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Evaluation of treatment efficacy using a Bayesian mixture piecewise linear model of longitudinal biomarkers
Author(s) -
Zhao Lili,
Feng Dai,
Neelon Brian,
Buyse Marc
Publication year - 2015
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.6445
Subject(s) - piecewise linear function , bayesian probability , prostate cancer , piecewise , function (biology) , prostate specific antigen , linear model , computer science , trajectory , mathematics , statistics , medicine , cancer , biology , mathematical analysis , geometry , evolutionary biology , physics , astronomy
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.