Bayesian Corrections of a Selection Bias in Genetics

When there is a rare disease in a population, it is inefficient to take a random sample to estimate a parameter. Instead one takes a random sample of all nuclear families with the disease by ascertaining at least one sibling (proband) of each family. In these studies, an estimate of the proportion of siblings with the disease will be inflated. Sometimes the situation is even worse; the investigator takes all the families that appear. Thus, there is a selection bias [1].