Using the SAEM Algorithm for Mechanistic Joint Models Characterizing the Relationship Between Nonlinear PSA Kinetics and Survival in Prostate Cancer Patients

Joint modeling is increasingly popular for investigating the relationship between longitudinal and time-to-event data. However, numerical complexity often restricts this approach to linear models for the longitudinal part. Here, we use a novel development of the Stochastic-Approximation Expectation Maximization algorithm that allows joint models defined by nonlinear mixed-effect models. In the context of chemotherapy in metastatic prostate cancer, we show that a variety of patterns for the Prostate Specific Antigen (PSA) kinetics can be captured by using a mechanistic model defined by nonlinear ordinary differential equations. The use of a mechanistic model predicts that biological quantities that cannot be observed, such as treatment-sensitive and treatment-resistant cells, may have a larger impact than PSA value on survival. This suggests that mechanistic joint models could constitute a relevant approach to evaluate the efficacy of treatment and to improve the prediction of survival in patients.