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A Review on Univariate Bayesian Frailty Models

S.G. Parekh1 , S.R. Patel2

Section:Review Paper, Product Type: Isroset-Journal
Vol.6 , Issue.1 , pp.255-258, Feb-2019


CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.255258


Online published on Feb 28, 2019


Copyright © S.G. Parekh, S.R. Patel . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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IEEE Style Citation: S.G. Parekh, S.R. Patel, “A Review on Univariate Bayesian Frailty Models,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.255-258, 2019.

MLA Style Citation: S.G. Parekh, S.R. Patel "A Review on Univariate Bayesian Frailty Models." International Journal of Scientific Research in Mathematical and Statistical Sciences 6.1 (2019): 255-258.

APA Style Citation: S.G. Parekh, S.R. Patel, (2019). A Review on Univariate Bayesian Frailty Models. International Journal of Scientific Research in Mathematical and Statistical Sciences, 6(1), 255-258.

BibTex Style Citation:
@article{Parekh_2019,
author = {S.G. Parekh, S.R. Patel},
title = {A Review on Univariate Bayesian Frailty Models},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {2 2019},
volume = {6},
Issue = {1},
month = {2},
year = {2019},
issn = {2347-2693},
pages = {255-258},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1171},
doi = {https://doi.org/10.26438/ijcse/v6i1.255258}
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v6i1.255258}
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1171
TI - A Review on Univariate Bayesian Frailty Models
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - S.G. Parekh, S.R. Patel
PY - 2019
DA - 2019/02/28
PB - IJCSE, Indore, INDIA
SP - 255-258
IS - 1
VL - 6
SN - 2347-2693
ER -

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Abstract :
The main idea of this review article is to review different univariate Bayesian frailty model, discussed by some authors, such as estimation of negative binomial distribution with Bayesian prior distribution as beta, Bayesian frailty estimation of Poisson distribution with gamma as frailty prior distribution, Bayesian frailty estimation of gamma distribution with gamma as frailty prior distribution, Bayesian frailty estimation of univariate normal distribution with frailty prior distribution as gamma and Bayesian estimation of inverse Gaussian distribution with uniform prior frailty model. In all these Bayesian estimation squared error loss function is used.

Key-Words / Index Term :
Bayesian frailty model, Bayesian prior distribution, Beta, Negative Binomial, Gamma, Inverse Gaussian, Normal, Poisson, Uniform distribution

References :
[1] Clayton, D., “A model for association in bivariate life tables and its applications to epidemiological studies of familial tendency in chronic disease incidence”, Biometrica, Vol.65, pp.141-151, 1979.
[2] Vaupel JW, Manton KG, Stallard E., “The impact of heterogeneity in individual frailty on the dynamics of mortality”, Demography, Vol.16, pp.439-454, 1979
[3] Cox D., “Regression models and life tables (with discussion)”, Journal of the Royal Statistical Society, Series B, Vol. 34, pp. 187-200, 1972.
[4] Hougaard, P., “Survival models for heterogeneous populations derived from stable distrib¬utions”, Biometrika, Vol. 73, pp.387 – 396, 1986a.
[5] Hougaard, P., “A class of multivariate failure timedistributions”, Biometrika, Vol. 73, pp. 671 – 678, 1986b.
[6] Akaike H, “Information measures and model selection”,Bull. Int. statist. Inst. Vol.50, pp.277-290, 1983.
[7] Le Cam L., “Maximum likelihood: an introduction”, Int.Statist. Rev. Vol.58, pp.153-172, 1990.
[8] Joshi VM., “The censoring concept and the likelihood principle”, J. Statist. Plann. Inference, Vol.26, pp.109- 111, 1990.
[9] Geyer CJ, Thompson EA. “Constrained Monte Carlo maximum likelihood for dependent data (with discussion)”, J. Roy. Statist. Soc., Ser B., Vol.54, pp.657-699, 1992.
[10] Aalen, O.O. “Modelling heterogeneity in survival analysis by the compound Poisson distri¬bution”, Annals of Applied Probability Vol. 4, pp. 951 – 972, 1992.
[11] McGilchrist, C.A., “REML estimation for survival models with frailty”, Biometrics, Vol.49, pp.221-225, 1993.
[12] Yashin, A.I., Vaupel, J.W., Iachine, I.A. “Correlated individual frailty: An advantageous approach to survival analysis of bivariate data”, Working Paper Series: Population Studies of Aging 7, CHS, Odense University, 1993.
[13] Yashin, A.I., Manton, K.G., Iachine, I.A.,“Genetic and environmental factors in duration studies: multivariate frailty models and estimation strategies”, Journal of Epidemiology and Bio-statistics, Vol.1, pp.115 – 120, 1996.
[14] Xue, X., Brookmeyer, R., “Bivariate frailty model for the analysis of multivariate survival time”, Lifetime Data Analysis, Vol. 2, pp. 277 – 290, 1996.
[15] Sahu, K.S., Dey, D.K., Aslanidou, H., Sinha, D., “A Weibull regression model with Gamma frailties for multivariate survival data”, Lifetime Data Analysis, Vol. 3, pp. 123 – 137, 1997.
[16] Yashin, A.I., Begun, A., Iachine, I.A., “Genetic factors in susceptibility to death: a com¬parative analysis of bivariate survival models”, Journal of Epidemiology and Biostatistics, Vol. 4, pp.53-60, 1999a.
[17] Ibrahim, J. G., Chen, M., and Sinha, D., “Bayesian Survival Analysis”, New York: Springer, 2001.
[18] Ripatti, S., Larsen, K., Palmgren, J., “Maximum likelihoodinference for multivariate frailty models using an automated MCEM algorithm”, Lifetime Data Analysis, Vol. 8, pp.349 – 360, 2002.
[19] Iachine, I.,“The Use of Twin and Family Survival Data in the Population Studies of Ag¬ing: Statistical Methods Based on Multivariate Survival Models”, Ph.D. Thesis. Monograph 8, Department of Statistics and Demography, University of Southern Denmark, 2002.
[20] Wienke, A., Lichtenstein, P., Yashin, A.I.,“A bivariate frailty model with a cure fraction for modeling familial correlations in diseases”, Biometrics, Vol.59, pp.1178 – 1183, 2003a.
[21] Santos dos, C. A. and Achcar, J. A., “A Bayesian analysis for multivariate survival data in the presence of covariates”, Journal of Statistical Theory and Applications, Vol. 9, pp.233-253, 2010.
[22] Kheiri, S., Kimber, A., Meshkani M.R., “Bayesian analysis of an inverse Gaussian correlated frailty model”, Computat. Statist. Data Anal, Vol.51, pp.5317-5326, 2007.
[23] Hangal, D., “Modeling survival data using frailty models”, CRC Press, 2011.
[24] Parekh, S.G., Ghosh, D. K. and Patel, S.R., “On frailty models for kidney infection data with exponential baseline distribution”, International Journal of Applied Mathematics & Statistical Sciences (JAMSS), Vol.4, Issue5, pp.31-40, 2015.
[25] Parekh, S.G. Ghosh, D. K. and Patel, S.R., “Some Bayesian Frailty models”, International Journal of Science and Research (IJSR), Vol.5, issue, 7, pp.1949-1952, 2016.
[26] Parekh, S.G. and Patel, S.R., “On estimation of some Univariate Bayesian frailty models”, International Journal of Statistics and Applied Mathematics, Vol.3, issue 2,pp.199-205, 2018.

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