Two‐stage targeted maximum likelihood estimation for mixed aggregate and individual participant data analysis with an application to multidrug resistant tuberculosis

Abstract

In this study, we develop a new method for the meta‐analysis of mixed aggregate data (AD) and individual participant data (IPD). The method is an adaptation of inverse probability weighted targeted maximum likelihood estimation (IPW‐TMLE), which was initially proposed for two‐stage sampled data. Our methods are motivated by a systematic review investigating treatment effectiveness for multidrug resistant tuberculosis (MDR‐TB) where the available data include IPD from some studies but only AD from others. One complication in this application is that participants with MDR‐TB are typically treated with multiple antimicrobial agents where many such medications were not observed in all studies considered in the meta‐analysis. We focus here on the estimation of the expected potential outcome while intervening on a specific medication but not intervening on any others. Our method involves the implementation of a TMLE that transports the estimation from studies where the treatment is observed to the full target population. A second weighting component adjusts for the studies with missing (inaccessible) IPD. We demonstrate the properties of the proposed method and contrast it with alternative approaches in a simulation study. We finally apply this method to estimate treatment effectiveness in the MDR‐TB case study.