A combined test of linkage heterogeneity

This paper focuses on the problem of testing for heterogeneity once linkage is established. In an investigation of genetic linkage, Morton first proposed a general purpose test to detect heterogeneity in the recombination fraction. Two more commonly used tests of linkage heterogeneity are the admixture test (A-test) of Smith, Ott, and Risch and Baron, and the B-test of Risch. All are likelihood-ratio tests, but they differ in the models specifying the heterogeneity. A new test of heterogeneity in the presence of linkage is presented here. I propose a mixture model of heterogeneity, which allows the recombination fraction to vary among families, as does the B-model, yet also allows some families to be unlinked, as the A-model does. This model contains the A and B models as special cases and thus allows a direct test (D-test), which can provide justification for choosing one of these extremes.