A general nonparametric framework for testing hypotheses about function-valued parameters

TL;DR

This paper introduces a versatile nonparametric testing framework for assessing whether function-valued parameters, derived from conditional distributions, remain constant across variables, with applications in treatment effect heterogeneity and biomarker identification.

Contribution

It develops a general, norm-based nonparametric test with a tractable null distribution, improving asymptotic behavior over existing methods.

Findings

The test has a well-defined limiting null distribution.

Simulation studies demonstrate the test's good operating characteristics.

Application to breast cancer data identifies potential predictive biomarkers.

Abstract

We present a general nonparametric approach for testing whether a statistical parameter defined through conditional distributions is constant across the conditioning variables. Such hypotheses arise naturally in problems such as assessing treatment effect heterogeneity, conditional associational effects, and conditional mean dependence. Our framework studies function-valued parameters obtained by evaluating a smooth statistical functional on conditional probability distributions. We establish an explicit connection between our test and procedures based on studying the norm of the function-valued parameter. Unlike many existing norm-based tests, which exhibit poor asymptotic behavior under the null, the proposed test statistic admits a tractable limiting null distribution. We illustrate the applicability of the proposed test through several examples, assess its operating characteristics in simulation studies, and apply it to data from a breast cancer trial to identify predictive biomarkers for response to adjuvant chemotherapy.