Abstract–Accelerated failure time (AFT) models give an intuitive estimator for survival data analysis, but there is a risk of model misspecification. As a serious problem of model misspecification, the test size is likely to be far from the nominal level. Many researchers provided asymptotic corrections of various test statistics under model misspecification. However, their corrected statistics do not have good performance in small samples; in particular, they cause an inflation of test size. Although, the Bartlett adjustment is a popular approach for small-sample correction of the likelihood ratio statistic under the null hypothesis, it is impossible to derive the adjustment factor analytically under model misspecification. In this article, we proposed a robust test to model misspecification in small samples. Our proposed method is based on the Bartlett adjustment and we used the nonparametric bootstrap method to estimate the adjustment factor. We applied the proposed method to the AFT models when the error distribution and/or mean structure are misspecified in small samples. Our simulation results showed that the test size for the proposed method was close to the nominal level, although the existing methods resulted in substantial inflation of the test size. We illustrated our proposed method using two empirical examples.

摘要——加速失效时间 (AFT) 模型为生存数据分析提供了一个直观的估计，但存在模型错误指定的风险。作为模型错误指定的严重问题，测试规模很可能与标称水平相差甚远。许多研究人员在模型错误指定的情况下提供了各种测试统计量的渐近校正。但是，他们的修正统计量在小样本中表现不佳；特别是，它们会导致测试规模膨胀。尽管 Bartlett 调整是在原假设下对似然比统计量进行小样本校正的流行方法，但在模型错误指定的情况下无法解析地推导出调整因子。在本文中，我们提出了一种稳健的测试来模拟小样本中的错误指定。我们提出的方法基于 Bartlett 调整，我们使用非参数引导法来估计调整因子。当错误分布和/或平均结构在小样本中被错误指定时，我们将所提出的方法应用于 AFT 模型。我们的模拟结果表明，尽管现有方法导致测试规模大幅膨胀，但所提出方法的测试规模接近名义水平。我们使用两个经验示例说明了我们提出的方法。我们的模拟结果表明，尽管现有方法导致测试规模大幅膨胀，但所提出方法的测试规模接近名义水平。我们使用两个经验示例说明了我们提出的方法。我们的模拟结果表明，尽管现有方法导致测试规模大幅膨胀，但所提出方法的测试规模接近名义水平。我们使用两个经验示例说明了我们提出的方法。