Estimation In A Competing Risks Proportional Hazards Model Under Length-Biased Sampling With Censoring
Cross-sectional sample, Cumulative incidence function, Functional delta-method, Gaussian process, Lexis diagram, Mixed Poisson process, Nonparametric estimation, Weak convergence
Lifetime Data Analysis
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 t0 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 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. © 2013 Springer Science+Business Media New York.
Department of Mathematics
Original Publication Date
DOI of published version
Dauxois, Jean Yves; Guilloux, Agathe; and Kirmani, Syed N.U.A., "Estimation In A Competing Risks Proportional Hazards Model Under Length-Biased Sampling With Censoring" (2014). Faculty Publications. 1506.