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Abstract:
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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. This problem, which arises in population genetics, is analogous to the well known selection bias problem in survey sampling. Here, we develop a Bayesian analysis to estimate the segregation ratio in nuclear families. We consider the situation in which the proband probabilities are allowed to vary with the number of affected siblings, and we investigate the effect of familial correlation among siblings within the same family. We discuss an example on cystic fibrosis and a simulation study to assess the effect of the familial correlation. In addition, we discuss an application in the study of single nucleotide polymorphism.
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