On parametrization, robustness and sensitivity analysis in a marginal structural Cox proportional hazards model for point exposure

In this paper, some new statistical methods are proposed, for making inferences about the parameter indexing a Cox proportional hazards marginal structural model for point exposure. Under the key assumption that unmeasured confounding is absent, we propose a new class of closed-form estimators that are doubly robust in the sense that they remain consistent and asymptotically normal for the effect of treatment provided the marginal structural model is correctly specified and, at least one of the following holds: (i) a model for the treatment assignment mechanism is correctly specified or, (ii) a model for part of the observed data likelihood not involving the treatment assignment mechanism is correctly specified. In order to ensure that condition (ii) provides a genuine opportunity for valid inference, we propose a new parametrization of the observed data law, that is congenial with the marginal proportional hazards assumption. In addition, because the assumption of no unmeasured confounding can seldom be established with certainty with observational data, a second contribution of the current paper is to propose a general framework for estimation without the assumption of no unmeasured confounding. For this purpose, a sensitivity analysis technique is developed, that allows an investigator to assess, under model (i), the extent to which unmeasured confounding may alter inferences about causal effects.