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.
KeywordsMarkov Chain Model Chronological Time Crude Survival Nonparametric Maximum Likelihood Estimator Compete Risk Data
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- Aalen, O. and Johansen, S. (1978), “An Empirical Transition Matrix for Nonhomogeneous Markov Chains Based on Censored Observations,” Scandinavian Journal of Statistics, 5, 141–150.Google Scholar
- Andersen, P. Borgan, O., Gill, R. and Keiding, N. (1993) Statistical Models Based on Counting Processes New York: Springer-Verlag.Google Scholar
- Cox, D.R. (1972), “Regression Models and Life Tables (with discussion),” Journal of the Royal Statistical Society, Series B 34, 187–220.Google Scholar
- Dambrosia, J.M. (1993), Personal communication.Google Scholar
- Keiding, N. (1991), “Age-specific Incidence and Prevalence: a Statistical Perspective,” Jour-nal of the Royal Statistical Society, Series A 154, 371–412.Google Scholar
- Kopylev, L. and Slud, E. (1994), “Aalen-Johansen Estimators for Marginal Survival Functions in Highly Stratified Competing Risk Data with Time-dependent Covariates,” Technical report in preparation.Google Scholar
- Murray, S. and Tsiatis, A. (1993), “A Nonparametric Approach to Incorporating Prognostic Longitudinal Covariate Information in Survival Estimation,” ENAR Invited Talk, April 1994.Google Scholar
- Schatzkin, A. and Slud, E. (1989), “ Competing Risks Bias Arising from an Omitted Risk Factor,” American Journal of Epidemiology, 129, 850–856.Google Scholar
- Yang, G. and He, S. (1994), “ Estimating Lifetime Distribution Under Different Sampling Plans,” Statistical Decision Theory and Related Topics, New York: Springer-Verlag, 73–87.Google Scholar