Zhao Lili, Feng Dai, Neelon Brian, Buyse Marc
Department of Biostatistics, University of Michigan, Ann Arbor, 48109, MI, U.S.A.
Stat Med. 2015 May 10;34(10):1733-46. doi: 10.1002/sim.6445. Epub 2015 Jan 29.
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.
前列腺特异性抗原（PSA）是前列腺癌患者临床试验中广泛使用的标志物。我们开发了一种混合模型来估计前列腺癌患者接受治疗后的PSA纵向轨迹。该模型通过两种函数的混合来拟合对治疗有反应和无反应的患者。有反应者由分段线性函数描述，该函数由截距、PSA下降率、PSA下降期和PSA上升率表示；无反应者由具有截距和PSA上升率的递增线性函数描述。每个轨迹以一定概率被分类为线性或分段线性函数，这两个函数的加权平均值充分表征了各种PSA轨迹模式。此外，这种混合结构使我们能够得出临床上有用的终点指标，如反应率和疾病进展时间，以及生物学上有意义的终点指标，如癌细胞杀伤分数和肿瘤生长延迟。我们将我们的模型与文献中最常用的动态模型进行比较，并展示了其优势。最后，我们使用来自两项多中心前列腺癌试验的数据说明了我们的方法。用于生成本文分析结果的R代码可根据要求提供。
