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 differe nces in sib-pair allele sharing that are associated with measurable environ ment or genes. When there are no covariates, the pattern of identical-by-de scent allele sharing in affected sib pairs is expected to fall within a sma ll triangular region of the potential parameter space, under most genetic m odels. By restriction of the estimated allele sharing to this triangle, imp roved power is obtained in tests for genetic linkage. When the affected-sib -pair model is generalized to allow for covariates that affect allele shari ng, however, new constraints and new methods for the application of constra ints are required. Three generalized constraint methods are proposed and ev aluated by use of simulated data. The results compare the power of the diff erent methods, with and without covariates, for a single-gene model with ag e-dependent onset and for quantitative and qualitative gene-environment and gene-gene interaction models. Covariates can improve the power to detect l inkage and can be particularly valuable when there are qualitative gene-env ironment interactions. In most situations, the best strategy is to assume t hat there is no dominance variance and to obtain constrained estimates for covariate models under this assumption.