Bayesian Versus Frequentist Approach of the Frailty Cox Model, Application to Calf Gastroenteritis

In the frailty Cox model, frequentist approaches often present problems of numerical resolution, convergence, and variance calculation. The Bayesian approach offers an alternative. The goal of this study was to compare, using real (calf gastroenteritis) and simulated data, the results obtained with the MCMC method used in the Bayesian approach versus two frequentist approaches: the Newton–Raphson algorithm to solve a penalized likelihood and the EM algorithm. The results obtained showed that when the number of groups in the population decreases, the Bayesian approach gives a less biased estimation of the frailty variance and of the group fixed effect than the frequentist approaches.