Marginal structural models (MSM) provide a powerful tool for estimating the causal effect of a treatment, particularly in the context of longitudinal data structures. These models, introduced by Robins, model the marginal distributions of treatment-specific counterfactual outcomes, possibly conditional on a subset of the baseline covariates. However, standard MSM cannot incorporate modification of treatment effects by time-varying covariates. In the context of clinical decision- making such time-varying effect modifiers are often of considerable interest, as they are used in practice to guide treatment decisions for an individual. In this article we introduce a generalization of marginal structural models, which we call history-adjusted marginal structural models (HA-MSM). These models allow estimation of adjusted causal effects of treatment, given the observed past, and are therefore more suitable for making treatment decisions at the individual level and for identification of time-dependent effect modifiers. We provide a practical introduction to HA-MSM relying on an example drawn from the treatment of HIV, and discuss parameters estimated, assumptions, and implementation using standard software.
Petersen, Maya L. and van der Laan, Mark J., "History-Adjusted Marginal Structural Models: Time-Varying Effect Modification" (April 2005). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 173.