Dependent competing risks with time-dependent covariates

This paper discusses two mechanisms with time-dependent covariates for dependence between competing-risk latent failure times under which the marginal survival functions are identifiable. The first is the finite-state nonhomogeneous Markov chain with two absorbing failure states, A and B, where ''marginal survival function for A'' is the probability that failure due to A does not occur before t when transitions to B are suppressed. Even in highly stratified models, the nonparametric survival estimator due to Aalen & Johansen (1978) is readily computable when transitions between each pair (i,j) states can occur only in one direction. A second mechanism of dependence, which hits apparently not been noted before, is cross-sectional sampling of a population with time-dependent eovariates and independent latent-failure variables measured on some time-scale other than study-time. The dependence is related to the ''bias'' implicit in oversampling individuals with long durations in covariate states before occurrence of study endpoints.