Han Xiaoxia, Zhang Yilong, Shao Yongzhao
Departments of Population Health, New York University School of Medicine, New York, NY10016, USA.
Merck Research Laboratories, Rahway, 07065, NJ, USA.
Stat Med. 2017 Nov 10;36(25):4041-4049. doi: 10.1002/sim.7414. Epub 2017 Jul 31.
As new biomarkers and risk prediction procedures are in rapid development, it is of great interest to develop valid methods for comparing predictive power of 2 biomarkers or risk score systems. Harrell C statistic has been routinely used as a global adequacy assessment of a risk score system, and the difference of 2 Harrell C statistics as a test statistic has been suggested in recent literature for comparison of predictive power of 2 biomarkers for censored outcome. In this study, we showed that such a test can have severely inflated type I errors as the difference between the 2 Harrell C statistics does not converge to zero under the null hypothesis of equal predictive power measured by concordance probabilities, as illustrated by 2 counterexamples and corresponding numerical simulations. We further investigate a necessary and sufficient condition under which the difference of 2 Harrell C statistics converges to zero under the null hypothesis.
随着新的生物标志物和风险预测程序迅速发展，开发用于比较两种生物标志物或风险评分系统预测能力的有效方法具有重大意义。哈雷尔C统计量一直被常规用作风险评分系统的整体充分性评估，最近的文献中建议将两个哈雷尔C统计量的差异作为检验统计量，用于比较两种生物标志物对删失结局的预测能力。在本研究中，我们表明，这样的检验可能会有严重膨胀的I型错误，因为在由一致性概率衡量的同等预测能力的原假设下，两个哈雷尔C统计量之间的差异不会收敛到零，这通过两个反例和相应的数值模拟得到了说明。我们进一步研究了在原假设下两个哈雷尔C统计量的差异收敛到零的充要条件。
