studies or the with-in study sample size, making it particularly applicable to the study of rare-event data.