Department of Biostatistics, Mailman School of Public Health, Columbia University, New York, NY 10032, USA.
Stat Med. 2010 Jun 15;29(13):1391-410. doi: 10.1002/sim.3876.
The predictiveness curve is a graphical tool that characterizes the population distribution of Risk(Y)=P(D=1|Y), where D denotes a binary outcome such as occurrence of an event within a specified time period and Y denotes predictors. A wider distribution of Risk(Y) indicates better performance of a risk model in the sense that making treatment recommendations is easier for more subjects. Decisions are more straightforward when a subject's risk is deemed to be high or low. Methods have been developed to estimate predictiveness curves from cohort studies. However, early phase studies to evaluate novel risk prediction markers typically employ case-control designs. Here, we present semiparametric and nonparametric methods for evaluating a continuous risk prediction marker that accommodates case-control data. Small sample properties are investigated through simulation studies. The semiparametric methods are substantially more efficient than their nonparametric counterparts under a correctly specified model. We generalize them to settings where multiple prediction markers are involved. Applications to prostate cancer risk prediction markers illustrate methods for comparing the risk prediction capacities of markers and for evaluating the increment in performance gained by adding a marker to a baseline risk model. We propose a modified Hosmer-Lemeshow test for case-control study data to assess calibration of the risk model that is a natural complement to this graphical tool.
预测曲线是一种图形工具，用于描述风险(Y) = P(D=1|Y)的总体分布，其中 D 表示二元结果，如在指定时间段内发生事件，Y 表示预测因子。风险(Y)的分布越广，风险模型的性能越好，因为对于更多的受试者，制定治疗建议就更容易。当一个人的风险被认为高或低时，决策就更简单了。已经开发了从队列研究中估计预测曲线的方法。然而，评估新型风险预测标志物的早期阶段研究通常采用病例对照设计。在这里，我们提出了用于评估连续风险预测标志物的半参数和非参数方法，该方法适用于病例对照数据。通过模拟研究研究了小样本特性。在正确指定的模型下，半参数方法比非参数方法效率高得多。我们将它们推广到涉及多个预测标志物的情况。前列腺癌风险预测标志物的应用说明了比较标志物风险预测能力的方法，以及评估通过向基线风险模型添加标志物获得的性能提高的方法。我们提出了一种用于病例对照研究数据的修改后的 Hosmer-Lemeshow 检验，以评估风险模型的校准，这是对该图形工具的自然补充。
