Exchangeable Models of Complex Inherited Diseases

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. C OMPLEX inherited diseases are, by definition, affected by more than one genetic locus. Although many alleles associated with higher risks of complex diseases have been identified, almost nothing is known about interactions among them or whether there is any commonality to the genetic architecture of different diseases. In this article, I examine a class of models of complex inherited diseases in which all loci increasing disease risk are equivalent in their effects. The goal is to find general properties of such models in randomly mating populations.I am particularly concerned with diseases that have prevalences in the range 0.1-2% and that are highly heritable, meaning that the concordance probability for monozygotic (MZ) twins is in the range 30-50% and the risk ratio for first-degree relatives [Risch's (1990) l 1 ] is in the range 4-10. Such diseases are regarded as common because their prevalence is much higher than monogenic diseases and because they constitute a major burden on health care systems in developed countries. Several diseases, including autism (Szatmari et al. I show that evidence of high heritability requires that there be a large variance in risk among individuals.Consequently, risk considered as a function of the number of causative alleles has to be steeply increasing in the narrow range of genotypes found in appreciable frequency in a population.Most recent analyses of complex diseases have been based on a model of multiplicative interactions across loci. The use of the multiplicative model is traceable to Risch (1990), who showed it provides a better fit to estimates of recurrence risk in first-, second-, and thirddegree relatives than do models of additive and heterogeneous interactions. Specifically, Risch (1990) showed that, under the multiplicative model, estimated recurrence risks for schizophrenia (and by implication other complex diseases) decreased more rapidly with the degree of relationship than is predicted by an additive model. He also showed that a model of genetic heterogeneity (Morton ...

Concepts and Misconceptions about the Polygenic Additive Model Applied to Disease

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An Excess of Risk-Increasing Low-Frequency Variants Can Be a Signal of Polygenic Inheritance in Complex Diseases

“…35 This model assumes that there is an underlying unmeasured trait related to disease risk and that individuals are affected with disease only when the value of the trait exceeds a particular threshold. Under such a model, we discovered that the statistical power to detect risk variants is higher than the power to detect protective variants, even when they have the same effect size with respect to the underlying unmeasured trait.…”

Epigenetic Inheritance and the Missing Heritability Problem

“…where the prime indicates the risk in a relative with relationship R. Following the notation in a previous article (Slatkin 2008), the causative allele at each locus is denoted by 1 and the other allele is denoted by a -. The frequency of 1 at locus i is p i .…”