Title: Correlated gamma frailty models for bivariate survival data based on reversed hazard rate

Authors: David D. Hanagal; Arvind Pandey

Addresses: Department of Statistics, University of Pune, Pune 411007, India ' Department of Statistics, University of Pune, Pune 411007, India

Abstract: Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyse 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 gamma correlated frailty models based on reversed hazard rate (RHR) with three different baseline distributions namely, the generalised log-logistic type I, the generalised 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.

Keywords: Bayesian estimation; correlated gamma frailty; generalised log-logistic distribution type I; generalised log-logistic type II; modified inverse Weibull distribution.

DOI: 10.1504/IJDS.2017.088102

International Journal of Data Science, 2017 Vol.2 No.4, pp.301 - 324

Received: 01 May 2015
Accepted: 30 Sep 2015
Published online: 24 Nov 2017 *

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