Estimation of multivariate frailty models with varying coefficients

The complicated structures can be modeled more efficiently and their flexibility can be increased through frailty models with varying coefficients.Therefore, such models are proposed in this article. The real challenge is to estimate varying coefficients by the penalized partial likelihood without closed form. The Laplace approximation is used to solve this problem. These varying coefficients are fitted using B-splines. Moreover, the variances of random effects are estimated by maximizing an approximate profile likelihood. The performance of the proposed methods are assessed with simulation studies and real data. The results show that the methods proposed are better than the counterpart in literature.