Sib‐pair linkage tests for disease susceptibility loci: Common tests vs. the asymptotically most powerful test

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Abstract
Several statistical tests for linkage between a disease susceptibility locus and a marker locus for sib-pair data are examined analytically. Two common statistics, a test based on the mean number of marker alleles shared identical by descent by sib-pairs, and a test based on the proportion of sib-pairs sharing exactly two marker alleles, are shown to be special cases of a more general statistic. We use this more general statistic to derive the asymptotically most powerful statistic for a given genetic alternative hypothesis, and then compare this statistic with the “mean” statistic and the “proportion” statistic. Results indicate that the “mean” statistic generally compares well with the most powerful statistic. However, in some instances the “mean” statistic may lose power, relative to the most powerful. To guard against this, a new statistic (the maximum of the “mean” and “proportions” statistics) is considered and its asymptotic distribution is derived. Results indicate that this new statistic performs well.