  In metastatic castration-resistant prostate cancer (mCRPC) clinical trials,
the assessment of treatment efficacy essentially relies on the time-to-death
and the kinetics of prostate-specific antigen (PSA). Joint modelling has been
increasingly used to characterize the relationship between a time-to-event and
a biomarker kinetics but numerical difficulties often limit this approach to
linear models. Here we evaluated by simulation the capability of a new feature
of the Stochastic Approximation Expectation-Maximization algorithm in Monolix
to estimate the parameters of a joint model where PSA kinetics was defined by a
mechanistic nonlinear mixed-effect model. The design of the study and the
parameter values were inspired from one arm of a clinical trial. Increasingly
high levels of association between PSA and survival were considered and results
were compared with those found using two simplified alternatives to joint
model, a two-stage and a joint sequential model. We found that joint model
allowed for a precise estimation of all longitudinal and survival parameters.
In particular the effect of PSA kinetics on survival could be precisely
estimated, regardless of the strength of the association. In contrast, both
simplified approaches led to bias on longitudinal parameters and two-stage
model systematically underestimated the effect of PSA kinetics on survival. In
summary we showed that joint model can be used to characterize the relationship
between a nonlinear kinetics and survival. This opens the way for the use of
more complex and physiological models to improve treatment evaluation and
prediction in oncology.
