New Lifetime Regression Model with Application to Prostate Cancer Data

Abstract

A new five-parameter extended fatigue lifetime model named the Weibull generalized gamma distribution is introduced, which generalizes different distributions widely used in survival and reliability analysis. Different mathematical properties are presented, such as stochastic representation, quantiles, minimum, stochastic orders, closedform expressions for the expectation, and Kullback-Leibler divergence. We estimate the model parameters by maximum likelihood. A Monte Carlo simulation is performed to study the asymptotic normality of the estimates. Further, we propose an extended regression model based on the logarithm of this distribution with two systematic components suitable for censored data, especially in the oncology area, as shown in the analysis of a prostate cancer dataset.