In longitudinal studies subjects are measured repeatedly on one or more
response variable, over time. Although the underlying evolution of such
response variables is often continuous in time, in practice the
measurements are observed at discrete time points. Moreover it is of
interest, particularly in longitudinal clinical trials, to test
significant differences between the underlying processes of the same
response variables for different treatment groups. The underlying
longitudinal processes are not observed precisely, as measurements are
subject to error. The main advantage of these studies is to be able to
distinguish between changes over time within individuals, variability
between subjects and pure measurement error. This is only possible
because there is data replication on the sequence of measurements for
each subject. In longitudinal clinical trials it is also common to
observe relevant events, generating time-to-event outcomes. In this
work we will focus on single events. 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 |