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Revisiting Non-Parametric Maximum Likelihood Estimation of Current Status Data with Competing Risks

Author

Listed:
  • Tamalika Koley

    (Indian Statistical Institute)

  • Anup Dewanji

    (Indian Statistical Institute)

Abstract

Re-parametrization is often done to make a constrained optimization problem an unconstrained one. This paper focuses on the non-parametric maximum likelihood estimation of the sub-distribution functions for current status data with competing risks. Our main aim is to propose a method using re-parametrization, which is simpler and easier to handle with compared to the constrained maximization methods discussed in Jewell and Kalbfleisch (Biostatistics. 5, 291–306, 2004) and Maathuis (2006), when both the monitoring times and the number of individuals observed at these times are fixed. Then the Expectation-Maximization (EM) algorithm is used for estimating the unknown parameters. We have also established some asymptotic results of these maximum likelihood estimators. Finite sample properties of these estimators are investigated through an extensive simulation study. Some generalizations have been discussed.

Suggested Citation

  • Tamalika Koley & Anup Dewanji, 2019. "Revisiting Non-Parametric Maximum Likelihood Estimation of Current Status Data with Competing Risks," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 39-59, June.
    • Handle: RePEc:spr:sankhb:v:81:y:2019:i:1:d:10.1007_s13571-018-0172-3
    DOI: 10.1007/s13571-018-0172-3
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    References listed on IDEAS

    as
    1. Nicholas P. Jewell, 2003. "Nonparametric estimation from current status data with competing risks," Biometrika, Biometrika Trust, vol. 90(1), pages 183-197, March.
    2. Michael G. Hudgens & Glen A. Satten & Ira M. Longini, 2001. "Nonparametric Maximum Likelihood Estimation for Competing Risks Survival Data Subject to Interval Censoring and Truncation," Biometrics, The International Biometric Society, vol. 57(1), pages 74-80, March.
    3. M. H. Maathuis & M. G. Hudgens, 2011. "Nonparametric inference for competing risks current status data with continuous, discrete or grouped observation times," Biometrika, Biometrika Trust, vol. 98(2), pages 325-340.
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