The knockoff filter is a powerful tool for controlled variable selection with false discovery rate (FDR) control. In this paper, we leverage e-values to allow the nominal FDR level to be switched post-hoc, after looking at the data and applying the knockoff procedure. This approach addresses a significant limitation of standard knockoffs: while frequently used in high-dimensional regressions, they often lack power in low-dimensional and sparse signal settings. One of the main reasons for this is that the knockoff filter requires a minimum number of selections that depends strictly on the nominal FDR level. By utilizing e-values, we can increase the nominal level in cases where the original procedure makes no discoveries, or decrease it to improve precision when discoveries are abundant. These improvements come without any costs, meaning the results of our post-hoc procedure are always more informative than those of the original knockoff filter. We extend this methodology to recently proposed derandomized knockoff procedures and demonstrate its utility in variable selection problems relevant to drug development using real clinical trial data.

翻译：Knockoff滤波器是一种用于控制变量选择并保证错误发现率（FDR）控制的有力工具。本文利用e值，允许在观察数据并应用knockoff程序后，事后调整名义FDR水平。该方法解决了标准knockoff方法的一个重要局限：虽然在高维回归中经常使用，但在低维和稀疏信号设置下往往缺乏效力。其主要原因之一是knockoff滤波器要求最小选择数量严格依赖于名义FDR水平。通过使用e值，我们可以在原始程序未发现任何变量的情况下提高名义水平，或在发现较多时降低名义水平以提高精度。这些改进无需任何代价，意味着我们的事后程序结果始终比原始knockoff滤波器提供更多信息。我们将此方法扩展到最近提出的去随机化knockoff程序，并利用真实临床试验数据展示了其在药物开发相关变量选择问题中的实用性。