The New Haseman-Elston Method and the Weighted Pairwise Correlation Statistic Are Variations on the Same Theme

Model free linkage analysis of quantitative traits has become increasingly popular in recent years. Its basic idea is to use the principle of similarity: Sib pairs that are genetically (dis)similar at a linked marker should be phenotypically (dis)similar and vice versa. The classical Haseman-Elston method, the new Haseman-Elston (nHE) method and the weighted pairwise correlation (WPC) method follow this principle. Similarities and differences between these approaches are discussed. It is proven that the nHE and the WPC statistic are identical under specific regularity conditions. It is furthermore demonstrated that the nHE and the WPC method are expected to yield similar results for a broad range of models. Finally, it is shown that it is impossible to a priori determine whether the nHE method or the WPC method has greater power to detect linkage under general genetic models.