We propose a nonparametric estimate of the scale-change parameter for characterizing the difference between two survival functions under the accelerated failure time model using an estimating equation based on restricted means. Advantages of our restricted means based approach compared to current nonparametric procedures is the strictly monotone nature of the estimating equation as a function of the scale-change parameter, leading to a unique root, as well as the availability of a direct standard error estimate, avoiding the need for hazard function estimation or re-sampling to conduct inference. We derive the asymptotic properties of the proposed estimator for fixed and for random point of restriction. In a simulation study, we compare the performance of the proposed estimator with parametric and nonparametric competitors in terms of bias, efficiency, and accuracy of coverage probabilities. The restricted means based approach provides unbiased estimates and accurate confidence interval coverage rates with efficiency ranging from 81% to 95% relative to fitting the correct parametric model. An example from a randomized clinical trial in head and neck cancer is provided to illustrate an application of the methodology in practice.

我们提出了尺度变化参数的非参数估计，用于使用基于受限均值的估计方程来表征加速失效时间模型下两个生存函数之间的差异。与当前的非参数程序相比，我们基于受限均值的方法的优点是作为尺度变化参数的函数的估计方程的严格单调性质，导致唯一的根，以及直接标准误差估计的可用性，避免需要进行风险函数估计或重新采样以进行推理。我们推导出所提出的估计量的渐近性质，用于固定和随机限制点。在模拟研究中，我们在偏差方面比较了所提出的估计器与参数和非参数竞争对手的性能，覆盖概率的效率和准确性。基于受限均值的方法提供了无偏估计和准确的置信区间覆盖率，相对于拟合正确的参数模型，效率从 81% 到 95% 不等。提供了一个头颈癌随机临床试验的例子来说明该方法在实践中的应用。