| Most diseases of interest to modern genetic epidemiologists are complex both in their etiology and measurement. That is, they result from a complicated interplay of various environmental and genetic factors, and they are subject to fuzzy, noisy and often multidimensional disease definitions. Although complex diseases are inherently multivariate, it is often difficult to see how multivariate methods may be used in family data. For example, there are several contradictory claims in the literature about the asymptotic distribution of the multivariate variance component likelihood ratio test for linkage analysis. We show that the previous claims are not correct, but computational efficient algorithms may be used to find the distribution. However, the likelihood ratio test is not robust to non-normality in this context, so several robust score tests for multivariate linkage analysis are developed. Via extensive simulations, we explore the statistical properties of these tests. Finally, a framework for using structural equation models (SEM) in family data is developed. This framework includes both a latent measurement model and a structural model with covariates. This allows for a wide variety of models, including latent growth curve models. It is shown how variance components such as polygenic, environmental and genetic variance components can be included in the SEM. |
