Transformed Gaussian model for joint modelling of longitudinal measurements and time-to-event

Inês Sousa 

University of Minho, Portugal
Lancaster University, UK

Abstract

We propose a model for the joint distribution of a longitudinal variable and a single time-to-event. This model, which we will call joint transformed Gaussian model, assumes a multivariate Gaussian distribution for the vector of repeated measurements expanded with the natural logarithm of failure time. The marginal distribution of time-to-event is log-Normal distributed, as well as the conditional distribution the repeated measurements. The variance covariance structure of this model is of main interest, so we consider different parametric structures for the covariance matrix of the proposed model. We will present an analysis of a data set as an example. Finally, we will discuss the possible extensions of this model in a multivariate setting.