临床试验中不同转组分析方法的比较

doi:10.12122/j.issn.1673-4254.2025.05.23

摘要/Abstract

摘要：

目的通过比较临床试验中处理转组的常用方法，为不同场景下发生转组后分析方法的选择提供参考。方法基于肿瘤临床试验中患者转组的数据特征，分别模拟不同场景（样本量、患者预后、转组概率、治疗效果、膨胀因子）中患者的生存时间，比较意向治疗法（ITT）、符合方案法（PP）、删失法（PPcents）、实际治疗法（Treated）、秩保留结构加速失效模型（RPSFTM）、逆概率删失加权法（IPCW）、两阶段估计模型（TSE）、参数迭代法（IPE）所估计的治疗效应误差、均方误差与覆盖率。结果样本量对各方法的结果影响不大。相较于传统方法，复杂方法（RPSFTM、IPCW、TSE、IPE）在各种情况下误差均较低。IPCW法在转组概率较高时误差显著增加。TSE法在风险较低且转组概率较高时，误差和均方误差最低。IPE法在转组概率较低时具有明显优势，但在膨胀因子较小时可能会略低估治疗效应。结论转组概率较低且膨胀因子较小的情况下优先考虑IPE法或IPCW法；在转组概率较低且膨胀因子较大的情况下选择IPE法；在转组概率较大，膨胀因子较小且风险比较小的情况下选TSE法；其余情况建议选择RPSFTM法。

关键词: 治疗转组, 逆概率删失加权法, 秩保持结构失效模型, 两阶段估计法, 迭代参数估计法

Abstract:

Objective To compare the commonly used methods for analyzing treatment switching in clinical trials to facilitate selection of optimal methods in different scenarios. Methods Based on the data characteristics of patient conversion in oncology clinical trials, we simulated the survival time of patients across different scenarios and compared the bias, mean square error and coverages of the treatment effects derived from different methods. Results The sample size had an almost negligible impact on the outcomes of the various methods. Compared to conventional methods, more complex methods (RPSFTM, IPCW, TSE, and IPE) resulted in lower errors across different scenarios. The IPCW method could cause a significant increase in errors in cases where the probability of conversion was high. The TSE method had the lowest error and mean squared error when the risk was low and the probability of conversion was high. The IPE method had an obvious advantage in the scenario with a low probability of conversion, but it may slightly underestimate the treatment effect when the inflation factor was small. Conclusion The choice of a specific method for analyzing cohort transition should be made based on considerations of both the probability of conversion and inflation factor in different scenarios.

Key words: treatment switching, inverse probability censoring weighting, rank preserving structural failure time models, two-stage estimation method, iterative parameter estimation method

梁芷玥, 徐利珊, 李柯柯, 于米铼, 安胜利. 临床试验中不同转组分析方法的比较[J]. 南方医科大学学报, 2025, 45(5): 1093-1102.

Zhiyue LIANG, Lishan XU, Keke LI, Milai YU, Shengli AN. A comparative study of different methods for treatment switching analysis in clinical trials[J]. Journal of Southern Medical University, 2025, 45(5): 1093-1102.

图/表 9

图1 IPCW流程图

Fig.1 IPCW process diagram.

表1 模拟参数设置

Tab.1 Setting of the simulation parameters

Variables	Assignment/Distribution
Simulation times	1000
Sample size	200, 500, 1000
Shape parameter $γ$	0.5
Scale parameter $λ$	1.33
observation time	3 years
Survival time	Weibull distribution
Entry time	Uniform distribution (0-1distribution)
Prognostic probability (good/poor)	Good: 30%, 75%
	Poor: 70%, 25%
Switching probability (good, poor)	(0.1, 0.25)
	(0.5, 0.75)
Switching time	Uniform distribution
Hazard ratios	0.7, 0.9
Inflation factor	1.2, 2

表1 模拟参数设置

Tab.1 Setting of the simulation parameters

Variables	Assignment/Distribution
Simulation times	1000
Sample size	200, 500, 1000
Shape parameter $γ$	0.5
Scale parameter $λ$	1.33
observation time	3 years
Survival time	Weibull distribution
Entry time	Uniform distribution (0-1distribution)
Prognostic probability (good/poor)	Good: 30%, 75%
	Poor: 70%, 25%
Switching probability (good, poor)	(0.1, 0.25)
	(0.5, 0.75)
Switching time	Uniform distribution
Hazard ratios	0.7, 0.9
Inflation factor	1.2, 2

表2 16　种场景下的参数值

Tab.2 Parameter values in 16 scenarios

Scenario	Hazard Ratios		Probability of good prognosis		Inflation factor		Switching probability (good : poor)
Scenario	0.7	0.9	30%	75%	1.2	2	10%:25%	50%:75%
1	√		√		√		√
2	√		√		√			√
3	√		√			√	√
4	√		√			√		√
5	√			√	√		√
6	√			√	√			√
7	√			√		√	√
8	√			√		√		√
9		√	√		√		√
10		√	√		√			√
11		√	√			√	√
12		√	√			√		√
13		√		√	√		√
14		√		√	√			√
15		√		√		√	√
16		√		√		√		√

图2 场景4、14样本量比较结果

Fig.2 Impact of sample size on errors of different methods in Scenario 4 and Scenario 14. A: Scenario 4; B: Scenario 14. ITT: Intention-to-Treat; PPExc: Per-Protocol method; PPCens: Censoring Method; Treated: As-Treated Method; IPCW: Inverse Probability Censoring Weighting; TSE: Two-Stage Estimation; RPSFTM: Rank Preserving Structural Failure Time Models; IPE: Iterative Parameter Estimation Algorithm.

图3 样本量为500时16种情况森林图

Fig.3 Forest plot for 16 scenarios with a sample size of 500.

表3 不同风险比对各方法的影响

Tab.3 Impact of different hazard ratios on outcomes of different methods

Scenario	Method	Mean Estimate	Bias	MSE	SE	Coverage (%)
Scenario6 beta=0.7 prob=0.75 a=1.2 prob1=(0.50, 0.75)	ITT	0.98	0.28	0.09	0.11	95.2
	PPEXC	0.76	0.06	0.02	0.11	94.9
	PPCENS	2.08	1.38	2.01	0.30	94.6
	Treated	0.92	0.22	0.06	0.11	95.9
	IPCW	0.85	0.15	0.03	0.10	95.2
	Two-Stage	0.84	0.14	0.03	0.10	95.2
	RPSFTM	0.98	0.28	0.08	0.05	99.4
	IPE	0.90	0.20	0.05	0.10	95.1
Scenario7 beta=0.7 prob=0.75 a=2 prob1=(0.10, 0.25)	ITT	0.98	0.28	0.09	0.11	95.4
	PPEXC	0.93	0.23	0.06	0.11	94.3
	PPCENS	1.11	0.41	0.19	0.13	95.3
	Treated	1.09	0.39	0.17	0.13	94.3
	IPCW	0.94	0.24	0.07	0.11	95.4
	Two-Stage	0.94	0.24	0.07	0.11	95.3
	RPSFTM	0.96	0.26	0.08	0.07	98.8
	IPE	0.80	0.10	0.02	0.09	95.6
Scenario14 beta=0.9 prob=0.75 a=1.2 prob1=(0.50, 0.75)	ITT	1.20	0.30	0.10	0.13	95.5
	PPEXC	0.98	0.08	0.02	0.13	94.9
	PPCENS	2.62	1.72	3.07	0.36	95.7
	Treated	1.01	0.11	0.02	0.11	95.8
	IPCW	1.06	0.16	0.04	0.11	94.8
	Two-Stage	1.04	0.14	0.03	0.11	94.6
	RPSFTM	1.00	0.10	0.01	0.01	100.0
	IPE	1.10	0.20	0.06	0.12	95.3
Scenario15 beta=0.9 prob=0.75 a=2 prob1=(0.10, 0.25)	ITT	1.24	0.34	0.13	0.14	95.3
	PPEXC	1.19	0.29	0.10	0.14	95.1
	PPCENS	1.42	0.52	0.30	0.17	95.2
	Treated	1.23	0.33	0.13	0.13	95.0
	IPCW	1.20	0.30	0.11	0.13	94.9
	Two-Stage	1.20	0.30	0.11	0.13	95.3
	RPSFTM	1.14	0.24	0.07	0.12	97.8
	IPE	1.01	0.11	0.02	0.11	95.1

表4 风险比较小时预后良好的概率对各方法的影响

Tab.4 Impact of the probability of "good" prognosis when the hazard ratio is low on outcomes of different methods

Scenario	Method	Mean Estimate	Bias	MSE	SE	Coverage (%)
Scenario1 beta=0.7 prob=0.3 a=1.2 prob1= (0.10, 0.25)	ITT	0.82	0.12	0.02	0.09	94.0
	PPEXC	0.73	0.03	0.01	0.09	93.9
	PPCENS	0.99	0.29	0.10	0.12	93.8
	Treated	1.19	0.49	0.25	0.13	95.3
	IPCW	0.76	0.06	0.01	0.09	93.7
	Two-Stage	0.77	0.07	0.01	0.09	93.4
	RPSFTM	0.84	0.14	0.03	0.09	96.4
	IPE	0.68	-0.02	0.01	0.08	93.6
Scenario5 beta=0.7 prob=0.75 a=1.2 prob1=(0.10, 0.25)	ITT	0.81	0.11	0.02	0.09	94.4
	PPEXC	0.75	0.05	0.01	0.09	94.3
	PPCENS	0.92	0.22	0.06	0.11	94.3
	Treated	0.89	0.19	0.05	0.10	95.1
	IPCW	0.77	0.07	0.01	0.09	94.6
	Two-Stage	0.78	0.08	0.01	0.09	94.3
	RPSFTM	0.82	0.12	0.02	0.09	97.6
	IPE	0.66	-0.04	0.01	0.07	94.9

表5 风险比较大时预后良好的概率对各方法的影响

Tab.5 Impact of the probability of "good" prognosis with a high hazard ratio on outcomes of different methods

Scenario	Method	Mean Estimate	Bias	MSE	SE	Coverage (%)
Scenario9 beta=0.9 prob=0.3 a=1.2 prob1=(0.10, 0.25)	ITT	1.02	0.12	0.03	0.11	95.0
	PPEXC	0.93	0.03	0.01	0.10	95.7
	PPCENS	1.25	0.35	0.14	0.14	96.0
	Treated	1.10	0.2	0.05	0.12	95.9
	IPCW	0.97	0.07	0.01	0.10	95.0
	Two-Stage	0.97	0.07	0.01	0.10	95.5
	RPSFTM	0.99	0.09	0.01	0.05	99.7
	IPE	0.85	-0.05	0.01	0.09	94.9
Scenario13 beta=0.9 prob=0.75 a=1.2 prob1=(0.10, 0.25)	ITT	1.02	0.12	0.03	0.11	94.8
	PPEXC	0.97	0.07	0.02	0.11	95.1
	PPCENS	1.17	0.27	0.09	0.13	94.2
	Treated	1.02	0.12	0.02	0.11	94.6
	IPCW	0.99	0.09	0.02	0.11	95.0
	Two-Stage	0.99	0.09	0.02	0.11	94.9
	RPSFTM	1.00	0.10	0.01	0.07	98.6
	IPE	0.83	-0.07	0.01	0.09	94.9

表6 不同场景下最佳方法选择

Tab.6 Best Method Selection Under Different Scenarios

Scenario	Hazard ratios		Prognostic probability (good)		Inflation factor		Switching probability (good, poor)		Method
Scenario	0.7	0.9	30%	75%	1.2	2	10%∶25%	50%∶75%	Method
1	√		√		√		√		IPE/IPCW
2	√		√		√			√	TSE
3	√		√			√	√		IPE
4	√		√			√		√	RPSFTM
5	√			√	√		√		IPE/IPCW
6	√			√	√			√	TSE
7	√			√		√	√		IPE
8	√			√		√		√	TSE
9		√	√		√		√		IPE/IPCW
10		√	√		√			√	RPSFTM
11		√	√			√	√		IPE
12		√	√			√		√	RPSFTM
13		√		√	√		√		IPE/IPCW
14		√		√	√			√	RPSFTM
15		√		√		√	√		IPE
16		√		√		√		√	RPSFTM

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