The genetic basis of many common human diseases is expected to be highly heterogeneous, with multiple causative loci and multiple alleles at some of the causative loci. Analyzing the association of disease with one genetic marker at a time can have weak power, because of relatively small genetic effects and the need to correct for multiple testing. Testing the simultaneous effects of multiple markers by multivariate statistics might improve power, but they too will not be very powerful when there are many markers, because of the many degrees of freedom. To overcome some of the limitations of current statistical methods for case-control studies of candidate genes, we develop a new class of nonparametric statistics that can simultaneously test the association of multiple markers with disease, with only a single degree of freedom. Our approach, which is based on 17-statistics, first measures a score over all markers for pairs of subjects and then compares the averages of these scores between cases and controls. Genetic scoring for a pair of subjects is measured by a "kernel" function, which we allow to be fairly general. However, we provide guidelines on how to choose a kernel for different types of genetic effects. Our global statistic has the advantage of having only one degree of freedom and achieves its greatest power advantage when the contrasts of average genotype scores between cases and controls are in the same direction across multiple markers. Simulations illustrate that our proposed methods have the anticipated type I - error rate and that they can be more powerful than standard methods. Application of our methods to a study of candidate genes for prostate cancer illustrates their potential merits, and offers guidelines for interpretation.
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