The additional statistical power of association studies for quantitative traits was derived when ungenotyped relatives with phenotypes are included in the analysis. It was shown that the extra power is a simple function of the coefficient of additive genetic relationship and the phenotypic correlation coefficient between the genotyped and ungenotyped relatives. For close relatives, such as pairs of fullsibs and identical twin pairs, gains in power in the range of 10 to 30% are achieved if only one of the pair is genotyped. The theoretical results were verified by simulations. It was shown that ignoring the error in estimating the genotype of the ungenotyped relative has little impact on the estimates and on statistical power, consistent with results from quantitative trait loci (QTL) linkage studies. For genome-wide association studies in which not all relatives with phenotypes can be genotyped, our study provides a prediction of the additional power of an analysis that includes phenotypes on ungenotyped individuals, and can be used in experimental design. We show that a two-step procedure, in which missing genotypes are imputed and subsequently an association analysis is performed, is efficient and powerful.
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