Cox比例风险回归模型C统计量的计算方法及其SAS实现

Calculation of C statistics for the Cox proportional hazards regression models and its implementation in SAS

目的 C统计量是评价Cox比例风险回归模型区分度的常见指标,然而,目前对C统计量的算法仍存在争议。本文将探讨C统计量的计算方法及其SAS实现,为编程输出Cox模型的C统计量提供参考。方法 运用PHREG过程估计研究观察期末的累积生存概率,判断实际生存时间与预期生存函数是否同趋势,并以此计算C统计量及其95%置信区间。以某注册登记研究为例,评价年龄、血压和心率对急性心衰患者出院后30d死亡率的预测区分度。结果 研究共纳入2836例急性心衰患者,年龄、基线收缩压和基线心率对出院后30d死亡的影响差异都具有统计学意义（均有P〈0.05）,其中年龄（单位：岁;风险比（hazardratio,HR）：1.029;95%置信区间（confi-denceinterval,CI）：1.022~1.037）和心率（单位：次/分;HR：1.011;95%CI：1.007~1.014）为危险因素,收缩压（单位：mmHg;HR：0.992;95%CI：0.989~0.995）为保护因素。模型C统计量达到0.638（95%CI：0.570~0.704）,可见模型具有一定的区分度,使用SAS程序能够得到所需结果。结论 C统计量是评价模型区分度的良好手段,并可以通过SAS程序求得。

Objective C statistics is one of the most widely-used indexes in accessing the discrimination of the Cox proportional hazards regression models. However, the calculation methods for C statistics have been controversial. Our study aims to investigate the calculation of C statistics and its implementation in SAS. Methods To calculate C statistics and its 95% confidence interval （ CI）, we used PROC PHREG to predict the survival function, and decided whether the predicted survival probabilities was consistent with the actual survival times. Taking a registry study as an example, we e- valuated the discrimination of a Cox regression model which predicted the 30-day mortality after discharge in patients with a- cute heart failure. Results A total of 2 836 patients were included in the final analysis. Older age （ Unit： years; hazard ratio （HR） ： 1. 029; 95% CI： 1. 022-1. 037）, lower systolic blood pressure （ Unit： mmHg; HR： 0, 992; 95 % CI： 0. 989- 0. 995） and increased pulse rate （ Unit： beats/min; HR： 1.011 ; 95% CI： 1. 007-1. 014） were all statistically significant predictors for 30-day post-discharge death. The C statistics of the model was 0. 638 （95% CI： 0. 570-0. 704）, indicating a certain degree of discrimination. Conclusions C statistics is a good index for accessing the discrimination of Cox regres- sion models, and it can be calculated by SAS programs.