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Abstract:
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We address the asymptotic and approximate distributions of a large class of test statistics with quadratic forms used in association studies. We show that the asymptotic distribution of them is basically a linear combination of chi-squares, which can be approximated by a chi-square based on the first two or four cumulants. Our methods are especially useful in two situations: (1)for genome screen, where the required significance level is much smaller than 0.05 due to multiple comparisons; (2) for candidate gene study based on haplotypes, when the phase information is unknown and a EM algorithm is needed for each permutation. With our methods, these two problems are easily solved. We assess our methods using extensive simulation studies based on two example statistics. Finally, we give an example to apply our methods to find the sample size needed for a candidate gene association study.
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