When to treat prostate cancer patients based on their PSA dynamics

Abstract

This paper provides an innovative approach to help clinicians decide when to start radiation therapy in prostate cancer patients. The decision is based on predictions of the time when the patient's prostate specific antigen (PSA) level reaches its lowest point (nadir). These predictions are based on a log quadratic model for how the PSA level changes over time. The distribution of the time of the PSA nadir (which might be linked to maximal tumor regression) is derived from an approximation to the ratio of two correlated normal random variables. Using a dynamic Kalman filter model, the parameter estimates are updated as new patient information becomes available. Clustering is incorporated to improve prior estimates of the curve parameters. The model balances the risk of beginning radiation therapy too soon so that hormone therapy has not achieved its maximum effect vs. waiting too long to start therapy so that there is an increased risk of tumor cells becoming resistant to the treatment. A comparison of clinically implementable policies (cumulative probability policy and threshold probability policy) based on this new approach is applied to a cohort of prostate cancer patients. It shows that our approach outperforms the current protocol.

Keywords:

• Cancer
• medical decision making
• Kalman filter
• disease modeling
• Bayesian updating
• cluster analysis

Acknowledgements

This work was partially supported by CIHR: New Emerging Team Grant - Access to Quality Cancer Care, the Natural Sciences and Engineering Research Council of Canada, the Itoko Muraoka Fellowship, the Bonder Scholarship for Applied Operations Research in Health Services and the Mathematics of Information Technology and Complex Systems. The authors thank Dr. Steven Shechter and members of the CIHR Team in Operations Research for Improved Cancer Care for their assistance and valuable comments. The authors thank the editors and the two anonymous referees for their helpful suggestions.