GAIN IN EFFICIENCY FROM USING GENERALIZED LEAST-SQUARES IN THE HASEMAN-ELSTON TEST

Techniques that test for linkage between a marker and a trait locus ba sed on the regression methods proposed by Haseman and Elston [1972] in volve testing a null hypothesis of no linkage by examination of the re gression coefficient. Modified Haseman-Elston methods accomplish this using ordinary least squares (OLS), weighted least squares (WLS), in w hich weights are reciprocals of estimated variances, and generalized e stimating equations(GEE). Methods implementing the WLS and GEE current ly use a diagonal covariance matrix, thus incorrectly treating the squ ared trait differences of two sib pairs within a family as uncorrelate d. Correctly specifying the correlations between sib pairs in a family yields the best linear unbiased estimator of the regression coefficie nt [Scheffe, 1959]. This estimator will be referred to as the generali zed least squares (GLS) estimator. We determined the null variance of the GLS estimator and the null variance of the WLS/OLS estimator. The correct null variance of the WLS/OLS estimate of the Haseman-Elston (H -E) regression coefficient may be either larger or smaller than the va riance of the WLS/OLS estimate calculated assuming that the squared si b-pair differences are uncorrelated. For a fully informative marker lo cus, the gain in efficiency using GLS rather than WLS/OLS under the nu ll hypothesis is approximately 11% in a large multifamily study with t hree siblings per family and 25% for families with four siblings each. (C) 1995 Wiley-Liss, Inc.