A principal-components approach based on heritability for combining phenotype information.

For many traits, genetically relevant disease definition is unclear. For this reason, researchers applying linkage analysis often obtain information on a variety of items. With a large number of items, however, the test statistic from a multivariate analysis may require a prohibitively expensive correction for the multiple comparisons. The researcher is faced, therefore, with the issue of choosing which variables or combinations of variables to use in the linkage analysis. One approach to combining items is to first subject the data to a principal components analysis, and then perform the linkage analysis of the first few principal components. However, principal-components analyses do not take family structure into account. Here, an approach is developed in which family structure is taken into account when combining the data. The essence of the approach is to define principal components of heritability as the scores with maximum heritability in the data set, subject to being uncorrelated with each other. The principal components of heritability may be calculated as the solutions to a generalized eigensystem problem. Four simulation experiments are used to compare the power of linkage analyses based on the principal components of heritability and the usual principal components. The first of the experiments corresponds to the null hypothesis of no linkage. The second corresponds to a setting where the two kinds of principal components coincide. The third corresponds to a setting in which they are quite different and where the first of the usual principal components is not expected to have any power beyond the type I error rate. The fourth set of experiments corresponds to a setting where the usual principal components and the principal components of heritability differ, but where the first of the usual principal components is not without power. The results of the simulation experiments indicate that the principal components of heritability can be substantially different from the standard principal components and that when they are different, substantial gains in power can result by using the principal components of heritability in place of the standard principal components in linkage analyses.