Genetic Epidemiology 19:1–17 (2000) GEPI 9904 © 2000 Wiley-Liss, Inc. Haseman and Elston Revisited Robert C. Elston,* Sarah Buxbaum, Kevin B. Jacobs, and Jane M. Olson Department of Epidemiology and Biostatistics, Rammelkamp Center for Education and Research, MetroHealth Campus, Case Western Reserve University, Cleveland, Ohio Haseman and Elston (H-E) [1972] proposed a method to detect quantitative trait loci by linkage to a marker. The squared sib-pair trait difference is regressed on the proportion of marker alleles the pair is estimated to share identical by de- scent: a significantly negative regression coefficient suggests linkage. It has been shown that a maximum likelihood method that directly models the sib-pair cova- riance has more power. This increase in power can also be obtained using the H- E regression procedure by changing the dependent variable from the squared difference to the mean-corrected product of the sibs’ trait values. Multiple sibs in a sibship can be accommodated by allowing for the correlations between pairs of products in a generalized least squares procedure. Multiple trait loci, includ- ing epistatic interactions, involve only multiple linear regression. Multivariate traits can use the method of Amos et al. [1990] to find the linear function of the traits that maximizes the evidence for linkage, which now leads more simply to a test of significance. Multiple markers can be the basis of a multipoint analysis. Results of simulation studies for a continuous trait are presented that investigate Type I error and power. A similar general scheme can be used to study affected sib pairs, testing whether their identity by descent sharing probabilities are greater than would be expected in the absence of linkage, and to study other types of relative pairs. Genet. Epidemiol. 19:1–17, 2000. © 2000 Wiley-Liss, Inc. Key words: genome scan; model-free linkage analysis; quantitative trait; sib pairs Contract grant sponsor: National Institute of General Medical Sciences; Contract grant number: GM 28356; Contract grant sponsor: National Center for Human Genome Research; Contract grant number: HG01577; Contract grant sponsor: National Heart, Lung and Blood Institute; Contract grant number: HL 55005; Contract grant sponsor: National Center for Research Resources; Contract grant number: RR 03655. *Correspondence to: Dr. Robert C. Elston, Department of Epidemiology and Biostatistics, Case West- ern Reserve University, MetroHealth Medical Center, R-258, 2500 MetroHealth Drive, Cleveland, OH 44109-1998. E-mail: rce@darwin.cwru.edu Received 10 February 1999; Accepted 30 April 1999