Morrell Christopher H, Brant Larry J, Sheng Shan, Metter E Jeffrey
Mathematics and Statistics Department, Loyola University Maryland, 4501 North Charles St., Baltimore, MD 21210-2699 USA.
J Appl Stat. 2012 Jun 1;39(6):1151-1175. doi: 10.1080/02664763.2011.644523.
Using several variables known to be related to prostate cancer, a multivariate classification method is developed to predict the onset of clinical prostate cancer. A multivariate mixed-effects model is used to describe longitudinal changes in prostate specific antigen (PSA), a free testosterone index (FTI), and body mass index (BMI) before any clinical evidence of prostate cancer. The patterns of change in these three variables are allowed to vary depending on whether the subject develops prostate cancer or not and the severity of the prostate cancer at diagnosis. An application of Bayes' theorem provides posterior probabilities that we use to predict whether an individual will develop prostate cancer and, if so, whether it is a high-risk or a low-risk cancer. The classification rule is applied sequentially one multivariate observation at a time until the subject is classified as a cancer case or until the last observation has been used. We perform the analyses using each of the three variables individually, combined together in pairs, and all three variables together in one analysis. We compare the classification results among the various analyses and a simulation study demonstrates how the sensitivity of prediction changes with respect to the number and type of variables used in the prediction process.
利用几个已知与前列腺癌相关的变量，开发了一种多变量分类方法来预测临床前列腺癌的发病情况。在出现任何前列腺癌临床证据之前，使用多变量混合效应模型来描述前列腺特异性抗原（PSA）、游离睾酮指数（FTI）和体重指数（BMI）的纵向变化。这三个变量的变化模式允许根据受试者是否患前列腺癌以及诊断时前列腺癌的严重程度而有所不同。贝叶斯定理的应用提供了后验概率，我们用它来预测个体是否会患前列腺癌，如果会，是高危癌症还是低危癌症。分类规则一次对一个多变量观测值依次应用，直到受试者被分类为癌症病例或直到使用了最后一个观测值。我们分别使用这三个变量中的每一个进行分析，将它们两两组合进行分析，以及将所有三个变量一起进行一次分析。我们比较了各种分析之间的分类结果，一项模拟研究展示了预测敏感性如何随着预测过程中使用的变量数量和类型而变化。
