Test of Significance for High-dimensional Thresholds with Application to Individualized Minimal Clinically Important Difference

TL;DR

This paper develops a novel high-dimensional hypothesis testing method for individualized clinical thresholds, addressing nonregular models and nonstandard distributions, with theoretical guarantees and practical applications in biomedical studies.

Contribution

It introduces a bias-corrected smoothed decorrelated score test for high-dimensional thresholds, handling nonregularity and providing asymptotic and bandwidth selection guarantees.

Findings

The proposed test controls type I error under null hypothesis.

Simulation studies demonstrate the method's effectiveness.

Application to clinical trial data shows practical utility.

Abstract

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.