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 Markov illness-death MSM and the frailty-based Markov illness-death MSM. For interpretation purposes, risk contrasts under the MSMs are defined. Inference under the illness-death MSM can be carried out using estimating equations with inverse probability weighting, while inference under the frailty-based illness-death 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.