Information and effective number of meioses in linkage analysis

In this paper we introduce two information criteria in linkage analysis. The setup is a sample of families with unusually high occurrence of a certain inheritable disease. Given phenotypes from all families, the two criteria measure the amount of information inherent in the sample for 1) testing existence of a disease locus harbouring a disease gene somewhere along a chromosome or 2) estimating the position of the disease locus. Both criteria have natural interpretations in terms of effective number of meioses present in the sample. Thereby they generalize classical performance measures directly counting number of informative meioses. Our approach is conditional on observed phenotypes and we assume perfect marker data. We analyze two extreme cases of complete and weak penetrance models in particular detail. Some consequences of our work for sampling of pedigrees are discussed. For instance, a large sibship family with extreme phenotypes is very informative for linkage for weak penetrance models, more informative than a number of small families of the same total size.