  Meta-analysis aggregates information across related studies to provide more
reliable statistical inference and has been a vital tool for assessing the
safety and efficacy of many high profile pharmaceutical products. A key
challenge in conducting a meta-analysis is that the number of related studies
is typically small. Applying classical methods that are asymptotic in the
number of studies can compromise the validity of inference, particularly when
heterogeneity across studies is present. Moreover, serious adverse events are
often rare and can result in one or more studies with no events in at least one
study arm. Practitioners often apply arbitrary continuity corrections or remove
zero-event studies to stabilize or define effect estimates in such settings,
which can further invalidate subsequent inference. To address these significant
practical issues, we introduce an exact inference method for comparing event
rates in two treatment arms under a random effects framework, which we coin
"XRRmeta". In contrast to existing methods, the coverage of the confidence
interval from XRRmeta is guaranteed to be at or above the nominal level (up to
Monte Carlo error) when the event rates, number of studies, and/or the
within-study sample sizes are small. Extensive numerical studies indicate that
XRRmeta does not yield overly conservative inference and we apply our proposed
method to two real-data examples using our open source R package.
