Lods, wrods, and mods: the interpretation of lod scores calculated under different models

In this paper we examine the relationships among classical lod scores, "wrod" scores (lod scores calculated under the wrong genetic model), and "mod" scores (lod scores maximized over genetic model parameters). We compare the behavior of these scores when the state of nature is linkage to their behavior when the state of nature is no linkage. We describe sufficient conditions for mod scores to be valid and discuss their use to determine the correct genetic model. We show that lod scores represent a likelihood-ratio test for independence. We explain the "ascertainment-assumption-free" aspect of using mod scores to determine mode of inheritance and we set this aspect into a well-established statistical framework. Finally, we summarize practical guidelines for the use of mod scores.