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A Bayesian approach for multi-stage models with linear time-dependent hazard rate

Author

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  • Pham Hoa

    (Mathematical Department, An Giang University; and Vietnam National University, Ho Chi Minh City, Vietnam)

  • Pham Huong T. T.

    (Mathematical Department, An Giang University; and Vietnam National University, Ho Chi Minh City, Vietnam)

Abstract

Multi-stage models have been used to describe progression of individuals which develop through a sequence of discrete stages. We focus on the multi-stage model in which the number of individuals in each stage is assessed through destructive samples for a sequence of sampling time. Moreover, the stage duration distributions of the model are effected by a time-dependent hazard rate. The multi-stage models become complex with a stage having time-dependent hazard rate. The main aim of this paper is to derive analytically the approximation of the likelihood of the model. We apply the approximation to the Metropolis–Hastings (MH) algorithm to estimate parameters for the model. The method is demonstrated by applying to simulated data which combine non-hazard rate, stage-wise constant hazard rate and time-dependent hazard rates in stage duration distributions.

Suggested Citation

  • Pham Hoa & Pham Huong T. T., 2019. "A Bayesian approach for multi-stage models with linear time-dependent hazard rate," Monte Carlo Methods and Applications, De Gruyter, vol. 25(4), pages 307-316, December.
    • Handle: RePEc:bpj:mcmeap:v:25:y:2019:i:4:p:307-316:n:4
    DOI: 10.1515/mcma-2019-2051
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    References listed on IDEAS

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    1. Jonas Knape & Kent M. Daane & Perry de Valpine, 2014. "Estimation of stage duration distributions and mortality under repeated cohort censuses," Biometrics, The International Biometric Society, vol. 70(2), pages 346-355, June.
    2. Hoeting, Jennifer A. & Tweedie, Richard L. & Olver, Christine S., 2003. "Transform Estimation of Parameters for Stage-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 503-514, January.
    3. Hoa Pham & Darfiana Nur & Huong T. T. Pham & Alan Branford, 2019. "A Bayesian approach for parameter estimation in multi-stage models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(10), pages 2459-2482, May.
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    1. Jonas Knape & Kent M. Daane & Perry de Valpine, 2014. "Estimation of stage duration distributions and mortality under repeated cohort censuses," Biometrics, The International Biometric Society, vol. 70(2), pages 346-355, June.

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