Regression models for linkage: issues of traits, covariates, heterogeneity, and interaction

Regression methods offer a common framework to analyze linkage for quantitative trait loci as well as linkage for affection status using affected sib-pairs. Although numerous papers on regression methods for linkage have been published, some common themes and important caveats tend to be scattered across the literature. For example, the typical approach is to regress a function of traits on identical-by-descent (IBD) information, but the reversal (regression of IBD on a function of traits) offers important insights. A second example is the use of regression equations to assess linkage heterogeneity or gene-environment interaction, and why these two different etiologies are difficult to distinguish with affected sib-pair data. A third example has to do with the differences, and similarities, between linear regression and non-linear regression methods for affected sib-pair data. The purposes of this paper are to review some recent developments in the linkage regression framework, to emphasize strengths and weaknesses of various proposed methods, and to highlight some important assumptions and caveats.