Locally Efficient Estimation of Nonparametric Causal Effects on Mean Outcomes in Longitudinal Studies

Marginal Structural Models (MSM) have been introduced by Robins (1998a) as a powerful tool for causal inference as they directly model causal curves of interest, i.e. mean treatment-specific outcomes possibly adjusted for baseline covariates. Two estimators of the corresponding MSM parameters of interest have been proposed, see van der Laan and Robins (2002): the Inverse Probability of Treatment Weighted (IPTW) and the Double Robust (DR) estimators. A parametric MSM approach to causal inference has been favored since the introduction of MSM. It relies on correct specification of a parametric MSM to consistently estimate the parameter of interest using the IPTW or DR estimator. In this paper, we develop an alternative nonparametric MSM approach to causal inference that extends the definition of causal parameters of interest. Such an approach is particularly suitable for investigating causal effects in practice as it does not require the assumption of a correctly specified MSM. We first propose a methodology to generate nonparametric parameters of interest for investigating causal curves in which the treatment is longitudinal. We provide insight on how to interpret these parameters in practice and choose the parameter of interest to best answer the causal question of interest. We also provide two estimators consistent with this approach, i.e. which do not entirely rely, even indirectly, on correct specification of a MSM: the unique IPTW and locally efficient DR estimators. All results are illustrated with a simulation study in which the practical performances of the DR estimators are evaluated for the first time using longitudinal non-survival data. In the last section, we compare the proposed nonparametric MSM approach to causal inference to the more typical parametric MSM approach and contribute to the general understanding of MSM estimation by addressing the issue of MSM misspecification