On a general class of conditional tests for family-based association studies in genetics: the asymptotic distribution, the conditional power, and optimality considerations

Family-based association tests (FBATs) provide simple and powerful tests to detect association between a genetic marker and a disease-susceptibility locus, manifest in subjects by a phenotype or disease trait. Here we propose a new class of conditional tests for family-based association studies that includes most of the established tests and their generalizations. The class of tests is very general; it can be applied to longitudinal and multivariate traits or phenotypes, multiple genetic markers, and many other situations not yet discussed in the literature. For any test in this class, we derive the asymptotic distribution under the null hypothesis, the conditional power under any alternative hypothesis, and the optimal offset for single degree of freedom tests. The proposed methodology is illustrated with a genetic study of asthma.