Choice of ascertainment model II. Discrimination between multi-proband models by means of birth order data

Probability models have been developed for family data, where each family has been selected or ascertained through a group of m probands, where m is a known parameter, not a random variable. The birth orders of the probands among the affected children are reported for each family. It is demonstrated that this information is sufficient for choice of ascertainment model. The conditional probability that an ascertained family with s children has r affected ones, depends, in addition to the segregation parameter, on the birth order of the youngest proband only. By means of the joint distribution of the birth orders of the other probands, it can be demonstrated if the ascertainment takes place through affected children near to or distant from each other in relative birth orders. Statistical methods have been developed for cases with two and cases with m probands.