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Title: Joint models for survival and multivariate longitudinal data Authors:  Marcella Mazzoleni - University of Milano Bicocca (Italy)
Mariangela Zenga - Universita degli Studi di Milano-Bicocca -DISMEQ (Italy) [presenting]
Abstract: The joint models analyse the effect of longitudinal covariates onto the risk of one or more events. They are composed of two sub-models, the longitudinal and the survival sub-model. For the longitudinal sub-model a multivariate mixed model can be proposed, considering fixed and random effects. Whereas for the survival sub-model, a Cox proportional hazards model is proposed, considering jointly the influence of two longitudinal covariates onto the risk of the event. The purpose is to extend an estimation method based on a joint likelihood formulation to the case in which the longitudinal sub-model is multivariate. The parameters estimation is based on the maximisation of the likelihood function achieved through the implementation of an Expectation-Maximisation (EM) algorithm. In the M-step a one-step Newton-Raphson update is used, as for some parameters estimators, it is not possible to obtain closed-form expression. In addition, a Gauss-Hermite approximation is applied for some of the integrals involved.