Incompatibility between hazard- and logistic-regression in modeling survival data with multiple causes of failure

This paper examines the relationship between outcomes from separate hazard modeling of two competing risks and those based on hazard-modeling of the overall risk combined with logistic-regression on the conditional probability of the risk of interest. The formulation presented in this paper generializes for continuous time models and allows for non-categorical covariates. Our analytical results show that the two approaches are incompatible because they address different issues. Such a straightforward explanation of the incompatibility between the two approaches is expected to prompt investigators to focus on identifying situations of when the issue addressed by each approach may be of substantive interest.[PUBLICATION ABSTRACT]