This work is motivated by learning the individualized minimal clinically important difference, a vital concept to assess clinical importance in various biomedical studies. We formulate the scientific question into a high-dimensional statistical problem where the parameter of interest lies in an individualized linear threshold. The goal is to develop a hypothesis testing procedure for the significance of a single element in this parameter as well as of a linear combination of this parameter. The difficulty dues to the high-dimensional nuisance in developing such a testing procedure, and also stems from the fact that this high-dimensional threshold model is nonregular and the limiting distribution of the corresponding estimator is nonstandard. To deal with these challenges, we construct a test statistic via a new bias-corrected smoothed decorrelated score approach, and establish its asymptotic distributions under both null and local alternative hypotheses. We propose a double-smoothing approach to select the optimal bandwidth in our test statistic and provide theoretical guarantees for the selected bandwidth. We conduct simulation studies to demonstrate how our proposed procedure can be applied in empirical studies. We apply the proposed method to a clinical trial where the scientific goal is to assess the clinical importance of a surgery procedure.

翻译：本研究源于个体化最小临床意义变化值的学习问题，该概念在各类生物医学研究中对于评估临床重要性至关重要。我们将这一科学问题转化为高维统计问题，其中目标参数存在于个体化线性阈值中。研究目标是建立假设检验程序，用于检验该参数中单个元素以及参数线性组合的显著性。建立此类检验程序的难点在于高维干扰项的存在，同时还源于该高维阈值模型的不正则性及其对应估计量极限分布的非标准性。为应对这些挑战，我们通过新的偏差校正平滑去相关得分方法构建检验统计量，并建立了其在原假设和局部备择假设下的渐近分布。我们提出了双平滑方法用于选择检验统计量中的最优带宽，并提供了所选带宽的理论保证。通过模拟研究展示了所提程序在实证研究中的应用。我们将所提方法应用于一项临床试验，该研究的科学目标是评估某种外科手术的临床重要性。