A0489
Title: A conformal test of linear models via permutation-augmented regressions
Authors: Leying Guan - Yale University (United States) [presenting]
Abstract: Permutation tests are widely recognized as robust alternatives to tests based on normal theory. Random permutation tests have been frequently employed to assess the significance of variables in linear models. Despite their widespread use, existing random permutation tests lack finite-sample and assumption-free guarantees for controlling type I errors in partial correlation tests. To address this ongoing challenge, a conformal test is developed through permutation-augmented regressions, referred to as PALMRT. PALMRT not only achieves power competitive with conventional methods but also provides reliable control of type I errors at no more than two alpha, given any targeted level alpha, for arbitrarily fixed designs and error distributions. This, through extensive simulations, is confirmed. Compared to the cyclic permutation test (CPT) and residual permutation test (RPT), which also offer theoretical guarantees, PALMRT does not compromise as much on power or set stringent requirements on the sample size, making it suitable for diverse biomedical applications. The differences in a long-Covid study are further illustrated when PALMRT validated key findings previously identified using the t-test after multiple corrections, while both CPT and RPT suffered from a drastic loss of power and failed to identify any discoveries. PALMRT is endorsed as a robust and practical hypothesis test in scientific research for its superior error control, power preservation, and simplicity.
