Causal Inference in Longitudinal Studies with History-Restricted Marginal Structural Models

Romain Neugebauer, Division of Biostatistics, School of Public Health, University of California, Berkeley
Mark J. van der Laan, Division of Biostatistics, School of Public Health, University of California, Berkeley
Ira B. Tager, Division of Epidemiology, School of Public Health, University of California, Berkeley

Abstract

Causal Inference based on Marginal Structural Models (MSMs) is particularly attractive to subject-matter investigators because MSM parameters provide explicit representations of causal effects. We introduce History-Restricted Marginal Structural Models (HRMSMs) for longitudinal data for the purpose of defining causal parameters which may often be better suited for Public Health research. This new class of MSMs allows investigators to analyze the causal effect of a treatment on an outcome based on a fixed, shorter and user-specified history of exposure compared to MSMs. By default, the latter represents the treatment causal effect of interest based on a treatment history defined by the treatments assigned between the study's start and outcome collection. Beyond allowing a more flexible causal analysis, the proposed HRMSMs also mitigate computing issues related to MSMs as well as statistical power concerns when designing longitudinal studies. We develop three consistent estimators of HRMSM parameters under sufficient model assumptions: the Inverse Probability of Treatment Weighted (IPTW), G-computation and Double Robust (DR) estimators. In addition, we show that the assumptions commonly adopted for identification and consistent estimation of MSM parameters (existence of counterfactuals, consistency, time-ordering and sequential randomization assumptions) also lead to identification and consistent estimation of HRMSM parameters.