Division of Biostatistics, Clinical Research Center, Kinki University School of Medicine, Osaka, Japan.
Clin Trials. 2013 Aug;10(4):515-21. doi: 10.1177/1740774513483601. Epub 2013 Apr 22.
In clinical trials, an outcome of interest may be undefined for individuals who die before the outcome is evaluated. One approach to deal with such issues is to consider the survivor causal effect (SCE), which is defined as the effect of treatment on the outcome among the subpopulation that would have survived under either treatment arm. Although several methods have been presented to estimate the SCE with time-to-event outcomes, they are difficult to implement in practice.
We present a simple method to create Kaplan-Meier curves and to estimate the hazard ratio (HR) for the SCE with time-to-event outcomes.
To develop such a method, we applied the weighted average method presented for the SCE to outcomes with no censoring, where weights are calculated using the probability that a patient would have survived had the patient been in the other treatment arm. By multiplying the weight to each patient, Kaplan-Meier curves can be created for the SCE to outcomes with censoring. The HR is then calculated using a weighted proportional hazard model. For this method, two assumptions need to be introduced to achieve unbiasedness.
The proposed method is illustrated using data from a randomized Phase II clinical trial, comparing two chemotherapy treatments with radiotherapy in patients with esophageal cancer. Here, we focus on the loco-regional control rate, which is calculated from the time after randomization until recurrence in the radiation field. The duration is undefined for patients who died without recurrence. The proposed method yielded a HR of 1.026 (95% confidence interval (CI): 0.627, 1.677). The standard method, where data of patients who died without progression were regarded as censored at the time of death, yielded a HR of 1.121 (95% CI: 0.688, 1.827).
The proposed method requires two assumptions. As a general problem, unfortunately, whether these assumptions hold cannot be confirmed from the observed data. Thus, we cannot confirm whether the Kaplan-Meier curves and the HR are unbiased.
We have proposed a simple method for the SCE with time-to-event outcomes, which is easy to implement in practice. The proposed method is a potentially valuable supplement to the standard method.
在临床试验中，对于在结局评估之前死亡的个体，感兴趣的结局可能无法定义。处理此类问题的一种方法是考虑生存者因果效应（SCE），它定义为在任何治疗组中本应存活的亚人群中，治疗对结局的影响。尽管已经提出了几种方法来估计具有时间事件结局的 SCE，但在实践中很难实施。
我们提出了一种简单的方法，用于创建 Kaplan-Meier 曲线并估计具有时间事件结局的 SCE 的风险比（HR）。
为了开发这种方法，我们将针对无删失结局提出的 SCE 加权平均方法应用于其中，其中权重是使用患者如果处于另一种治疗臂中本应存活的概率计算的。通过将权重乘以每个患者，可以为具有删失的 SCE 创建 Kaplan-Meier 曲线。然后使用加权比例风险模型计算 HR。对于这种方法，需要引入两个假设才能实现无偏性。
使用来自一项比较食管癌患者两种化疗联合放疗的随机 II 期临床试验的数据说明了该方法。在这里，我们重点关注局部区域控制率，它是从随机化后到辐射野内复发的时间计算的。对于没有复发而死亡的患者，持续时间无法定义。该方法得出的 HR 为 1.026（95%置信区间（CI）：0.627，1.677）。标准方法是将没有进展而死亡的患者的数据视为在死亡时删失，得出的 HR 为 1.121（95%CI：0.688，1.827）。
该方法需要两个假设。作为一个普遍问题，不幸的是，无法从观察数据中确认这些假设是否成立。因此，我们无法确认 Kaplan-Meier 曲线和 HR 是否无偏。
我们提出了一种用于具有时间事件结局的 SCE 的简单方法，在实践中易于实施。该方法是标准方法的一个有价值的补充。
