Application of Cluster Variation Method to Genetic Linkage Analysis
In this paper we discuss the application of the Cluster Variation Method to the problem of genetic linkage analysis. The objective of genetic linkage analysis is to link an observed affection status (phenotype) of all individuals in a pedigree to the inheritance pattern observed certain locations on the chromosome. The Bayesian approach introduced by [7] is computationally intractable for large pedigrees and we propose to apply the Cluster Variation Method to approximately compute quantities such as the likelihood of the data. We obtain good results on an important subproblem, the computation of the intractable probability distribution of the inheritance pattern. These results encourage the incorporation of the disease model into the inheritance model. 1 Genetic Linkage Analysis One of the major questions in genetics is to link an observed disease to a certain region on the chromosome. When a disease is thought to be (partially) genetic, scientists collect a large data base of pedigree data from families in which usually a few affected individuals occur. Most or all of the family members are genotyped with markers, a technique which can be used to reconstruct the way genetic information has passed along the generations (very similar to tests for fathership). The objective of genetic linkage analysis is to link an observed affection status (phenotype) of all individuals in a pedigree to the inheritance pattern observed certain locations on the chromosome. The affection status can be directly observed for each individual in the pedigree. The disease model that determines the relation between affection status and genotype may be unknown as well as the number of locations on the chromosome that cause the disease. Through DNA-analysis there is information about the inheritance pattern, i.e. information about which genes were passed on from parents to children. For reconstructing the inheritance pattern in a pedigree, there exist algorithms, which are exact and make use of all available marker data. They are either exponential in the number of locations on the chromosome taken into account [1] or the size of the pedigree [6]. For each locus on the chromosome, the inheritance pattern within a pedigree is denoted by the inheritance vector , which contains two binary valued variables for each non-founder1. The subscript denotes the location at the chromosomes. The binary vari1Non-founders are individuals in the pedigree whose parents are also in the pedigree.