Exchangeable Models of Complex Inherited Diseases

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Abstract
A model of unlinked diallelic loci affecting the risk of a complex inherited disease is explored. The loci are equivalent in their effect on disease risk and are in Hardy–Weinberg and linkage equilibrium. The goal is to determine what assumptions about dependence of disease risk on genotype are consistent with data for diseases such as schizophrenia, bipolar disorder, autism, and multiple sclerosis that are relatively common (0.1–2% prevalence) and that have high concordance rates for monozygotic twins (30–50%) and high risks to first-degree relatives of affected individuals (risk ratios exceeding 4). These observations are consistent with a variety of models, including generalized additive, multiplicative, and threshold models, provided that disease risk increases rapidly for a narrow range of numbers of causative alleles. If causative alleles are in relatively high frequency, then the combined effects of numerous causative loci are necessary to substantially elevate disease risk.