G-computation Estimation of Nonparametric Causal Effects on Time-Dependent Mean Outcomes in Longitudinal Studies

Two approaches to Causal Inference based on Marginal Structural Models (MSM) have been proposed. They provide different representations of causal effects with distinct causal parameters. Initially, a parametric MSM approach to Causal Inference was developed: it relies on correct specification of a parametric MSM. Recently, a new approach based on nonparametric MSM was introduced. This later approach does not require the assumption of a correctly specified MSM and thus is more realistic if one believes that correct specification of a parametric MSM is unlikely in practice. However, this approach was described only for investigating causal effects on mean outcomes collected at the end of longitudinal studies. In this paper we first generalize the nonparametric MSM approach to the investigation of causal effects on time-dependent outcomes, i.e. for outcomes collected throughout longitudinal studies. This article then develops the G-computation estimation of the corresponding nonparametric MSM parameters and compares its implementation to its analogue in the parametric MSM approach. Finally, we propose new algorithms to address an important computing limitation independent of the MSM approach chosen but inherent to the implementation of the G-computation estimator a) with continuous treatment and/or b) in longitudinal studies with long follow-up and time dependent outcomes. These new algorithms for the implementation of the G-computation estimator lead to a generalization of nonparametric causal effects and should allow broader application of these methodologies in real life studies. Results are illustrated with two simulation studies