The relationship between the sibling recurrence-risk ratio and genotype relative risk

Abstract

The recurrence-risk ratio of disease in siblings, lambdaS, is a standard parameter used in genetic analysis to estimate the statistical power for detection of a disease locus. However, the relationship between the underlying risk conferred by a disease-susceptibility allele and lambdaS has not been well described. The former is generally quantified as a genotype relative risk, gamma, and measures the ratio of disease risks between those with and those without the susceptibility genotype(s). We demonstrate that lambdaS varies significantly more with respect to gamma and the disease-allele frequency for two-locus multiplicative models than for other two-locus and for single-locus models. For the single- and two-locus dominant-inheritance models that we studied, when a disease-susceptibility allele had a frequency >/=.2, lambdaS had an upper limit of <10. In general, lambdaS values >10 are possible only under recessive inheritance, dominant inheritance with relatively rare (<5%) disease-susceptibility alleles, or when two or more disease loci have alleles acting either epistatically or multiplicatively. We introduce the idea of a restricted sib recurrence-risk ratio (lambda*S) estimated by restriction of sibships to those ascertained through a proband who already has a putative high-risk allele. A lambda*S larger than the lambdaS value estimated from randomly selected probands can serve as an indirect way of testing whether the posited susceptibility allele increases disease risk. Our results demonstrate that a lambdaS of 2-3 may portend successful mapping for a variety of genetic models but that, for some two-locus models, a lambdaS as high as 10 does not guarantee underlying genes easily mapped by linkage.

Figures

Figure 1

A, Relationship between λS and γ for disease-susceptibility allele frequencies of .01–.5 under a single-locus dominant-inheritance model. B, Relationship between λS and γ for disease-susceptibility-allele frequencies of .01–.5 under a single-locus recessive-inheritance model.

Figure 2

A, Relationship between λS and γ, for disease-susceptibility-allele frequencies of .01–.5, under a two-locus epistatic-inheritance model (epistatic model 1), in which at least one disease-susceptibility allele from each locus must be present for increased disease risk. B, Relationship between λS and γ, for disease-susceptibility-allele frequencies of .01–.5, under a two-locus epistatic-inheritance model (epistatic model 2), in which two copies of a disease-susceptibility allele from each locus must be present for increased disease risk. C, Relationship between λS and γ, for disease-susceptibility allele frequencies of .01–.5, under a two-locus epistatic-inheritance model (epistatic model 3), in which a total of three or more copies of a disease-susceptibility allele from both loci must be present for increased disease risk.

Figure 3

A, Relationship between λS and γ, for disease-susceptibility-allele frequencies of .01–.5, under a two-locus dominant-additive-inheritance model. B, Relationship between λS and γ, for disease-susceptibility-allele frequencies of .01–.5, under a two-locus recessive-additive-inheritance model.

Figure 4

A, Relationship between λS and γ, for disease-susceptibility-allele frequencies of .01–.5, under a two-locus dominant-multiplicative -inheritance model. B, Relationship between λS and γ, for disease-susceptibility-allele frequencies of .01–.5, under a two-locus recessive-multiplicative-inheritance model.