Articles |
A note on cause-specific residual life
Department of Biostatistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, U.S.A. jeong{at}nsabp.pitt.edu
Department of Biostatistics, University of North Carolina, Chapel Hill, North Carolina 27599, U.S.A. jfine{at}bios.unc.edu
Received for publication 1 September 2008.
Revision received 1 October 2008.
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Abstract |
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In medical research, investigators often wish to characterize the distributions of remaining lifetimes. While nonparametric analyses of residual life distributions have been widely studied with independently right-censored data, residual life analysis has not been examined in the competing risks setting, with multiple, potentially dependent, failure types. We define the cause-specific residual life distribution as the residual cumulative incidence function conditionally on survival to a given time. Because of the improper form of the cause-specific distribution, the mean cause-specific residual lifetime does not exist, theoretically. We develop nonparametric inferences for the cause-specific residual life function and its corresponding quantiles, which may exist. Theoretical justification, including uniform consistency and weak convergence, is established. Simulation studies and a breast cancer data analysis demonstrate the practical utility of the methods.
Key Words: Conditional cumulative incidence function • Dependent censoring • Empirical process • Pivotal statistic • Quantile residual life