On the estimation of hazard rate in mixed populations with its application

Abstract

Mixture of survival and hazard functions have been widely applied to the analysis of data from heterogeneous populations. From the Bayesian point of view, two different predictive mixture hazard rates can be considered: prior and posterior predictive hazard rates. In this paper, we consider a heterogeneous population consists of two sub-populations with different hazard rates where each one follows a Cox proportional hazards model. A prior predictive mixture hazard model is proposed to estimate the hazard rate of the population through the assessment of some potential regression covariates. Under right-censoring, the estimating equations based on martingale are developed to estimate the parameters of the assumed mixture model. The large sample properties of the proposed estimators are established. The finite sample behavior of the resulting estimators is evaluated through simulation studies, and the approach is also applied to a kidney cancer data set collected from a clinical trial.

Keywords:

• Geometric mixture
• heterogeneous populations
• martingale estimating equations
• predictive mixture hazard rate
• proportional hazards model