Marginal Structural Illness-Death Models for Semi-Competing Risks Data

The three-state illness death model has been established as a general approach for regression analysis of semi-competing risks data. For observational data the marginal structural models (MSM) are a useful tool, under the potential outcomes framework to define and estimate parameters with causal interpretations. In this paper we introduce a class of marginal structural illness death models for the analysis of observational semi competing risks data. We consider two specific such models, the usual Markov illness death MSM and the general Markov illness death MSM where the latter incorporates a frailty term. For interpretation purposes, risk contrasts under the MSMs are defined. Inference under the usual Markov MSM can be carried out using estimating equations with inverse probability weighting, while inference under the general Markov MSM requires a weighted EM algorithm. We study the inference procedures under both MSMs using extensive simulations, and apply them to the analysis of mid-life alcohol exposure on late life cognitive impairment as well as mortality using the Honolulu-Asia Aging Study data set. The R codes developed in this work have been implemented in the R package semicmprskcoxmsm that is publicly available on CRAN.