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A Mixture Model for the Regression Analysis of Competing Risks Data

Author

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  • Martin G. Larson
  • Gregg E. Dinse

Abstract

A parametric mixture model provides a regression framework for analysing failure‐time data that are subject to censoring and multiple modes of failure. The regression context allows us to adjust for concomitant variables and to assess their effects on the joint distribution of time and type of failure. The mixing parameters correspond to the marginal probabilities of the various failure types and are modelled as logistic functions of the covariates. The hazard rate for each conditional distribution of time to failure, given type of failure, is modelled as the product of a piece‐wise exponential function of time and a log‐linear function of the covariates. An EM algorithm facilitates the maximum likelihood analysis and illuminates the contributions of the censored observations. The methods are illustrated with data from a heart transplant study and are compared with a cause‐specific hazard analysis. The proposed mixture model can also be used to analyse multivariate failure‐time data.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssc:v:34:y:1985:i:3:p:201-211
    DOI: 10.2307/2347464
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    Cited by:

    1. Beenstock, Michael & Rahav, Giora, 2002. "Testing Gateway Theory: do cigarette prices affect illicit drug use?," Journal of Health Economics, Elsevier, vol. 21(4), pages 679-698, July.
    2. Beilin Jia & Donglin Zeng & Jason J. Z. Liao & Guanghan F. Liu & Xianming Tan & Guoqing Diao & Joseph G. Ibrahim, 2022. "Mixture survival trees for cancer risk classification," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(3), pages 356-379, July.
    3. Rebecca A. Betensky & David A. Schoenfeld, 2001. "Nonparametric Estimation in a Cure Model with Random Cure Times," Biometrics, The International Biometric Society, vol. 57(1), pages 282-286, March.
    4. Xu Ruimin & McNicholas Paul D & Desmond Anthony F & Darlington Gerarda A, 2011. "A First Passage Time Model for Long-Term Survivors with Competing Risks," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-15, May.
    5. 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.
    6. Okumu Argan Wekesa & Mwalili Samuel & Mwita Peter, 2012. "Modelling Credit Risk for Personal Loans Using Product-Limit Estimator," International Journal of Financial Research, International Journal of Financial Research, Sciedu Press, vol. 3(1), pages 22-32, January.
    7. 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.
    8. repec:jss:jstsof:02:i07 is not listed on IDEAS
    9. Contreras-Cristan, Alberto, 2007. "Using the EM algorithm for inference in a mixture of distributions with censored but partially identifiable data," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2769-2781, February.
    10. Cheng Yu, 2009. "Modeling Cumulative Incidences of Dementia and Dementia-Free Death Using a Novel Three-Parameter Logistic Function," The International Journal of Biostatistics, De Gruyter, vol. 5(1), pages 1-19, November.
    11. Yingwei Peng & Keith B. G. Dear, 2000. "A Nonparametric Mixture Model for Cure Rate Estimation," Biometrics, The International Biometric Society, vol. 56(1), pages 237-243, March.
    12. N. Balakrishnan & M. V. Koutras & F. S. Milienos & S. Pal, 2016. "Piecewise Linear Approximations for Cure Rate Models and Associated Inferential Issues," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 937-966, December.
    13. Wycinka Ewa, 2019. "Competing Risk Models of Default in the Presence of Early Repayments," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 23(2), pages 99-120, June.
    14. Sankaran, P.G. & Anisha, P., 2012. "Additive hazards models for gap time data with multiple causes," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1454-1462.
    15. Mo Leo S. F. & Yau Kelvin K. W., 2010. "Survival Mixture Model for Credit Risk Analysis," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 4(2), pages 1-20, July.
    16. Pierpaolo De Blasi & Nils L. Hjort, 2007. "The Bernstein-Von Mises Theorem in Semiparametric Competing Risks Models," ICER Working Papers - Applied Mathematics Series 17-2007, ICER - International Centre for Economic Research.
    17. 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.
    18. S. R. Haile & J.-H. Jeong & X. Chen & Y. Cheng, 2016. "A 3-parameter Gompertz distribution for survival data with competing risks, with an application to breast cancer data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(12), pages 2239-2253, September.

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