Abstract
In this manuscript, we propose a new mixture shared gamma frailty model based on Gompertz as baseline distribution. The Bayesian approach of Markov Chain Monte Carlo technique was employed to estimate the parameters involved in the models. A simulation study was performed to compare the true values and the estimated values of the parameters. Comparison with the existing model was done by using Bayesian comparison techniques and a better model for the infectious disease data is suggested.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs41096-020-00073-z/MediaObjects/41096_2020_73_Fig1_HTML.png)
Similar content being viewed by others
References
Aalen OO (1980) A model for non-parametric regression analysis of counting processes. In: Klonecki W, Kozek A, Rosinski J (eds) Lecture notes on statistics 2: mathematical statistics and probability theory. Springer, New York
Clayton DG (1978) A model for association in bivariate life tables and its applications to epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65:141–151. https://doi.org/10.1093/biomet/65.1.141
Gelman A, Rubin DB (1992) A single series from the Gibbs sampler provides a false sense of security. In: Bernardo JM, Berger JO, Dawid AP, Smith AFM (eds) Bayesian statistics, vol 4. Oxford Univ. Press, Oxford
Geweke J (1992) Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In: Bernardo JM, Berger JO, Dawid AP, Smith AFM (eds) Bayesian statistics, vol 4. Oxford University Press, Oxford
Gompertz B (1825) On nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philos Trans R Soc Lond 115:513–583. https://doi.org/10.1098/rstl.1825.0026
Hanagal DD, Pandey A (2016) Shared gamma frailty models based on additive hazards. J Indian Soc Probab Stat 17(2):161–184
Ibrahim JG, Chen M-H, Sinha D (2001) Bayesian survival analysis. Springer, New York
Kass RE, Raftery AE (1995) Bayes factors. J Am Stat Assoc 90(430):773–795
Lin DY, Ying Z (1994) Semiparametric analysis of the additive risk model. Biometrica 81(1):61–71
Lin DY, Ying Z (1995) Semiparametric analysis of general additive-multiplicative hazards models for counting processes. Ann Stat 23(5):1712–1734
McGilchrist CA, Aisbett CW (1991) Regression with frailty in survival analysis. Biometrics 47:461–466
Oakes D (1982) A model for association in bivariate survival data. J R Stat Soc B 44:414–422
Parner E (1998) Asymptotic theory for correlated gamma-frailty model. Ann Stat 26:183–214
Sahu SK, Dey DK, Aslanidou H, Sinha D (1997) A Weibull regression model with gamma frailties for multivariate survival data. Life Time Data Anal 3:123–137. https://doi.org/10.1023/A:1009605117713
Santos CA, Achcar JA (2010) A Bayesian analysis for multivariate survival data in the presence of covariates. J Stat Theor Appl 9:233–253
Yin G, Ibrahim JG (2005) A class of Bayesian shared gamma frailty models with multivariate failure time data. Biometrics 61:208–216. https://doi.org/10.1111/j.0006-341X.2005.030826.x
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Pandey, A., Bhushan, S. & Ralte, L. A Mixture Shared Gamma Frailty Model Under Gompertz Baseline Distribution. J Indian Soc Probab Stat 21, 187–200 (2020). https://doi.org/10.1007/s41096-020-00073-z
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41096-020-00073-z