Gamma regression improves Haseman-Elston and variance components linkage analysis for sib-pairs

Existing standard methods of linkage analysis for quantitative phenotypes rest on the assumptions of either ordinary least squares (Haseman and Elston [1972] Behav. Genet. 2:3-19; Sham and Purcell [2001] Am. J. Hum. Genet. 68:1527-1532) or phenotypic normality (Almasy and Blangero [1998] Am. J. Hum. Genet. 68:1198-1199; Kruglyak and Lander [1995] Am. J. Hum. Genet. 57:439-454). The limitations of both these methods lie in the specification of the error distribution in the respective regression analyses. In ordinary least squares regression, the residual distribution is misspecified as being independent of the mean level. Using variance components and assuming phenotypic normality, the dependency on the mean level is correctly specified, but the remaining residual coefficient of variation is constrained a priori. Here it is shown that these limitations can be addressed (for a sample of unselected sib-pairs) using a generalized linear model based on the gamma distribution, which can be readily implemented in any standard statistical software package. The generalized linear model approach can emulate variance components when phenotypic multivariate normality is assumed (Almasy and Blangero [1998] Am. J. Hum Genet. 68: 1198-1211) and is therefore more powerful than ordinary least squares, but has the added advantage of being robust to deviations from multivariate normality and provides (often overlooked) model-fit diagnostics for linkage analysis.