A Model-free Approach for Testing Association

TL;DR

This paper introduces a model-free, permutation-based omnibus testing approach for detecting associations between outcomes and features, applicable to various data types and distributions, demonstrated in lung cancer biomarker analysis.

Contribution

It develops a computationally efficient, assumption-free maximal permutation test that can identify linear, nonlinear, and quantile associations in complex data.

Findings

Maintains proper level and high power across different association types.

Effective in heavy-tailed and outlier-prone data.

Useful for feature screening in high-dimensional settings.

Abstract

The question of association between outcome and feature is generally framed in the context of a model on functional and distributional forms. Our motivating application is that of identifying serum biomarkers of angiogenesis, energy metabolism, apoptosis, and inflammation, predictive of recurrence after lung resection in node-negative non-small cell lung cancer patients with tumor stage T2a or less. We propose an omnibus approach for testing association that is free of assumptions on functional forms and distributions and can be used as a black box method. This proposed maximal permutation test is based on the idea of thresholding, is readily implementable and is computationally efficient. We illustrate that the proposed omnibus tests maintain their levels and have strong power as black box tests for detecting linear, nonlinear and quantile-based associations, even with outlier-prone and heavy-tailed error distributions and under nonparametric setting. We additionally illustrate the use of this approach in model-free feature screening and further examine the level and power of these tests for binary outcome. We compare the performance of the proposed omnibus tests with comparator methods in our motivating application to identify preoperative serum biomarkers associated with non-small cell lung cancer recurrence in early stage patients.