Department of Biostatistics, The University of North Carolina at Chapel Hill, Chapel Hill, NC, USA.
Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, MD, USA.
Clin Trials. 2023 Aug;20(4):370-379. doi: 10.1177/17407745231173055. Epub 2023 May 11.
Due to the many benefits of understanding treatment effect heterogeneity in a clinical trial, an exploratory post hoc subgroup analysis is often performed to find subpopulations of patients with conditional average treatment effect that suggests better treatment efficacy than in the overall population. A naive re-substitution approach uses all available data to identify a subgroup and then proceeds with estimation and inference using the same data set. This approach generally leads to an overly optimistic estimate of conditional average treatment effect. In this article, in a post hoc analysis, we estimate the target optimal subgroup through maximizing a utility function, from candidates systematically identified with a penalized regression. We then compare two resampling-based bias-correction methods, cross-validation and debiasing bootstrap, for obtaining approximately unbiased estimates and valid inference of conditional average treatment effect in the identified subgroup, with either an empirical or an augmented estimator. Our results show that both the cross-validation and the debiasing bootstrap methods reduce the re-substitution bias effectively. The cross-validation method appears to have less biased point estimates, smaller standard error estimates, but poorer coverages than the debiasing bootstrap method when using the empirical estimator and the sample size is moderate. Using the augmented estimator in the debiasing bootstrap method leads to less biased point estimates but poorer coverages. We conclude that bias correction should be a part of every exploratory post hoc subgroup analysis to eliminate re-substitution bias and to obtain a proper confidence interval for the estimated conditional average treatment effect in the selected subgroup.
由于了解临床试验中治疗效果异质性有许多好处，因此通常会进行探索性事后亚组分析，以找到具有条件平均治疗效果的患者亚组，这表明治疗效果优于总体人群。一种简单的再替换方法使用所有可用数据来识别亚组，然后使用相同的数据集进行估计和推断。这种方法通常会导致条件平均治疗效果的估计过于乐观。在本文的事后分析中，我们通过最大化效用函数来估计目标最优亚组，该效用函数来自通过惩罚回归系统地确定的候选者。然后，我们比较了两种基于重采样的偏差校正方法，交叉验证和去偏自举，用于在识别的亚组中获得条件平均治疗效果的近似无偏估计和有效推断，无论是使用经验估计器还是增强估计器。我们的结果表明，交叉验证和去偏自举方法都可以有效地减少再替换偏差。当使用经验估计器且样本量适中时，交叉验证方法的点估计偏差较小，标准误差估计较小，但覆盖率比去偏自举方法差。在去偏自举方法中使用增强估计器会导致点估计偏差较小，但覆盖率较差。我们得出的结论是，偏差校正应该是每个探索性事后亚组分析的一部分，以消除再替换偏差，并为选定亚组中估计的条件平均治疗效果获得适当的置信区间。
