Evaluation of treatment efficacy using a Bayesian mixture piecewise linear model of longitudinal biomarkers

• Published in: Statistics in medicine Vol. 34; no. 10; pp. 1733 - 1746
• Main Authors: Zhao, Lili, Feng, Dai, Neelon, Brian, Buyse, Marc
• Format: Journal Article
• Language: English
• Published: England Blackwell Publishing Ltd 10.05.2015; Wiley Subscription Services, Inc
• Subjects: Antigens; Bayes Theorem; Bayesian analysis; Bayesian hierarchical model; Biomarkers; Biomarkers, Tumor - blood; change point; Clinical trials; Clinical Trials as Topic - statistics & numerical data; Computer Simulation; Disease Progression; Endpoint Determination; Humans; Linear Models; longitudinal data; Longitudinal Studies; Male; Markov Chains; Mathematical functions; Mathematical models; mixture model; Monte Carlo Method; Multicenter Studies as Topic - statistics & numerical data; Prostate cancer; Prostate-Specific Antigen - blood; Prostate-Specific Antigen - drug effects; Prostatic Neoplasms - blood; Prostatic Neoplasms - drug therapy; Prostatic Neoplasms - pathology; PSA; Treatment Outcome; tumor growth profile; Bayesian hierarchical model; mixture model; tumor growth profile; change point; PSA; longitudinal data
• ISSN: 0277-6715; 1097-0258; 1097-0258
• DOI: 10.1002/sim.6445

Prostate‐specific antigen (PSA) is a widely used marker in clinical trials for patients with prostate cancer. We develop a mixture model to estimate longitudinal PSA trajectory in response to treatment. The model accommodates subjects responding and not responding to therapy through a mixture of two functions. A responder is described by a piecewise linear function, represented by an intercept, a PSA decline rate, a period of PSA decline, and a PSA rising rate; a nonresponder is described by an increasing linear function with an intercept and a PSA rising rate. Each trajectory is classified as a linear or a piecewise linear function with a certain probability, and the weighted average of these two functions sufficiently characterizes a variety of patterns of PSA trajectories. Furthermore, this mixture structure enables us to derive clinically useful endpoints such as a response rate and time‐to‐progression, as well as biologically meaningful endpoints such as a cancer cell killing fraction and tumor growth delay. We compare our model with the most commonly used dynamic model in the literature and show its advantages. Finally, we illustrate our approach using data from two multicenter prostate cancer trials. The R code used to produce the analyses reported in this paper is available on request. Copyright © 2015 John Wiley & Sons, Ltd.