A new interval mapping approach based on a general sib-pair regression model with a modified Wald test

Various regression models based on sib-pair data have been developed for mapping quantitative trait loci (QTL) in humans since the seminal paper published in 1972 by Haseman and Elston. Fulker and Cardon [D.W. Fulker, L.R. Cardon, A sib-pair approach to interval mapping of quantitative trait loci, Am. J. Hum. Genet. 54 (1994) 1092–1103] adapted the idea of interval mapping [E.S. Lander, D. Botstein, Mapping Mendelian factors underlying quantitative traits using RFLP linkage maps, Genetics 121 (1989) 185–199] to the Haseman–Elston regression model in order to increase the power of QTL mapping. However, in the interval mapping approach of Fulker and Cardon, the statistic for testing QTL effects does not obey the classical statistical theory and hence critical values of the test can not be appropriately determined. In this article, we consider a new interval mapping approach based on a general sib-pair regression model. A modified Wald test is proposed for the testing of QTL effects. The asymptotic distribution of the modified Wald test statistic is provided and hence the critical values or the $p$-values of the test can be well determined. Simulation studies are carried out to verify the validity of the modified Wald test and to demonstrate its desirable power.