Power of variance component linkage analysis to detect quantitative trait loci

Expressions are derived for the sample size required to achieve a given power in variance component linkage analysis of a quantitative trait in unascertained samples. For simplicity an additive model, comprising effects due to a single QTL, residual additive genetic factors, and individual-specific random environmental variation, is considered. Equations are given relating sample size to trait heritability for sibpairs, sib trios, nuclear families having two and three sibs, and arbitrary relative pairs. The effects of nonzero residual additive genetic variance and parental information are discussed, and a scale relationship for sample sizes with sibships and nuclear families is derived. For larger sampling structures such as extended pedigrees the inheritance space is randomly sampled and the relevant equations are solved numerically. Comparative power curves are presented for sibships of size 2-4 and for an extended pedigree of 48 individuals. Simulation results for sibpairs confirm the validity of the theoretical results.