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.

中文翻译：

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一种用于测试关联的无模型方法

结果和特征之间的关联问题通常是在基于功能和分布形式的模型的背景下构建的。我们的激励应用是识别血管生成、能量代谢、细胞凋亡和炎症的血清生物标志物，预测肿瘤分期为 T2a 或更低的淋巴结阴性非小细胞肺癌患者肺切除术后复发。我们提出了一种用于测试关联的综合方法，该方法无需对函数形式和分布进行假设，并且可以用作通用方法。该提议的最大置换测试基于阈值化的思想，易于实现且计算效率高。我们证明了提议的综合测试保持其水平并且具有强大的检测线性、非线性和基于分位数的关联，即使有离群点倾向和重尾误差分布以及在非参数设置下。我们还说明了这种方法在无模型特征筛选中的使用，并进一步检查这些测试对二元结果的水平和能力。在我们的激励应用中，我们将提议的综合测试与比较方法的性能进行比较，以确定与早期患者非小细胞肺癌复发相关的术前血清生物标志物。