Maximum-likelihood estimation in linkage heterogeneity models including additional information via the EM algorithm

In linkage analysis, estimated recombination fractions between a disease gene and several markers are used to assign the disease gene to a particular chromosome region. For rare diseases, locus heterogeneity leads to different recombination fractions in different families, and a set of pedigrees can be regarded as a mixture. Information which can help to classify the different families may be available and can be included in the model. This is demonstrated for a data set of X-linked retinitis pigmentosa families. The joint distribution of the position of the disease gene and the additional information on the penetrance of tapetal reflex among obligate female carriers is studied. A model including the additional information is fitted to the data using the EM algorithm. The algorithm uses for every pedigree the lod score curve which can be obtained from a standard (multipoint) linkage analysis.