Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: A Bayesian analysis of mixed survival modelst | 505 Genet Sei Evol 1996 28 505-529 Elsevier INRA Original article - A Bayesian analysis of mixed survival models V Ducrocq 1 G Casella2 1 Department of Animal Science Cornell University 2 Biometrics Unit Cornell University Ithaca NY 14852 USA Received 13 August 1996 accepted 1 October 1996 Summary - In proportional hazards models the hazard of an animal A t ie its probability of dying or being culled at time t given it is alive prior to t is described as A t Ao t ew 0 where Ao t is a baseline hazard function and ew 0 represents the effect of covariates w on culling rate. A distribution can be attached to elements Sq in 0 identifying for example genetic effects and leading to mixed survival models also called frailty models. To estimate the parameters T of the distribution of frailty terms a Bayesian analysis is proposed. Inferences are drawn from the marginal posterior density tt t which can be derived from the joint posterior density via Laplacian integration a powerful technique related to saddlepoint approximations. The validity of this technique is shown here on simulated examples by comparing the resulting approximate tt t to the one obtained by algebraic integration. This exact calculation is feasible in very specific cases only whereas the saddlepoint approximation can be applied to situations where A0 t is arbitrary Cox models or parametric eg Weibull where the frailty terms are correlated through a known relationship matrix or in more general models with stratification and or time-dependent covariates. The influence of the censoring rate and the data structure is also illustrated. survival analysis mixed model variance component estimation Bayesian analysis proportional hazards model Resume Une analyse bayésienne des modèles de survie mixtes. Dans le cas des modèles à risques proportionnels la fonction de risque d un animal A t c est-à-dire sa probabilite de mourir OU d etre reforme au temps t sachant qu il est vivant juste avant t a la forme A t A0 t ew e
