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Correlated Positive Stable Frailty Models Based on Reversed Hazard Rate

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  • David D. Hanagal

    (Savitribai Phule Pune University)

Abstract

Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyze the bivariate data on related survival times (e.g., matched pairs’ experiments, twin, or family data), the shared frailty models were suggested. Shared frailty models are used despite their limitations. To overcome their disadvantages, correlated frailty models may be used. In this paper, we introduce the correlated positive stable frailty models based on reversed hazard rate with three different baseline distributions namely, the generalized log-logistic type I, the generalized log-logistic type II, and the modified inverse Weibull. We introduce the Bayesian estimation procedure using Markov-Chain Monte-Carlo (MCMC) technique to estimate the parameters involved in these models. We present a simulation study to compare the true values of the parameters with the estimated values. We also apply the proposed models to the Australian twin dataset, and a better model is suggested.

Suggested Citation

  • David D. Hanagal, 2022. "Correlated Positive Stable Frailty Models Based on Reversed Hazard Rate," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 14(1), pages 42-65, April.
    • Handle: RePEc:spr:stabio:v:14:y:2022:i:1:d:10.1007_s12561-021-09313-7
    DOI: 10.1007/s12561-021-09313-7
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    References listed on IDEAS

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    1. Kheiri, Soleiman & Kimber, Alan & Reza Meshkani, Mohammad, 2007. "Bayesian analysis of an inverse Gaussian correlated frailty model," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5317-5326, July.
    2. Hanagal, David D. & Pandey, Arvind, 2014. "Gamma shared frailty model based on reversed hazard rate for bivariate survival data," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 190-196.
    3. Jason P. Fine & David V. Glidden & Kristine E. Lee, 2003. "A simple estimator for a shared frailty regression model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 317-329, February.
    Full references (including those not matched with items on IDEAS)

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