J. Ott et D. Rabinowitz, A principal-components approach based on heritability for combining phenotype information, HUMAN HERED, 49(2), 1999, pp. 106-111
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.