Robust Estimation of Inverse Probability Weights for Marginal Structural Models

Marginal structural models (MSMs) are becoming increasingly popular as a tool to make causal inference from longitudinal data. Unlike standard regression models, MSMs can adjust for time-dependent observed confounders while avoiding the bias due to the adjustment for covariates affected by the treatment. Despite their theoretical appeal, a main practical difficulty of MSMs is the required estimation of inverse probability weights. Previous studies have found that MSMs can be highly sensitive to misspecification of treatment assignment model even when the number of time periods is moderate. To address this problem, we generalize the Covariate Balancing Propensity Score (CBPS) methodology of Imai and Ratkovic (2014) to longitudinal analysis settings. The CBPS estimates the inverse probability weights such that the resulting covariate balance is improved. Unlike the standard approach, the proposed methodology incorporates all covariate balancing conditions across multiple time periods. Since the number of these conditions grows exponentially as the number of time period increases, we also propose a low-rank approximation in order to ease the computational burden. Our simulation and empirical studies suggest that the CBPS significantly improves the empirical performance of MSMs by making the treatment assignment model more robust to misspecification. Open-source software is available for implementing the proposed methods.