Faculty Publications

Estimation In A Competing Risks Proportional Hazards Model Under Length-Biased Sampling With Censoring

Document Type

Article

Keywords

Cross-sectional sample, Cumulative incidence function, Functional delta-method, Gaussian process, Lexis diagram, Mixed Poisson process, Nonparametric estimation, Weak convergence

Journal/Book/Conference Title

Lifetime Data Analysis

Volume

20

Issue

2

First Page

276

Last Page

302

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 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

Department of Mathematics

Original Publication Date

1-1-2014

DOI of published version

10.1007/s10985-013-9248-6

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