Distribution of model-based multipoint heterogeneity lod scores

The distribution of two-point heterogeneity lod scores (HLOD) has been intensively investigated because the conventional χ(2) approximation to the likelihood ratio test is not directly applicable. However, there was no study investigating th e distribution of the multipoint HLOD despite its wide application. Here we want to point out that, compared with the two-point HLOD, the multipoint HLOD essentially tests for homogeneity given linkage and follows a relatively simple limiting distribution ½χ²₀+ ½χ²₁, which can be obtained by established statistical theory. We further examine the theoretical result by simulation studies.