Regression-based quantitative-trait-locus mapping in the 21st century.

In the beginning, there was Haseman-Elston regression. This tool for human QTL mapping, developed in 1972, was simple and inspired. The idea was to take pairs of siblings and regress the squared differences in their trait values on their identity-by-descent (IBD) sharing at a marker. If the marker is linked to the trait, high levels of IBD sharing should be associated with a small difference in trait values, and the regression slope should be negative. Thus, linkage can be tested with a regression t test. This method (with some extensions) was predominant in human studies for >20 years, which was primarily a reflection of the fact that too little human QTL mapping was being performed to prompt the development of more sophisticated methods. In the mid-1990s, we saw the first important alternative to Haseman-Elston regression, maximum-likelihood–based variance-components estimation (see, e.g., Amos 1994; Almasy and Blangero 1998). Variance components is seamlessly applicable to any type of pedigree, whereas Haseman-Elston regression is not, and it has substantially higher power than Haseman-Elston when trait distributions are approximately Gaussian. It has superseded Haseman-Elston as the method of choice for most studies, particularly when large pedigrees are used. However, variance components relies heavily on normality assumptions and can fail dramatically when those assumptions are violated either by nonnormality of the trait distribution or by selected sampling. Attempts to “robustify” variance components have had mixed success (see Feingold [2001] for a more complete discussion), so there is still a role for regression-based methods, which are intrinsically more robust. In the past 5 years, there has been an avalanche of attempts to improve the power of Haseman-Elston regression and to bring regression-based QTL mapping up to date. This was set off by Wright's (1997) Letter to the Editor suggesting that it is beneficial to use the trait values of both members of a sib pair rather than just the squared difference (although this was, in fact, pointed out by Gaines and Elston [1969]). Since then, there have been six articles suggesting “revised Haseman-Elston” (regression-based) methods that use the bivariate data—by Drigalenko (1998), Elston et al. (2000), Xu et al. (2000), Forrest (2001), Sham and Purcell (2001), and Visscher and Hopper (2001). I believe that this is a complete list, but I offer profound apologies to anyone I may have omitted. There have also been three new articles discussing score statistics that have properties similar to the regression-based methods, by Tang and Siegmund (2001), Putter et al. (2002), and Wang and Huang (2002). The best of these new methods have succeeded in matching the power of variance components while retaining the robustness of the regression framework. However, they are all limited to sibships, or, in some cases, to sib pairs. In this issue of the Journal, Sham et al. (2002) take the logical next step, by developing a regression-based method that can be applied to extended pedigrees. Those of us trying to map human QTLs have a much richer set of tools available to us than we did 5 years ago. However, the abundance of new methods has made it difficult to make choices. Only true aficionados can keep up with the literature. In this editorial, I briefly review the newest options. I will describe the new regression-based methods and score statistics, compare their strengths and weaknesses, and conclude by describing how the current offering from Sham et al. (2002 [in this issue]) fits in. I will start, however, with a disclaimer. Because all of these methods are very new, they have not been tested extensively. Most of my observations below are based on statistical theory, and I'm sure that further study of the statistics will prove at least some of my guesses wrong. A related caveat is that all of the theory I rely on is large-sample theory, and even among statistics that are asymptotically identical there may be important differences in small-sample behavior.