Title: Modelling bivariate survival data based on reversed hazard rate

Authors: David D. Hanagal; Arvind Pandey

Addresses: Department of Statistics University of Pune Ganeshkhind, 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. The shared frailty models are frequently used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of random factor (frailty) and the baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and distribution of frailty. In this paper, we introduce the shared gamma frailty models with the reversed hazard rate. We introduce the Bayesian estimation procedure using the Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in the model. We present a simulation study to compare the true values of the parameters with the estimated values. Also, we apply the proposed model to Australian twin dataset and suggest a better model.

Keywords: generalised Weibull distribution; Bayesian estimation; log-logistic distribution; Markov Chain Monte Carlo; MCMC; reversed hazard rate; RHR; shared gamma frailty; modelling; bivariate survival data; shared frailty models; survival analysis; simulation; heterogeneity; disease risk; death risk.

DOI: 10.1504/IJMMNO.2015.068907

International Journal of Mathematical Modelling and Numerical Optimisation, 2015 Vol.6 No.1, pp.72 - 100

Received: 24 Jul 2014
Accepted: 22 Oct 2014
Published online: 19 Apr 2015 *

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