Mathematical Model Predicts Outcomes in Prostate Cancer Therapy

May 1, 2020

The model was able to use data from each treatment cycle to estimate intratumor subpopulations and accurately predict the outcomes in each subsequent cycle.

A study published in Nature Communications demonstrated that a mathematical model based on cellular dynamics in prostate cancer can have a highly predictive power in a retrospective data set from patients with biochemically recurrent prostate cancer undergoing intermittent androgen deprivation therapy (IADT).1

Particularly, researchers demonstrated that the model can use data from each treatment cycle to estimate intratumor subpopulations and accurately predict the outcomes in each subsequent cycle. Additionally, in patients who are predicted to fail therapy in the next cycle the model could help predict alternative treatments for which a response would be more likely.

“Fully harnessing the potential of intermittent prostate cancer therapy requires identifying ADT resistance mechanisms, predicting individual responses and determining potentially highly patient-specific, clinically actionable triggers for pausing and resuming intermittent-ADT cycles,” study lead author Renee Brady, PhD, a post-doctoral fellow in the Department of Integrated Mathematical Oncology at Moffitt, said in a press release.2

The researchers simulated prostate-specific antigen (PSA) dynamics with enrichment of prostate cancer stem-like cells (PCaSC) during treatment as a plausible mechanism of resistance evolution. Simulated PCaSC proliferation patterns were then correlated with longitudinal serum PSA measurements in 70 patients with prostate cancer.

By integrating data that becomes available with each additional treatment cycle to adaptively inform tumor population dynamics in a leave-one-out study, the model simulations were able to predict patient-specific evolution of resistance with an overall accuracy of 89% (sensitivity, 73%; specificity, 91%). 

“Model simulations based on response dynamics from the first IADT cycle identify patients who would benefit from concurrent docetaxel, demonstrating the feasibility and potential value of adaptive clinical trials guided by patient-specific mathematical models of intratumoral evolutionary dynamics,” the authors wrote. 

The study analysis produced 4 important clinical findings, according to the researchers, including:

  • PSA dynamics provide actionable triggers for prostate cancer treatment personalization, vis-à-vis static PSA values with largely debated clinical utility.

  • IADT outcomes in prior studies might be adversely affected by the long induction periods that accelerate selection for treatment-resistant populations.

  • Patient-specific PSA treatment threshold relative to pretreatment burden rather than a fixed value for all patients may significantly improve IADT responses.

  • Early treatment response dynamics during IADT could identify patients that may benefit from concurrent docetaxel treatment and, possibly more importantly, identify patients who are adequately treated with IADT alone.

“Our study demonstrated the value of ongoing model simulations in predicting outcomes from each treatment cycle throughout the course of therapy,” the authors wrote. “This ability to learn from early treatment cycles and predict subsequent responses adds an essential degree of personalization and flexibility to a cancer treatment protocol – a game theoretic strategy termed Bellman’s Principle of Optimality that greatly increases the physician’s advantage.”

Notably, model validation demonstrated that with 2 uniform parameters learned from the training cohort, only 63% of the data were accurately captured in the testing cohort. Although this might be perceived as a limitation, the researchers suggest that the primary objective of the study was to develop a predictive model that could be clinically actionable, not to fit data with the highest accuracy. 

“Allowing for more patient-specific parameters substantially increases data fit but compromises the ability to predict cycle-by-cycle dynamics as insufficient data are collected to inform each model parameter on a per-patient basis,” the authors wrote. “As additional data become available, the developed framework may be generalizable and able to predict how [patients with prostate cancer] of different stages will respond to IADT with comparable accuracy. Further work in patients with more advanced or metastatic [prostate cancer] is needed.”


1. Brady-Nicholls R, Nagy JD, Gerke TA, et al. Prostate-specific antigen dynamics predict individual responses to intermittent androgen deprivation. Nature Communications. doi:10.1038/s41467-020-15424-4.

2. Moffitt Researchers Develop Mathematical Model to Predict Patient Outcomes to Adaptive Prostate Cancer Therapy [news release]. Tampa, Florida. Published April 9, 2020. Accessed April 14, 2020.