Nonlinear Mixed-Effect Models for Prostate-Specific Antigen Kinetics and Link with Survival in the Context of Metastatic Prostate Cancer: a Comparison by Simulation of Two-Stage and Joint Approaches

Abstract

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 modeling 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.

Modeling the Relationship Between Exposure to Abiraterone and Prostate-Specific Antigen Dynamics in Patients with Metastatic Castration-Resistant Prostate Cancer

“…Many recent modeling studies offer thoughtful and detailed analyses of the relationship between PSA dynamics and survival in prostate cancer [25,26,32]; however, these analyses do not consider the exposure-response relationship, only use either simulated data or a previously developed pharmacokinetic model based on pooled data from unrelated, smaller or earlier-phase clinical trials, or are focused on earlier prostate cancer disease states. Our model builds on the previous literature by evaluating the PSA dynamics for an agent targeting androgen biosynthesis for CRPC treatment, a therapeutic strategy that has become increasingly important for this patient population and for which an exposure-survival relationship through PSA dynamics has not been fully described.…”

A Tumor Growth Inhibition Model Based on M‐Protein Levels in Subjects With Relapsed/Refractory Multiple Myeloma Following Single‐Agent Carfilzomib Use

“…We developed the tumor size model first (TGI model), estimated ECTS, and then developed the OS model. Joint modeling is theoretically better, as it is estimating model parameters from a joint likelihood that combines uncertainty in parameter estimates . In this work, we therefore did not take into account the uncertainty in ECTS prediction in the OS model.…”

A Review of Modeling Approaches to Predict Drug Response in Clinical Oncology

“…Recently, Desmée, et al32 using a simulation approach showed that joint modeling of PSA kinetics and survival time produces a precise estimation of PSA time-course and survival parameters, compared with two simplified alternatives, two-stage and joint sequential models. They suggested the developed method as a way to improve treatment prediction and evaluation in oncology.…”

“…2 depicts a schematic diagram of the model used in the work by Desmée, et al32 In the absence of treatment, it is assumed that prostatic cancer cells, C , proliferate with rate Kprol and eliminate with rate Kd . PSA is produced and secreted with rate Kp and eliminated from the blood with rate Ke .…”