Smoothing spline frailty model
Frailty model has been a popular tool to model heterogeneity of individuals in different subpopulations. In the model, an individual's hazard rate depends partly on a frailty term, which is an unobservable random variable and assumed to act multiplicatively on the hazard. In this presentation, we propose a penalized likelihood approach. Via the minimization of a functional consisting of negative full log likelihood and roughness penalty, the baseline hazard function and the frailties are jointly estimated, one nonparametrically by smoothing splines and the other parametrically with log normal distribution. The performance of the model is demonstrated by empirical studies and real data examples.