Zhao L, Banerjee M
Biostatistics Unit University of Michigan Comprehensive Cancer Center, University of Michigan, Ann Arbor.
Department of Biostatistics University of Michigan, Ann Arbor.
Comput Stat Data Anal. 2012 Feb 1;56(2):362-369. doi: 10.1016/j.csda.2011.07.011.
Racial differences in prostate cancer incidence and mortality have been reported. Several authors hypothesize that African Americans have a more rapid growth rate of prostate cancer compared to Caucasians, that manifests in higher recurrence and lower survival rates in the former group. In this paper we propose a Bayesian piecewise mixture model to characterize PSA progression over time in African Americans and Caucasians, using follow-up serial PSA measurements after surgery. Each individual's PSA trajectory is hypothesized to have a latent phase immediately following surgery followed by a rapid increase in PSA indicating regrowth of the tumor. The true time of transition from the latent phase to the rapid growth phase is unknown, and can vary across individuals, suggesting a random change point across individuals. Furthermore, some patients may not experience the latent phase due to the cancer having already spread outside the prostate before undergoing surgery. We propose a two-component mixture model to accommodate patients both with and without a latent phase. Within the framework of this mixture model, patients who do not have a latent phase are allowed to have different rates of PSA rise; patients who have a latent phase are allowed to have different PSA trajectories, represented by subject-specific change points and rates of PSA rise before and after the change point. The proposed Bayesian methodology is implemented using Markov Chain Monte Carlo techniques. Model selection is performed using deviance information criteria based on the observed and complete likelihoods. Finally, we illustrate the methods using a prostate cancer dataset.
已有报道称前列腺癌的发病率和死亡率存在种族差异。几位作者推测，与白种人相比，非裔美国人的前列腺癌生长速度更快，这表现为前者更高的复发率和更低的生存率。在本文中，我们提出了一种贝叶斯分段混合模型，以利用手术后的随访系列前列腺特异性抗原（PSA）测量值来描述非裔美国人和白种人随时间的PSA进展情况。假设每个个体的PSA轨迹在手术后立即有一个潜伏期，随后PSA迅速升高，表明肿瘤复发。从潜伏期到快速生长阶段的真正转变时间是未知的，并且可能因个体而异，这表明个体间存在随机变化点。此外，一些患者可能由于癌症在手术前已经扩散到前列腺以外而没有经历潜伏期。我们提出了一种双组分混合模型来适应有和没有潜伏期的患者。在这个混合模型的框架内，没有潜伏期的患者被允许有不同的PSA上升速率；有潜伏期的患者被允许有不同的PSA轨迹，由个体特异性变化点以及变化点前后的PSA上升速率表示。所提出的贝叶斯方法使用马尔可夫链蒙特卡罗技术来实现。基于观察到的和完整的似然性，使用偏差信息准则进行模型选择。最后，我们使用一个前列腺癌数据集来说明这些方法。
