Mapping Quantitative Trait Loci Using Multiple Phenotypes in General Pedigrees

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Abstract
The use of correlated phenotypes may dramatically increase the power to detect the underlying quantitative trait loci (QTLs). Current approaches for multiple phenotypes include regression-based methods, the multivariate variance of components method, factor analysis and structural equations. Issues with these methods include: 1) They are computation intensive and are subject to problems of optimization algorithms; 2) Existing claims on the asymptotic distribution of the likelihood ratio statistic for the multivariate variance of components method are contradictory and erroneous; 3) The dimension reduction of the parameter space under the null hypothesis, a phenomenon that is unique to multivariate analyses, makes the asymptotic distribution of the likelihood ratio statistic more complicated than expected. In this article, three cases of varying complexity are considered. For each case, the efficient score statistic, which is asymptotically equivalent to the likelihood ratio statistic, is derived, so is its asymptotic distribution. These methods are straightforward to calculate. Finite-sample properties of these score statistics are studied through extensive simulations. These score statistics are for use with general pedigrees.