Maximum-Likelihood-Binomial method for genetic model-free linkage analysis of quantitative traits in sibships

Sib-pair linkage studies are widely used to investigate the genetic factors implicated in complex quantitative traits. To analyze these data, we propose a Maximum-Likelihood-Binomial (MLB) approach, which considers the sibship as a whole and relies on the idea of binomial distributions of parental alleles among offsprings. The method is based on the introduction of a latent binary variable capturing the linkage information between the observed quantitative trait and the marker, and the final likelihood can be expressed assuming a parametric distribution for the studied trait but also without any assumption on this distribution. The test for linkage is a simple likelihood ratio test involving a single parameter. The performances of the MLB method are assessed by a simulation study in different kinds of family samples. In the case of families with various sibship sizes, both MLB approaches (assuming or not a parametric distribution for the quantitative trait) provide very consistent results in terms of type I errors and yield power levels generally higher than those of the classical Haseman-Elston method. In the case of extremely discordant sib pairs, we analytically show that, for a common asymptotic type I error, the distribution-free MLB statistic is expected to be more powerful than the test proposed by Risch and Zhang [(1995) Science 268:1584-1589]. In samples including both extremely concordant and discordant sib-pairs, simulation studies show that the MLB approach is at least as powerful as the EDAC method [Gu et al. (1996) Genet Epidemiol 13:513-533]. This MLB method, which can be easily extended to perform multipoint analysis and to account for genetic heterogeneity, appears to be quite an interesting alternative for mapping quantitative trait loci in humans.