Ascertainment and goodness of fit of variance component models for pedigree data

The multivariate normal parameterization of the polygenic model (Lange et al., 1976) provides a great deal of flexibility for analyzing quantitative data on pedigrees. The likelihood approach employed ensures statistical efficiency and allows for hypothesis testing using the likelihood ratio criterion. The parameterization also facilitates ascertainment correction and goodness-of-fit testing (Spence et al., 1977; Ott, 1979; Hopper and Mathews, 1982; Boehnke, 1983). We reviewed these results and then described a simulation study undertaken to determine their utility when applied to data. Pedigree data were generated under polygenic and mixed models and sampled either randomly or via probands. We found that the variance components of the model were accurately estimated for random sampling, but less so for ascertained data analyzed by conditioning on probands. Goodness-of-fit tests employing test statistics corresponding to individual phenotypes and entire pedigrees were conservative, but pedigree tests did demonstrate reasonable power to reject a variety of mixed model alternatives. In addition, we found that the pedigree test statistics could be used to enrich a sample of pedigrees for those pedigrees segregating at a major locus, providing an objective criterion for choosing pedigrees to be included in a linkage analysis.