The Semi-Competing Risk Problem Revisited.

Clinical trials and cohort studies often aim to assess treatment effects or exposure associations in relation to the risk of one or more diseases, with death of the study participant as a competing risk. If the diseases under study are major health concerns, it may not be appropriate to assume that death acts as an independent source of right-censoring. When this occurs, a summary of treatment or exposure influences should consider disease incidence and death jointly. Here we consider some modeling approaches to doing so, starting with type-specific (cause-specific) hazard functions. We also model marginal hazard rates for disease-free survival and death, along with their dual outcome hazard functions, with emphasis on Cox models for each hazard function. Furthermore, a simple hazard ratio summary statistic is proposed for covariate effects on disease incidence and death jointly. Analyses of data from the Women's Health Initiative hormone therapy trials provide illustration.