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Estimation in a Competing Risks Proportional Hazards Model Under Length-biased Sampling with Censoring

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  • Jean-Yves Dauxois

    (Crest)

  • Agathe Guilloux

    (Crest)

  • Syed N. U. A. Kirmani

    (Crest)

Abstract

Consider a population of individuals who experience two causes of death.We observe the ones alive at time t0 and follow them until death or possiblecensoring time. Given this length biased sample, we introduce an estimator ofthe survival function of "initial survival times" (i.e. for the entire population)under the assumption of proportional hazards for the two causes of death. Thelarge sample behavior of our estimator is also studied.

Suggested Citation

  • Jean-Yves Dauxois & Agathe Guilloux & Syed N. U. A. Kirmani, 2004. "Estimation in a Competing Risks Proportional Hazards Model Under Length-biased Sampling with Censoring," Working Papers 2004-02, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2004-02
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    References listed on IDEAS

    as
    1. Dauxois, Jean-Yves, 2000. "A new method for proving weak convergence results applied to nonparametric estimators in survival analysis," Stochastic Processes and their Applications, Elsevier, vol. 90(2), pages 327-334, December.
    2. Jens Lund, 2000. "Sampling Bias in Population Studies—How to Use the Lexis Diagram," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 589-604, December.
    3. Cheng, Philip E. & Lin, Gwo Dong, 1987. "Maximum likelihood estimation of a survival function under the koziol-green proportional hazards model," Statistics & Probability Letters, Elsevier, vol. 5(1), pages 75-80, January.
    4. Jean-Yves Dauxois & Agathe Guilloux, 2004. "Estimating the Cumulative incidence Functions under Length-biased Sampling," Working Papers 2004-01, Center for Research in Economics and Statistics.
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