A maximally selected test of symmetry about zero

Area of Science:

• Statistics
• Biostatistics
• Pharmacovigilance

Background:

• Testing for symmetry about zero is a fundamental statistical problem.
• Assessing medication safety requires detecting asymmetry in pre- and post-treatment measures.
• Traditional tests may lack power in detecting clinically relevant asymmetries.

Purpose of the Study:

• Introduce a novel statistical test, the maximally selected McNemar (MM) test, for assessing symmetry about zero.
• Evaluate the performance of the MM test compared to existing statistical methods.
• Demonstrate the utility of the MM test in a real-world medication safety study.

Main Methods:

• Developed a new test that sequentially discards observations below increasing data-defined thresholds.
• Utilized McNemar's statistic at each threshold, with the maximum value serving as the test statistic.
• Obtained the exact distribution of the maximally selected McNemar statistic and computed critical values and p-values.

Main Results:

• The MM test demonstrated slightly lower power than t-test and Wilcoxon Signed Rank Test for symmetric normal distributions.
• The MM test was substantially more powerful than t-test, Wilcoxon Signed Rank Test, and Sign Test for asymmetric mixtures of normal distributions.
• The MM test was applied to data from a driving study assessing residual effects of a hypnotic medication.

Conclusions:

• The MM test offers a powerful new approach for detecting asymmetry, particularly in complex data distributions.
• The test's ability to down-weight small, less relevant observations enhances its power for safety assessments.
• The MM test is a valuable tool for pharmacovigilance and analyzing pre-post treatment data in clinical studies.