The allele-based association test or the allelic test, comparing allele frequency difference between case and control groups, is locally most powerful. However, the classical allelic test is limited in applications because it is sensitive to the Hardy--Weinberg equilibrium (HWE) assumption, not applicable to continuous traits, and not easy to account for covariate effects or sample correlation. To develop a generalized robust allelic test, we propose a unifying regression model with individual allele as the response variable. We show that the score test statistic derived from this novel regression framework contains a correction factor that explicitly adjusts for the departure from HWE and encompasses the classical allelic test as a special case. When the trait of interest is continuous, the corresponding allelic test evaluates a weighted difference between individual-level allele frequency estimate and sample estimate where the weight is proportional to an individual's trait value, and the test remains valid under Y-dependent sampling. Finally, the proposed method allows for joint allele-based association analyses of multiple (continuous or binary) phenotypes, in the presence of covariates, sample correlation and population heterogeneity. To support our analytical findings, we provide empirical evidence from both simulation and application studies.
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