A new type of double exponential Cox model with a gamma frailty

Cox model is the most popular model for analyzing survival data. Gamma frailty is a commonly used method for modeling the heterogeneity of subjects. However, under the gamma frailty model, the marginal hazard would have effects of covariates dying out as time t tends to infinity. To overcome this defect of the gamma frailty model, we propose a new type of double exponential gamma frailty Cox model which allows covariates having different effects on the hazard functions at early times and latter. A sieve maximum likelihood estimation procedure is carried out and the Bernstein polynomials are employed to approximate the nondecreasing cumulative baseline functions. The consistency and asymptotically normality of the resulting estimators are derived with detailed proofs. Numerical simulation studies are conducted to evaluate finite sample performances of the proposed estimators. Finally, an application to a set of survival data of the chronic heart failure patients from the University of Virginia Health System is provided for illustration.

Duke Scholars

Author Mengqi Xie