An application of targeted maximum likelihood estimation to the meta-analysis of safety data

Safety analysis to estimate the effect of a treatment on an adverse event poses a challenging statistical problem even in randomized controlled trials because these events are typically rare, so studies originally powered for efficacy are underpowered for safety outcomes. A meta-analysis of data pooled across multiple studies may increase power, but missingness in the outcome or failed randomization can introduce bias. This article illustrates how targeted maximum likelihood estimation (TMLE) can be applied in a meta-analysis to reduce bias in causal effect estimates, and compares performance with other estimators in the literature. A simulation study in which missingness in the outcome is at random or completely at random highlights the differences in estimators with respect to the potential gains in bias and efficiency. Risk difference, relative risk, and odds ratio of the effect of treatment on 30-day mortality are estimated from data from eight randomized controlled trials. When an outcome event is rare there may be little opportunity to improve efficiency, and associations between covariates and the outcome may be hard to detect. TMLE attempts to exploit the available information to either meet or exceed the performance of a less sophisticated estimator.