A Review on Joint Modelling of Longitudinal Measurements and Time-To-Even

Abstract

In longitudinal studies subjects are measured for one or more response variable, over time. Although the underlying evolution of such response variables is continuous in time, in practice the measurements are observed at discrete time points. In longitudinal clinical trials it is also common to observe relevant events, generating time-to-event data. If both types of data are available, we might be interested in the association between the two processes, longitudinal and time-to-event. Commonly, when death is considered the event, the observation sequence of longitudinal measurements is terminated by the event process. When the two observed processes are related, the analysis of the data set should be suited to the specific objectives. We distinguish three situations: if the interest is to analyse the longitudinal outcome response variable with drop-out at the time-to-event; to analyse time-to-event, whilst exploiting correlation with a noisy version of a time-varying risk factor; or to analyse the relationship between the two processes. Joint models assume a full distribution for the joint distribution of longitudinal and time-to-event processes, which includes a description of the relation between the two processes.