Analysis of affected sib pairs, with covariates--with and without constraints

Covariate models have previously been developed as an extension to affected-sib-pair methods in which the covariate effects are jointly estimated with the degree of excess allele sharing. These models can estimate the differences in sib-pair allele sharing that are associated with measurable environment or genes. When there are no covariates, the pattern of identical-by-descent allele sharing in affected sib pairs is expected to fall within a small triangular region of the potential parameter space, under most genetic models. By restriction of the estimated allele sharing to this triangle, improved power is obtained in tests for genetic linkage. When the affected-sib-pair model is generalized to allow for covariates that affect allele sharing, however, new constraints and new methods for the application of constraints are required. Three generalized constraint methods are proposed and evaluated by use of simulated data. The results compare the power of the different methods, with and without covariates, for a single-gene model with age-dependent onset and for quantitative and qualitative gene-environment and gene-gene interaction models. Covariates can improve the power to detect linkage and can be particularly valuable when there are qualitative gene-environment interactions. In most situations, the best strategy is to assume that there is no dominance variance and to obtain constrained estimates for covariate models under this assumption.