  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.
