Interval estimation of the overall treatment effect in a meta-analysis of a few small studies with zero events

When a meta-analysis consists of a few small trials that report zero events, accounting for heterogeneity in the (interval) estimation of the overall effect is challenging. Typically, we predefine meta-analytical methods to be employed. In practice, data poses restrictions that lead to deviations from the pre-planned analysis, such as the presence of zero events in at least one study arm. We aim to explore heterogeneity estimators behaviour in estimating the overall effect across different levels of sparsity of events. We performed a simulation study that consists of two evaluations. We considered an overall comparison of estimators unconditional on the number of observed zero cells and an additional one by conditioning on the number of observed zero cells. Estimators that performed modestly robust when (interval) estimating the overall treatment effect across a range of heterogeneity assumptions were the Sidik-Jonkman, Hartung-Makambi and improved Paul-Mandel. The relative performance of estimators did not materially differ between making a predefined or data-driven choice. Our investigations confirmed that heterogeneity in such settings cannot be estimated reliably. Estimators whose performance depends strongly on the presence of heterogeneity should be avoided. The choice of estimator does not need to depend on whether or not zero cells are observed.