Double robust estimation in longitudinal marginal structural models

In this article we consider estimation of causal parameters in a marginal structural model for the discrete intensity of the treatment specific counting process (e.g. hazard of a treatment specific survival time) based on longitudinal observational data on treatment, covariates and survival. We define three estimators: the inverse probability of treatment weighted (IPTW) estimator, the maximum likelihood estimator (MLE), and a double robust (DR) estimator. The DR estimator is obtained by following a general methodology for constructing double robust estimating functions in censored data models as described in van der Laan and Robins (Unified Methods for Censored Longitudinal Data and Causality, 2002). The double-robust estimator is consistent and asymptotically linear when either the treatment mechanism or the partial likelihood of the observed data is consistently estimated. We illustrate the superiority of the DR estimator relative to the IPTW and ML estimators in a simulation study. The proposed methodology is also applied to estimate the causal effect of exercise on physical functioning in a longitudinal study of seniors in Sonoma County.