  Joint modelling of longitudinal and time-to-event data has received much
attention recently. Increasingly, extensions to standard joint modelling
approaches are being proposed to handle complex data structures commonly
encountered in applied research. In this paper we propose a joint model for
hierarchical longitudinal and time-to-event data. Our motivating application
explores the association between tumor burden and progression-free survival in
non-small cell lung cancer patients. We define tumor burden as a function of
the sizes of target lesions clustered within a patient. Since a patient may
have more than one lesion, and each lesion is tracked over time, the data have
a three-level hierarchical structure: repeated measurements taken at time
points (level 1) clustered within lesions (level 2) within patients (level 3).
We jointly model the lesion-specific longitudinal trajectories and
patient-specific risk of death or disease progression by specifying novel
association structures that combine information across lower level clusters
(e.g. lesions) into patient-level summaries (e.g. tumor burden). We provide
user-friendly software for fitting the model under a Bayesian framework.
Lastly, we discuss alternative situations in which additional clustering
factor(s) occur at a level higher in the hierarchy than the patient-level,
since this has implications for the model formulation.
