Marginal Structural Models to Estimate the Joint Causal Effect of Nonrandomized Treatments

Abstract

Even in the absence of unmeasured confounding factors or model misspecification, standard methods for estimating the causal effect of time-varying treatments on survival are biased when (a) there exists a time-dependent risk factor for survival that also predicts subsequent treatment, and (b) past treatment history predicts subsequent risk factor level. In contrast, methods based on marginal structural models (MSMs) can provide consistent estimates of causal effects when unmeasured confounding and model misspecification are absent. MSMs are a new class of causal models whose parameters are estimated using a new class of estimators—inverse-probability-of-treatment weighted estimators. We use a marginal structural Cox proportional hazards model to estimate the joint effect of zidovudine (AZT) and prophylaxis therapy for Pneumocystis carinii pneumonia on the survival of HIV-positive men in the Multicenter AIDS Cohort Study, an observational study of homosexual men. We obtained an estimated causal mortality rate (hazard) ratio of .67 (conservative 95% confidence interval .46-.98) for AZT and of 1.14 (.79, 1.64) for prophylaxis therapy. These estimates will be consistent for the true causal rate ratios when the functional forms chosen for our models are correct and data have been obtained on all time-independent and time-dependent covariates that predict both subsequent treatment and mortality.

KEY WORDS:

• Causal inference
• Confounding
• Counterfactual variables
• Dependent censoring
• Intermediate variables
• Semiparametric models
• Survival analysis