Exact Max Tests In Case-control Association Analysis With Its Applications

Testing association using MAX tests is now a common strategy in genetic association studies. A MAX test is the maximization of several one degree-of-freedom Cochran-Armitage trend tests that are respectively optimal for some common genetic models such as the dominant, recessive or additive models. In addition to their robustness to model misspecification, MAX tests were shown to be more powerful than the Pearson chi-square test. Significance of the MAX tests can be assessed by either the permutation method, which could reach any accuracy but is computationally intensive, or the large sample approximation, which is not exact. In this paper, we propose an efficient algorithm, MaXact, to calculate the exact p-values of MAX tests. The proposed method is similar to permutation method in that it calculates the exact p-value but is much more computational efficient. It is comparable to approximation methods in computational efficiency but can produce exact p-values. Simulation and real data analysis show that the computing expense of an exact MAX test is close to that of a Pearson chi-square test or an allelic test for moderate sample sizes and is about n-order more efficient than a permutation method with n replicates. The proposed method is built in an R package, MaXact, which is available on CRAN. For multiple SNPs association study, we build a control variate based on MaXact, to reduce the number of permutation replicates to estimate the final p-value. This procedure can be applied in genome-wide association studies.