Extension of the lod score: the mod score

In 1955 Morton proposed the lod score method both for testing linkage between loci and for estimating the recombination fraction between them. If a disease is controlled by a gene at one of these loci, the lod score computation requires the prior specification of an underlying model that assigns the probabilities of genotypes from the observed phenotypes. To address the case of linkage studies for diseases with unknown mode of inheritance, we suggested (Clerget-Darpoux et al., 1986) extending the lod score function to a so-called mod score function. In this function, the variables are both the recombination fraction and the disease model parameters. Maximizing the mod score function over all these parameters amounts to maximizing the probability of marker data conditional on the disease status. Under the absence of linkage, the mod score conforms to a chi-square distribution, with extra degrees of freedom in comparison to the lod score function (MacLean et al., 1993). The mod score is asymptotically maximum for the true disease model (Clerget-Darpoux and Bonaïti-Pellié, 1992; Hodge and Elston, 1994). Consequently, the power to detect linkage through mod score will be highest when the space of models where the maximization is performed includes the true model. On the other hand, one must avoid overparametrization of the model space. For example, when the approach is applied to affected sibpairs, only two constrained disease model parameters should be used (Knapp et al., 1994) for the mod score maximization. It is also important to emphasize the existence of a strong correlation between the disease gene location and the disease model. Consequently, there is poor resolution of the location of the susceptibility locus when the disease model at this locus is unknown. Of course, this is true regardless of the statistics used. The mod score may also be applied in a candidate gene strategy to model the potential effect of this gene in the disease. Since, however, it ignores the information provided both by disease segregation and by linkage disequilibrium between the marker alleles and the functional disease alleles, its power of discrimination between genetic models is weak. The MASC method (Clerget-Darpoux et al., 1988) has been designed to address more efficiently the objectives of a candidate gene approach.