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.
See Imai, Kosuke and Marc Ratkovic,
(2014). `` Covariate Balancing Propensity
Score,'' Journal of the Royal Statistical Society,
Series B (Statistical Methodology), Vol. 76, No. 1 (January),
pp. 243-263. which introduces the basic idea of CBPS in the
cross-section setting. |