A unified approach to modelling linkage to quantitative and qualitative traits

For quantitative traits with a genetic component, random effects approaches are used to test for linkage at observed marker loci. We propose to use these approaches also for binary outcomes observed in sib pairs derived from a population-based cohort study. In addition to a random effect modelling correlation due to polygenic effect, a random effect is included to model the correlation between siblings due to sharing alleles identical by descent (IBD) at the observed marker locus. A two-step analysis is proposed. Firstly, score statistics are computed to test whether correlation is present in the data. Secondly, random effects models are fitted, yielding heritability estimates. To illustrate the methods, data on the contribution of the COL2A1 gene to various binary and quantitative outcomes including the presence of Heberden's nodes and bone mineral density (BMD) are analysed. For most of the traits studied, the score statistics were significant, indicating the presence of genetic effects. For BMD and for Heberden's nodes, the variance explained by the marker locus was 44% (P = 0.0008) and 15% (P = 0.38) respectively. We conclude that the score statistics can be used as a preliminary data analysis. In more sophisticated analysis, heritabilities can be estimated by fitting random effects models.