Combining meta-analysis with multiple imputation for one-step, privacy-protecting estimation of causal treatment effects in multi-site studies

Missing data complicates statistical analyses in multi-site studies, especially when it is not feasible to centrally pool individual-level data across sites. We combined meta-analysis with within-site multiple imputation for one-step estimation of the average causal effect (ACE) of a target population comprised of all individuals from all data-contributing sites within a multi-site distributed data network, without the need for sharing individual-level data to handle missing data. We considered two orders of combination and three choices of weights for meta-analysis, resulting in six approaches. The first three approaches, denoted as RR + metaF, RR + metaR and RR + std, first combined results from imputed data sets within each site using Rubin's rules and then meta-analyzed the combined results across sites using fixed-effect, random-effects and sample-standardization weights, respectively. The last three approaches, denoted as metaF + RR, metaR + RR and std + RR, first meta-analyzed results across sites separately for each imputation and then combined the meta-analysis results using Rubin's rules. Simulation results confirmed very good performance of RR + std and std + RR under various missing completely at random and missing at random settings. A direct application of the inverse-variance weighted meta-analysis based on site-specific ACEs can lead to biased results for the targeted network-wide ACE in the presence of treatment effect heterogeneity by site, demonstrating the need to clearly specify the target population and estimand and properly account for potential site heterogeneity in meta-analyses seeking to draw causal interpretations. An illustration using a large administrative claims database is presented.