Random‐effects meta‐analysis for systematic reviews of phase I clinical trials: Rare events and missing data

Phase I trials aim to establish appropriate clinical and statistical parameters to guide future clinical trials. With individual trials typically underpowered, systematic reviews and meta‐analysis are desired to assess the totality of evidence. A high percentage of zero or missing outcomes often complicate such efforts. We use a systematic review of pediatric phase I oncology trials as an example and illustrate the utility of advanced Bayesian analysis. Standard random‐effects methods rely on the exchangeability of individual trial effects, typically assuming that a common normal distribution sufficiently describes random variation among the trial level effects. Summary statistics of individual trial data may become undefined with zero counts, and this assumption may not be readily examined. We conduct Bayesian semi‐parametric analysis with a Dirichlet process prior and examine the assumption. The Bayesian semi‐parametric analysis is also useful for visually summarizing individual trial data. It provides alternative statistics that are computed free of distributional assumptions about the shape of the population of trial level effects. Outcomes are rarely entirely missing in clinical trials. We utilize available information and conduct Bayesian incomplete data analysis. The advanced Bayesian analyses, although illustrated with the specific example, are generally applicable. © 2016 The Authors. Research Synthesis Methods Published by John Wiley & Sons Ltd.