Distribution of the admixture test for the detection of linkage under heterogeneity

The admixture test for the detection of linkage under heterogeneity is considered. We show that the null distribution of this test statistic has half its weight concentrated on zero and the other half on a complicated distribution that can be approximated by max (X1,X2) where X1 and X2 are independent X1(2) variables. We also investigate the stability of the size of the test for small samples. The power of this test to detect linkage, when heterogeneity is present, can be substantially greater than the standard test that assumes homogeneity. Even when heterogeneity is not present, the test is only slightly less powerful than the homogeneous test. This would suggest the use of the admixture test in preference to the homogeneous test if the presence of heterogeneity is at all suspected.