Covariance components models for longitudinal family data

A longitudinal family study is an epidemiological design that involves repeated measurements over time in a sample that includes families. Such studies, that may also include relative pairs and unrelated individuals, allow closer investigation of not only the factors that cause a disease to arise, but also the genetic and environmental determinants that modulate the subsequent progression of that disease. Knowledge of such determinants may pay high dividends in terms of prognostic assessment and in the development of new treatments that may be tailored to the prognostic profile of individual patients. Unfortunately longitudinal family studies are difficult to analyse. They conflate the complex within-family correlation structure of a cross-sectional family study with the correlation over time that is intrinsic to longitudinal repeated measures. Here we describe an approach to analysis that is relatively straightforward to implement, yet is flexible in its application. It represents a natural extension of a Gibbs-sampling-based approach to the analysis of cross-sectional family studies that we have described previously. The approach can be applied to pedigrees of arbitrary complexity. It is applicable to continuous traits, repeated binary disease states, and repeated counts or rates with a Poisson distribution. It not only supports the analysis of observed determinants, including measured genotypes, but also allows decomposition of the correlation structure, thereby permitting conclusions to be drawn about the effect of unobserved genes and environment on key features of disease progression, and hence to estimate the heritability of these features. We demonstrate the efficacy of our methods using a range of simulated data analyses, and illustrate its practical application to longitudinal blood pressure data measured in families from the Framingham Heart Study.