Department of Biostatistics, Vanderbilt University Medical Center, Nashville, Tennessee.
Center for Quantitative Sciences, Vanderbilt University Medical Center, Nashville, Tennessee.
JAMA Oncol. 2021 Jul 1;7(7):1041-1044. doi: 10.1001/jamaoncol.2021.0289.
In immune checkpoint inhibitor (ICI) trials, long tails and crossovers in survival curves-which violate the proportional hazards (PH) assumption-are commonly observed, making cure or restricted mean survival time models preferable for analysis of ICI survival data. Cox PH analysis, however, still appears in major medical journals, leading to potential misinterpretation of clinical significance.
To convert inappropriate Cox hazard ratios (HRs) to appropriate PH cure model treatment-effect estimates (HR for short-term survivors and difference in proportions [DP] for long-term survivors) for more accurate interpretation of published ICI trials.
This study uses the Taylor expansion technique to demonstrate the mathematical relationship between Cox PH and PH cure models for data with long-term survival, and based on this relationship, proposes the Cox-TEL (Cox PH-Taylor expansion adjustment for long-term survival data) adjustment method. The proposed Cox-TEL method requires only 2 inputs: the reported Cox HRs and Kaplan-Meier-estimated survival probabilities.
Comprehensive simulations show the strength of the proposed method in terms of power, bias, and type I error rate; these results, which are close to PH cure model estimates, were further verified in a melanoma data set (N = 285; Cox HR = 0.71; 95% CI, 0.51-0.91; Cox-TEL HR = 0.83; 95% CI, 0.60-1.07; PH cure HR = 0.86; 95% CI, 0.61-1.11; Cox-TEL DP = 0.10; 95% CI, 0.01-0.23; PH cure DP = 0.10; 95% CI, 0.00-0.21). The magnitude of potential difference between reported and adjusted HRs using real-world ICI trial results is demonstrated. For example, in the CheckMate 067 trial (nivolumab/ipilimumab combination therapy vs ipilimumab), the Cox HR was 0.54 (95% CI, 0.44-0.67), and the Cox-TEL HR was 0.90 (95% CI, 0.73-1.11).
The findings of this study suggest the need to revisit published ICI survival data analysis to address potential misinterpretation. The Cox-TEL method not only is designed for this purpose, but also is user friendly and easy to implement using published clinical trial data and a freely available R software package.
在免疫检查点抑制剂（ICI）试验中，生存曲线的长尾和交叉 - 违反比例风险（PH）假设 - 是常见的，因此对于分析 ICI 生存数据，治愈或限制平均生存时间模型更为合适。然而，Cox PH 分析仍然出现在主要医学期刊中，导致对临床意义的潜在误解。
为了更准确地解释已发表的 ICI 试验，将不合适的 Cox 风险比（HR）转换为合适的 PH 治愈模型治疗效果估计值（短期幸存者的 HR 和长期幸存者的差异比例 [DP]）。
本研究使用泰勒展开技术，展示了 Cox PH 和 PH 治愈模型之间的数学关系，适用于具有长期生存数据，并基于该关系，提出了 Cox-TEL（Cox PH-Taylor 展开调整用于长期生存数据）调整方法。所提出的 Cox-TEL 方法仅需要 2 个输入：报告的 Cox HR 和 Kaplan-Meier 估计的生存概率。
综合模拟结果表明，该方法在功效、偏差和 I 型错误率方面具有优势；这些结果与 PH 治愈模型估计值接近，在黑色素瘤数据集（N=285；Cox HR=0.71；95%CI，0.51-0.91；Cox-TEL HR=0.83；95%CI，0.60-1.07；PH 治愈 HR=0.86；95%CI，0.61-1.11；Cox-TEL DP=0.10；95%CI，0.01-0.23；PH 治愈 DP=0.10；95%CI，0.00-0.21）中得到了进一步验证。还展示了使用真实世界的 ICI 试验结果报告和调整后的 HR 之间潜在差异的大小。例如，在 CheckMate 067 试验（nivolumab/ipilimumab 联合治疗与 ipilimumab）中，Cox HR 为 0.54（95%CI，0.44-0.67），而 Cox-TEL HR 为 0.90（95%CI，0.73-1.11）。
本研究的结果表明，有必要重新审视已发表的 ICI 生存数据分析，以解决潜在的误解。Cox-TEL 方法不仅旨在解决此问题，而且易于使用，并且可以使用已发表的临床试验数据和免费提供的 R 软件包轻松实现。
