Exact MAX tests in genetic association analysis

The three common genetic models (or modes of inheritance) in association analysis are the dominant, additive, and recessive models. It is known that the Cochran-Armitage trend test (CATT) which correctly incorporates information from genetic models, is more powerful than the commonly used Pearson’s chi-square test. However, the true genetic model is usually unknown in practice, and the power of the CAT test could be substantially reduced with a wrongly specified genetic model. To achieve a power that is close to that of a correctly specified CAT test, it is natural to apply trend tests under different possible genetic models and to report the most significant test result. This results in a MAX-type testing procedure, and it was found that this test is usually more powerful than the Pearson’s chi-square test. Although the significance (i.e., p value) of the MAX-type test can be accessed by either large sample approximation or permutation methods, requirements for sample size or simulation replicates are demanding with respect to accuracy and efficiency. This paper proposes an approach to calculate the exact p values of MAX-type tests based on the combinatorial counting method. The simulation results show that the exact method is more accurate than the large sample approximation methods and more computationally efficient than the permutation method, and our method can be readily applied to genome-wide association studies (GWASs). The proposed method is built in an R package, MaXact, which is available at the https://github.com/Myuan2019/MaXact/.