 
Summary: Genetic Epidemiology 30: 471484 (2006)
Estimating the Power of Variance Component Linkage Analysis
in Large Pedigrees
WeiMin ChenĂ and Goncalo R. Abecasis
Department of Biostatistics, University of Michigan, Ann Arbor, MI
Variance component linkage analysis is commonly used to map quantitative trait loci (QTLs) in general pedigrees. Large
pedigrees are especially attractive for these studies because they provide greater power per genotyped individual than
small pedigrees. We propose accurate and computationally efficient methods to calculate the analytical power of variance
component linkage analysis that can accommodate large pedigrees. Our analytical power computation involves the
approximation of the noncentrality parameter for the likelihoodratio test by its Taylor expansions. We develop efficient
algorithms to compute the second and third moments of the identical by descent (IBD) sharing distribution and enable
rapid computation of the Taylor expansions. Our algorithms take advantage of natural symmetries in pedigrees and can
accurately analyze many large pedigrees in a few seconds. We verify the accuracy of our power calculation via simulation
in pedigrees with 25 generations and 28 siblings per sibship. We apply this proposed analytical power calculation to 98
quantitative traits in a cohort study of 6,148 Sardinians in which the largest pedigree includes 625 phenotyped individuals.
Simulations based on eight representative traits show that the difference between our analytical estimation of the expected
LOD score and the average of simulated LOD scores is less than 0.05 (1.5%). Although our analytical calculations are for
a fully informative marker locus, in the settings we examined power was similar to what could be attained with a single
nucleotide polymorphism (SNP) mapping panel (with 41 SNP/cM). Our algorithms for power analysis together
with polygenic analysis are implemented in a freely available computer program, POLY. Genet. Epidemiol. 30:471484, 2006.
