Joint multipoint linkage analysis of multivariate qualitative and quantitative traits. I. Likelihood formulation and simulation results

Abstract

We describe a variance-components method for multipoint linkage analysis that allows joint consideration of a discrete trait and a correlated continuous biological marker (e.g., a disease precursor or associated risk factor) in pedigrees of arbitrary size and complexity. The continuous trait is assumed to be multivariate normally distributed within pedigrees, and the discrete trait is modeled by a threshold process acting on an underlying multivariate normal liability distribution. The liability is allowed to be correlated with the quantitative trait, and the liability and quantitative phenotype may each include covariate effects. Bivariate discrete-continuous observations will be common, but the method easily accommodates qualitative and quantitative phenotypes that are themselves multivariate. Formal likelihood-based tests are described for coincident linkage (i.e., linkage of the traits to distinct quantitative-trait loci [QTLs] that happen to be linked) and pleiotropy (i.e., the same QTL influences both discrete-trait status and the correlated continuous phenotype). The properties of the method are demonstrated by use of simulated data from Genetic Analysis Workshop 10. In a companion paper, the method is applied to data from the Collaborative Study on the Genetics of Alcoholism, in a bivariate linkage analysis of alcoholism diagnoses and P300 amplitude of event-related brain potentials.

Figure 1

Genetic model for simulated data: random environmental effect (E), major genes with additive effects (MG4, MG5, and MG6), observable quantitative trait (Q4), unobservable quantitative trait (liability) (Q5), observable discrete disease trait derived from Q5 (D5), residual environmental correlation (.40) (ρ_e), and population prevalence of D5 (30%) (K_P). Unlabeled numbers indicate the percentage of relative additive genetic and environmental variance components for each trait. (Adapted from MacCluer et al. [1997])

Figure 2

Multipoint LOD scores for GAW10 data on chromosome 8, in univariate and bivariate linkage analyses of Q4 and D5

Figure 3

Multipoint LOD scores for GAW10 data on chromosome 9, in univariate and bivariate linkage analyses of Q4 and D5