A new gamma frailty joint modeling approach for recurrent event and terminal event

In this article, we propose a new joint gamma frailty mod eling approach for recurrent event data with informative ter minal event by adopting a new type of double exponential Cox model to the terminal event. The proposed model over comes the drawback that the marginal effects of covariates die out over time in gamma frailty Cox models. A sieve max imum likelihood approach is carried out for parameter esti mation, and the Bernstein polynomials are employed to ap proximate the non-decreasing cumulative baseline functions. The EM algorithm is utilized for optimization. Asymptotic properties of the estimators are provided. Simulation stud ies are conducted to evaluate the finite sample behavior of the proposed estimators. A real dataset of readmissions of patients diagnosed with colorectal cancer is analyzed for il lustration.