Optimal sampling for pedigree analysis: sequential schemes for sibships

Methods for inferring the mode of inheritance of a trait from familial data are becoming widely used. It is therefore important to assess alternative procedures for the collection of the relevant data. Cannings and Thompson (1977, Clinical Genetics 12, 208-212) and Thompson and Cannings (1979. In Genetic Analysis of Common Diseases, 363-382, New York: Liss) have advocated sequential schemes on the grounds that these admit simple methods for the correction of the likelihood function for ascertainment bias. Here it is shown that sequential procedures may also greatly increase efficiency, as measured by (statistical) information gained per individual sampled. Although attention is restricted to sampling sibships, and to a simple genetic model, the measures introduced are more widely applicable. A practical procedure for the construction of schemes, via a relationship between expected log likelihood and entropy, is also presented. This too is more widely applicable. A numerical example demonstrates the gains which can be achieved in practice, relative to alternative hypotheses which have been considered in several medical-genetic studies.