A model‐free approach for testing association

The question of association between outcome and feature is generally framed in the context of a model based 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 tumour stage T2a or less. We propose an omnibus approach for testing the association that is free of assumptions on functional forms and distributions and can be used as a general method. This proposed maximal permutation test is based on the idea of thresholding, is readily implementable and is computationally efficient. We demonstrate that the proposed omnibus tests maintain their levels and have strong power 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 the preoperative serum biomarkers associated with non‐small cell lung cancer recurrence in early stage patients.