Lunch Seminar Mathematics & Statistics (LSE) - 2020/2021

Interviene: Marcella Mazzoleni, Università di Bergamo

Link: aula virtuale Teams 

Abstract

The joint models analyse the effect of longitudinal covariates onto the risk of an event. 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. Whereas for the survival sub-model, a Cox proportional hazards model is proposed, considering jointly the influence of more than one longitudinal covariate onto the risk of the event.

The purpose of the work is to extend the estimation method based on a joint likelihood formulation to the case in which the longitudinal sub-model is multivariate through the implementation of an Expectation-Maximisation (EM) algorithm which maximises the joint likelihood function, using Newton Raphson update and Gauss-Hermite quadrature rule.

The goodness of fit is tested using some diagnostics elements, such as the estimated survival function and the residuals for both survival and longitudinal sub-models, for instance longitudinal, martingale, deviance, and Cox-Snell residuals. Moreover, dynamic predictions are implemented for the survival and longitudinal sub-model, updating the survival function and the longitudinal trajectories at later points in time.