Detecting a minor average treatment effect is a major challenge in large-scale applications, where even minimal improvements can have a significant economic impact. Traditional methods, reliant on normal distribution-based or expanded statistics, often fail to identify such minor effects because of their inability to handle small discrepancies with sufficient sensitivity. This work leverages a counterfactual outcome framework and proposes a maximum probability-driven two-armed bandit (TAB) process by weighting the mean volatility statistic, which controls Type I error. The implementation of permutation methods further enhances the robustness and efficacy. The established strategic central limit theorem (SCLT) demonstrates that our approach yields a more concentrated distribution under the null hypothesis and a less concentrated one under the alternative hypothesis, greatly improving statistical power. The experimental results indicate a significant improvement in the A/B testing, highlighting the potential to reduce experimental costs while maintaining high statistical power.

MOTIVATION: The Sequence Kernel Association Test (SKAT) and its extensions are the most popular methods for studying the association between phenotypes and a set of single nucleotide polymorphisms. Their practical application is very wide, but most of these methods are designed for continuous and binary phenotypes. Ordered categorical phenotypes are also very common in practice, so there is an urgent need to develop SKAT-type tests for proportional odds model. RESULTS: To accommodate ordered categorical phenotypes, we propose a test named the Sequence Kernel Association Test for the Proportional Odds Model (POM-SKAT). It constructs a score test for the variance of the coefficients of interest using a quasi-likelihood and the P-value is evaluated by approximating the asymptotic distribution of the test statistic with the Pearson Type III distribution. Simulation studies demonstrate that our method performs well and achieves high power in detecting gene-phenotype associations. We apply POM-SKAT to rheumatoid arthritis data provided by Genetic Analysis Workshop 16, identifying multiple relevant gene variants. AVAILABILITY AND IMPLEMENTATION: Code is available at GitHub (https://github.com/amss-stat/POM-SKAT).

MOTIVATION: Testing the association between multiple phenotypes with a set of genetic variants simultaneously, rather than analyzing one trait at a time, is receiving increasing attention for its high statistical power and easy explanation on pleiotropic effects. The kernel-based association test (KAT), being free of data dimensions and structures, has proven to be a good alternative method for genetic association analysis with multiple phenotypes. However, KAT suffers from substantial power loss when multiple phenotypes have moderate to strong correlations. To handle this issue, we propose a maximum KAT (MaxKAT) and suggest using the generalized extreme value distribution to calculate its statistical significance under the null hypothesis. RESULTS: We show that MaxKAT reduces computational intensity greatly while maintaining high accuracy. Extensive simulations demonstrate that MaxKAT can properly control type I error rates and obtain remarkably higher power than KAT under most of the considered scenarios. Application to a porcine dataset used in biomedical experiments of human disease further illustrates its practical utility. AVAILABILITY AND IMPLEMENTATION: The R package MaxKAT that implements the proposed method is available on Github https://github.com/WangJJ-xrk/MaxKAT.