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