title: Evaluation of treatment efficacy using a Bayesian mixture piecewise linear model of longitudinal biomarkers.
abstract: 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.
authors: Department of Biostatistics, University of Michigan, Ann Arbor, 48109, MI, U.S.A.
authors: Lili
authors: L
authors: Zhao
authors: Dai
authors: D
authors: Feng
authors: Brian
authors: B
authors: Neelon
authors: Marc
authors: M
authors: Buyse
mesh_terms: D001499:Bayes Theorem; D014408:Biomarkers, Tumor / Q000097:blood*; D002986:Clinical Trials as Topic / Q000706:statistics & numerical data*; D003198:Computer Simulation; D018450:Disease Progression; D023381:Endpoint Determination; D006801:Humans; D016014:Linear Models; D008137:Longitudinal Studies; D008297:Male; D008390:Markov Chains; D009010:Monte Carlo Method; D015337:Multicenter Studies as Topic / Q000706:statistics & numerical data; D017430:Prostate-Specific Antigen / Q000097:blood* / Q000187:drug effects; D011471:Prostatic Neoplasms / Q000097:blood* / Q000188:drug therapy / Q000473:pathology; D016896:Treatment Outcome
chemical_list: D014408:Biomarkers, Tumor; D017430:Prostate-Specific Antigen
keywords: Bayesian hierarchical model; PSA; change point; longitudinal data; mixture model; tumor growth profile
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