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RETRACTED ARTICLE: Positive Stable Shared Frailty Models Based on Additive Hazards

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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 experiment, twin or family data), the shared frailty models were suggested. These models are based on the assumption that frailty acts multiplicatively to hazard rate. In this paper, we assume that frailty acts additively to hazard rate. We introduce the positive stable shared frailty models with three different baseline distributions namely, the generalized log-logistic and the generalized Weibull distributions. We introduce the Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in these models. We apply these models to a real-life bivariate survival data set of McGilchrist and Aisbett (Biometrics 47:461–466, 1991) related to the kidney infection data and a better model is suggested for the data.

Suggested Citation

  • David D. Hanagal, 2021. "RETRACTED ARTICLE: Positive Stable Shared Frailty Models Based on Additive Hazards," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(3), pages 431-453, December.
    • Handle: RePEc:spr:stabio:v:13:y:2021:i:3:d:10.1007_s12561-020-09299-8
    DOI: 10.1007/s12561-020-09299-8
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    References listed on IDEAS

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    1. Hanagal, David D., 2010. "Modeling heterogeneity for bivariate survival data by the compound Poisson distribution with random scale," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1781-1790, December.
    2. David D. Hanagal & Susmita M. Bhambure, 2017. "Modeling Australian twin data using shared positive stable frailty models based on reversed hazard rate," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(8), pages 3754-3771, April.
    3. 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.
    4. Guosheng Yin & Jianwen Cai, 2004. "Additive hazards model with multivariate failure time data," Biometrika, Biometrika Trust, vol. 91(4), pages 801-818, December.
    5. David D. Hanagal & Richa Sharma, 2015. "Analysis of Bivariate Survival Data using Shared Inverse Gaussian Frailty Model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(7), pages 1351-1380, April.
    6. 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.
    7. David D. Hanagal & Susmita M. Bhambure, 2017. "Shared gamma frailty models based on reversed hazard rate for modeling Australian twin data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(12), pages 5812-5826, June.
    8. David D. Hanagal & Susmita M. Bhambure, 2016. "Modeling bivariate survival data using shared inverse Gaussian frailty model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(17), pages 4969-4987, September.
    9. David W.Hosmer & Patrick Royston, 2002. "Using Aalen's linear hazards model to investigate time-varying effects in the proportional hazards regression model," Stata Journal, StataCorp LP, vol. 2(4), pages 331-350, November.
    10. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
    11. Bacon, Robert W, 1993. "A Note on the Use of the Log-Logistic Functional Form for Modelling Saturation Effects," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 55(3), pages 355-361, August.
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