A double exponential gamma-frailty model for clustered survival data

We propose a double exponential gamma-frailty model for clustered survival data. This model addresses the limitation of shared gamma-frailty models, where the marginal effects of covariates diminish over time. To estimate parameters, we utilise a sieve maximum likelihood approach and employ Bernstein polynomials for approximating nondecreasing cumulative baseline functions. The estimators' asymptotic properties are also provided. The proposed method is demonstrated through numerical simulations and survival data from a diabetic retinopathy study and a colorectal cancer study.