A bivariate problem in human genetics: ascertainment of families through a correlated trait

In genetic analysis of pedigree data, nonrandom sampling occurs commonly and appropriate adjustments for the ascertainment procedure are necessary for the correct interpretation of results. In this paper we consider ascertainment models for the situation in which proband selection is made on the basis of one trait, but the desired object of analysis is another related trait for which the individuals in the pedigree also are measured. The ascertainment function corresponding to the most useful bivariate form, that involving two correlated quantitative traits, is described explicitly under suitable assumptions. As its form is mathematically intractable for purposes of pedigree analysis, an approximation is developed. Such ascertainment models accomplish corrections for ascertainment while permitting adjustment for covariates, analysis of traits correlated with the trait used in selection, and multivariate analysis of nonrandomly sampled pedigrees using linear combinations of traits.