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 $tf(t)$, 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 consoring 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.
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Jean-Yves Dauxois, Agathe Guilloux, Syed N.U.A. Kirmani. Estimation in a Competing Risks Proportional Hazards Model Under Length-biased Sampling With Censoring. Lifetime Data Analysis, Springer Verlag, 2014, 20 (2), pp.276-302. ⟨10.1007/s10985-013-9248-6⟩. ⟨hal-00605669⟩

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