title: Estimation in a competing risks proportional hazards model under length-biased sampling with censoring.
abstract: What population does the sample represent? The answer to this question is of crucial importance when estimating a survivor function in duration studies. As is well-known, in a stationary population, survival data obtained from a cross-sectional sample taken from the population at time t(0) represents not the target density f (t) but its length-biased version proportional to t f (t), for t > 0. The problem of estimating survivor function from such length-biased samples becomes more complex, and interesting, in presence of competing risks and censoring. This paper lays out a sampling scheme related to a mixed Poisson process and develops nonparametric estimators of the survivor function of the target population assuming that the two independent competing risks have proportional hazards. Two cases are considered: with and without independent censoring before length biased sampling. In each case, the weak convergence of the process generated by the proposed estimator is proved. A well-known study of the duration in power for political leaders is used to illustrate our results. Finally, a simulation study is carried out in order to assess the finite sample behaviour of our estimators.
authors: Université de Toulouse-INSA, IMT, UMR CNRS 5219, 135, Avenue de Rangueil, 31077 , Toulouse cedex 4, France, jean-yves.dauxois@insa-toulouse.fr.
authors: Jean-Yves
authors: JY
authors: Dauxois
authors: Agathe
authors: A
authors: Guilloux
authors: Syed N U A
authors: SN
authors: Kirmani
mesh_terms: D015982:Bias; D003198:Computer Simulation; D006801:Humans; D015993:Life Tables; D009010:Monte Carlo Method; D016016:Proportional Hazards Models; D012306:Risk; D018709:Statistics, Nonparametric; D016019:Survival Analysis