Power of regression and maximum likelihood methods to map QTL from sib-pair and DZ twin data

A common study design to map quantitative trait loci (QTL) is to compare the phenotypes and marker genotypes of two or more siblings in a sample of unrelated sib groups, and to test for linkage between chromosome location and quantitative trait values. The simplest case is sib pairs only, in particular dizygotic twin pairs, and a simple and elegant regression method was proposed by Haseman & Elston in 1972 to test for linkage. Since then, several other methods have been proposed to test for linkage. In this study, we derived the statistical power of linear regression and maximum likelihood methods to map QTL from sib pair data analytically, and determined which methods are superior under which set of population parameters. In particular, we considered four regression-based and three maximum likelihood-based approaches, and derived asymptotic approximations of the mean test statistic and statistical power for each method. It was found, both analytically and by computer simulation, that the revisited or new Haseman-Elston method (based upon the mean-corrected crossproduct of the observations on sib-pairs) is less powerful than a full maximum likelihood approach and is also inferior to the Haseman-Elston method under a realistic range of values for the population parameters. We found that a simple regression method, based upon both the squared difference and the mean-corrected squared sum of the observations on sib-pairs, is as powerful as a full maximum likelihood approach. Our derivations of statistical power for regression and maximum likelihood methods provide a simple way to compare alternative methods and obviate the need to perform elaborate computer simulations. DZ twin pairs are likely to be more powerful for linkage analysis than ordinary siblings because they may share more common environmental effects, thereby increasing the proportion of within-family variance that is explained by a QTL.