协变量适应性随机化的临床试验统计分析方法介绍

doi:10.12092/j.issn.1009-2501.2026.08.011

中国临床药理学与治疗学 ›› 2026, Vol. 31 ›› Issue (8): 1101-1111.doi: 10.12092/j.issn.1009-2501.2026.08.011

• 综述与讲座 • 上一篇

协变量适应性随机化的临床试验统计分析方法介绍

杨雨轩¹(), 朱思宇¹, 尹明港¹, 潘建红²^,*(), 段重阳¹^,*()

1. 南方医科大学，多器官损伤防治全国重点实验室，广州 510515，广东
2. 国家药品监督管理局药品审评中心，北京 100022

收稿日期:2025-04-21 修回日期:2025-06-16 出版日期:2026-08-26 发布日期:2026-09-09
通讯作者: 潘建红,段重阳 E-mail:yuxuanyang402@qq.com;panjh@cde.org.cn;donyduang@126.com
作者简介:杨雨轩，男，研究方向：临床试验设计与分析。E-mail：yuxuanyang402@qq.com
基金资助:
国家自然科学基金（82273727）；广州市科技计划项目基金（2023A04J2266）

An introduction to statistical analysis methods for clinical trials using covariate-adaptive randomization

Yuxuan YANG¹(), Siyu ZHU¹, Minggang YIN¹, Jianhong PAN²^,*(), Chongyang DUAN¹^,*()

1. State Key Laboratory of Multi-organ Injury Prevention and Treatment, Southern Medical University, Guangzhou 510515, Guangdong, China
2. Center for Drug Evaluation, National Medical Products Administration, Beijing 100022, China

Received:2025-04-21 Revised:2025-06-16 Online:2026-08-26 Published:2026-09-09
Contact: Jianhong PAN,Chongyang DUAN E-mail:yuxuanyang402@qq.com;panjh@cde.org.cn;donyduang@126.com

摘要/Abstract

摘要：

因可以平衡试验组间可能对试验结果产生影响的预后因素，协变量适应性随机化目前被越来越多地应用于药物临床试验之中。而在进行此类试验的统计分析时，研究者通常认为需要对随机化控制的协变量进行一定调整，因此回归模型以及分层分析常被用于该类试验的统计推断。然而，尚未有研究系统讨论上述方法的合理性以及适用性。为此，本研究对既往文献进行了梳理，讨论了传统统计推断方法在协变量适应性随机化临床试验中的适用性，并对近些年提出的“稳健”统计推断方法进行了介绍与探讨。此外，为进一步方便临床研究人员的使用，本文还对所讨论的方法进行了实例代码演示。

关键词: 适应性随机化, 分层分析, 协变量调整, 稳健分析方法, 软件操作

Abstract:

Covariate-adaptive randomization is increasingly used in drug clinical trials because it helps balance prognostic factors that may affect trial outcomes between treatment groups. When performing statistical analyses of such trials, researchers usually consider it necessary to adjust for the covariates used in randomization. Therefore, regression models and stratified analyses are commonly employed for statistical inferences. However, no systematic studies have been conducted to discuss the rationality and applicability of these methods. To address this gap, the present study reviews the existing literature, examines the adaptability of traditional statistical inference methods for trials using covariate-adaptive randomization, and introduces the "robust" statistical inference methods proposed in recent years. In addition, to facilitate practical implementation by clinical researchers, example code is provided to demonstrate the application of these methods.

Key words: adaptive-randomization, stratified analysis, covariate-adjusted, robust analysis method, software operation

中图分类号:

杨雨轩, 朱思宇, 尹明港, 潘建红, 段重阳. 协变量适应性随机化的临床试验统计分析方法介绍[J]. 中国临床药理学与治疗学, 2026, 31(8): 1101-1111.

Yuxuan YANG, Siyu ZHU, Minggang YIN, Jianhong PAN, Chongyang DUAN. An introduction to statistical analysis methods for clinical trials using covariate-adaptive randomization[J]. Chinese Journal of Clinical Pharmacology and Therapeutics, 2026, 31(8): 1101-1111.

图/表 4

参考文献 22

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结局类型	传统方法	协变量调整方法	“稳健”方法
连续结局	方差分析	协方差分析	异质协方差分析方法
二分类结局	基于Logistic模型的Wald检验	-	增强逆倾向加权估计量、线性校正法、联合校正法
生存结局	Log-Rank检验、基于Cox模型的Score检验	分层Log-Rank检验、基于Cox模型调整协变量的Score检验	协变量调整的Log-Rank检验、协变量调整的分层Log-Rank检验、稳健Score检验

结局类型	传统方法	协变量调整方法	“稳健”方法
连续结局	方差分析	协方差分析	异质协方差分析方法
二分类结局	基于Logistic模型的Wald检验	-	增强逆倾向加权估计量、线性校正法、联合校正法
生存结局	Log-Rank检验、基于Cox模型的Score检验	分层Log-Rank检验、基于Cox模型调整协变量的Score检验	协变量调整的Log-Rank检验、协变量调整的分层Log-Rank检验、稳健Score检验

组别		方法
组别		方差分析	协方差分析	异质协方差分析方法
治疗组
0	均值估计	3.168	3.183	3.115
	标准误	0.2321	0.2393	0.1796
1	均值估计	3.003	2.971	2.950
	标准误	0.0929	0.0843	0.0815
2	均值估计	2.824	2.847	2.872
	标准误	0.0945	0.0916	0.0905
组间比较
0-1	均值差估计	0.165	0.211	0.165
	标准误	0.244	0.248	0.198
0-2	均值差估计	0.345	0.336	0.243
	标准误	0.247	0.255	0.205

组别		方法
组别		方差分析	协方差分析	异质协方差分析方法
治疗组
0	均值估计	3.168	3.183	3.115
	标准误	0.2321	0.2393	0.1796
1	均值估计	3.003	2.971	2.950
	标准误	0.0929	0.0843	0.0815
2	均值估计	2.824	2.847	2.872
	标准误	0.0945	0.0916	0.0905
组间比较
0-1	均值差估计	0.165	0.211	0.165
	标准误	0.244	0.248	0.198
0-2	均值差估计	0.345	0.336	0.243
	标准误	0.247	0.255	0.205

组别		方法
组别		方差分析	协方差分析	异质协方差分析方法	$ \widehat{{\theta }_{AIPW}} $	$ \widehat{{\theta }_{LC}} $	$ \widehat{{\theta }_{JC}} $
治疗组
0	概率估计	0.553	0.558	0.552	0.548	0.545	0.560
	标准误	0.0311	0.0340	0.0289	0.0319	0.0323	0.0297
1	概率估计	0.763	0.755	0.756	0.767	0.767	0.771
	标准误	0.0278	0.0268	0.0268	0.0273	0.0273	0.0272
2	概率估计	0.712	0.719	0.722	0.712	0.712	0.711
	标准误	0.0307	0.0301	0.0301	0.0308	0.0308	0.0308
组间比较
0-1	概率差估计	?0.210	?0.197	?0.204	?0.219	?0.222	?0.210
	标准误	0.0399	0.0416	0.0378	0.0400	0.0403	0.0384
0-2	概率差估计	?0.159	?0.161	?0.171	?0.163	?0.167	?0.155
	标准误	0.0430	0.0451	0.0418	0.0438	0.0441	0.0423

协变量适应性随机化的临床试验统计分析方法介绍

An introduction to statistical analysis methods for clinical trials using covariate-adaptive randomization

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方法	P 值
$ {T}_{L} $	0.400
$ {T}_{SL} $	0.289
$ {T}_{S} $	0.400
$ {T}_{RS} $	0.269
$ {T}_{CL} $	0.206
$ {T}_{CSL} $	0.288