Analytic power calculation for QTL linkage analysis of small pedigrees

Power calculation for QTL linkage analysis can be performed via simple algebraic formulas for small pedigrees, but requires intensive computation for large pedigrees, in order to evaluate the expectation of the test statistic over all possible inheritance vectors at the test position. In this report, we show that the non-centrality parameter for an arbitrary pedigree can be approximated by the sum of the variances of the correlations between all pairs of relatives, each variance being weighted by a factor that is determined by the mean correlation of the pair. We show that this approximation is sufficiently accurate for practical purposes in small to moderately large pedigrees, and that large sibships are more efficient than other family structures under a range of genetic models.