Parametric Regression Approach for Gompertz Survival Times with Competing Risks

Regression models play a vital role in the study of data regarding survival of subjects. The Cox proportional hazards model for regression analysis has been frequently used in survival modelling. In survival studies, it is also possible that survival time may occur with multiple occurrences of event or competing risks. The situation of competing risks arises when there are more than one mutually exclusive causes of death (or failure) for the person (or subject). In this paper, we developed a parametric regression model using Gompertz distribution via the Cox proportional hazards model with competing risks. We discussed point and interval estimation of unknown parameters and cumulative cause-specific hazard function with maximum-likelihood method and Bayesian method of estimation. The Bayes estimates are obtained based on non-informative priors and symmetric as well as asymmetric loss functions. To observe the finite sample behaviour of the proposed model under both estimation procedures, we carried out a Monte Carlo simulation analysis. To demonstrate our methodology, we also included real data analysis.