Shared random-effect models for the joint analysis of longitudinal and time-to-event data: application to the prediction of prostate cancer recurrence

In the last decade, joint modeling research has expanded very rapidly in bio- statistics and medical research. This type of models enables the simultaneous study of a longitudinal marker and a correlated time-to-event. Among them, the shared random-effect models that define a mixed model for the longitudinal marker and a survival model for the time-to-event including characteristics of the mixed model as covariates received the main interest. Indeed, they extend naturally the survival model with time-dependent covariates and offer a flexible framework to explore the link between a longitudinal biomarker and a risk of event. The objective of this paper is to briefly review the shared random-effect model methodology and detail its implementation and evaluation through a real example from the study of prostate cancer progression after a radiation therapy. In particular, different specifications of the dependency between the longitudinal biomarker, the prostate-specific antigen (PSA), and the risk of clinical recurrence are investigated to better understand the link between the PSA dynamics and the risk of clinical recurrence. These different joint models are compared in terms of goodness-of-fit and adequation to the joint model assumptions but also in terms of predictive accuracy using the expected prognostic cross-entropy. Indeed, in addition to better understand the link between the PSA dynamics and the risk of clinical recurrence, the perspective in prostate cancer studies is to provide dynamic prognostic tools of clinical recurrence based on the biomarker history