Methods for calculating the power of detecting quantitative trait loci (QTL) in family-based linkage studies have been investigated extensively in the past two decades [16]–[18], [27]. These methods were developed to calculate the power of detecting a QTL but can be generalized for variance components estimation, e.g. estimating the genetic variance using pedigree information. The non-centrality parameter of the test-statistic from a maximum likelihood analysis of variance components is , where L is the likelihood function, and and are the variance covariance matrix under the null and alternative hypotheses respectively [17], [18]. For a specific balanced pedigree design, e.g. fullsibs or nuclear families, the determinant (or inverse) of the V matrix can be computed explicitly, so that the NCP can be calculated without making approximation [16], [17]. For an arbitrary pedigree, can be calculated approximately using Taylor expansions given the variance in family relatedness [18], [27]. Therefore, all these methods explicitly or implicitly require a known pedigree. When the correlations between relatives are small, the first order approximation of the NCP in Rijsdijk et al [18] can be written in
