A Bayesian approach to Cox-Gompertz model

Year 2016, Volume: 45 Issue: 5, 1621 - 1640, 01.10.2016

Nihal Ata Tutkun , Haydar Demirhan

Abstract

Survival analysis has a wide application area from medicine to marketing and Cox model takes an important part in survival analysis. When the distribution of survival data is known or it is appropriate to assume a survival distribution, use of a parametric form of Cox model is employed. In this article, we take into account Cox-Gompertz model from the Bayesian perspective. Considering the difficulties in parameter estimation in classical setting, we propose a simple Bayesian approach for Cox-Gompertz model. We derive full conditional posterior distributions of all parameters in Cox-Gompertz model to run Gibbs sampling. Over an extensive simulation study, estimation accuracies of the classical Cox model and classical and Bayesian settings of Cox-Gompertz model are compared with each other by generating exponential, Weibull, and Gompertz distributed survival data sets. Consequently, if survival data follows Gompertz distribution, most accurate parameter estimates are obtained by the Bayesian setting of Cox-Gompertz model. We also provide a real data analysis to illustrate our approach. In the data analysis, we observe the importance of use of the most accurate model over the survival probabilities of censored observations.

Keywords

Gompertz, Cox model, Gibbs sampling, Bayesian analysis, full conditional, Newton-Raphson, parametric model

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