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Large Sample Properties of Mixture Models with Covariates for Competing Risks

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  • Choi, K. C.
  • Zhou, X.

Abstract

We study the large-sample properties of a class of parametric mixture models with covariates for competing risks. The models allow general distributions for the survival times and incorporate the idea of long-term survivors. Asymptotic results are obtained under a commonly assumed independent censoring mechanism and some modest regularity conditions on the survival distributions. The existence, consistency, and asymptotic normality of maximum likelihood estimators for the parameters of the model are rigorously derived under general sufficient conditions. Specific conditions for particular models can be derived from the general conditions for ready check. In addition, a likelihood-ratio statistic is proposed to test various hypotheses of practical interest, and its asymptotic distribution is provided.

Suggested Citation

  • Choi, K. C. & Zhou, X., 2002. "Large Sample Properties of Mixture Models with Covariates for Competing Risks," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 331-366, August.
    • Handle: RePEc:eee:jmvana:v:82:y:2002:i:2:p:331-366
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    References listed on IDEAS

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    1. Maller, R. A., 1993. "Quadratic Negligibility and the Asymptotic Normality of Operator Normed Sums," Journal of Multivariate Analysis, Elsevier, vol. 44(2), pages 191-219, February.
    2. Ghitany, M. E. & Maller, R. A. & Zhou, S., 1994. "Exponential Mixture Models with Long-Term Survivors and Covariates," Journal of Multivariate Analysis, Elsevier, vol. 49(2), pages 218-241, May.
    3. H. Vu & R. Maller & X. Zhou, 1998. "Asymptotic Properties of a Class of Mixture Models for Failure Data: The Interior and Boundary Cases," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(4), pages 627-653, December.
    4. Martin G. Larson & Gregg E. Dinse, 1985. "A Mixture Model for the Regression Analysis of Competing Risks Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(3), pages 201-211, November.
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    Cited by:

    1. Judex Hyppolite, 2017. "Alternative approaches for econometric modeling of panel data using mixture distributions," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-34, December.
    2. Mioara Alina Nicolaie & Jeremy M. G. Taylor & Catherine Legrand, 2019. "Vertical modeling: analysis of competing risks data with a cure fraction," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 1-25, January.
    3. Angelica Hernandez-Quintero & Jean-François Dupuy & Gabriel Escarela, 2011. "Analysis of a semiparametric mixture model for competing risks," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 305-329, April.

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