Ascertainment in the sequential sampling of pedigrees

One aim in the analysis of pedigree data may be to infer the mode of inheritance of a characteristic. If only “interesting” pedigrees are analysed, the ascertainment bias may lead to some modes of inheritance being unintentionally preferred. Also, it is clearly most efficient in attempting to make such inferences, if a decision on whether to continue sampling a pedigree is made conditional on the types of individuals who have been observed; an a priori decision to examine 500 members of a pedigree may lead to much wasted effort, since the pedigree may prove to be largely uninformative. The present paper shows that provided all observed families are included in the analysis, even those which appeared “uninteresting” or “sporadic” and were not sampled further, and provided a decision to continue sampling is made conditional on types observed up to that point, the correct likelihood for the mode of inheritance may be easily computed. This opens the way for a more detailed study of the wider problem of optimal sampling rules on pedigrees.