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

For many traits, genetically relevant disease definition is unclear. For th is reason, researchers applying linkage analysis often obtain information o n a variety of items. With a large number of items, however, the test stati stic from a multivariate analysis may require a prohibitively expensive cor rection for the multiple comparisons. The researcher is faced, therefore, w ith the issue of choosing which variables or combinations of variables to u se in the linkage analysis. One approach to combining items is to first sub ject the data to a principal components analysis, and then perform the link age analysis of the first few principal components. However, principal-comp onents analyses do not take family structure into account. Here, an approac h is developed in which family structure is taken into account when combini ng the data. The essence of the approach is to define principal components of heritability as the scores with maximum heritability in the data set, su bject to being uncorrelated with each other. The principal components of he ritability may be calculated as the solutions to a generalized eigensystem problem. Four simulation experiments are used to compare the power of linka ge analyses based on the principal components of heritability and the usual principal components. The fi rst of the experiments corresponds to the nul l hypothesis of no linkage. The second corresponds to a setting where the t wo kinds of principal components coincide. The third corresponds to a setti ng in which they are quite different and where the first of the usual princ ipal components is not expected to have any power beyond the type I error r ate. 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 comp onents of heritability can be substantially different from the standard pri ncipal components and that when they are different, substantial gains in po wer can result by using the principal components of heritability in place o f the standard principal components in linkage analyses.