Predicting recurrence risks under epistatic models

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

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.

Predictions of a 2-locus model for disease heterogeneity: application to adrenoleukodystrophy

Adrenoleukodystrophy (ALD) is an X-linked disorder that exhibits a wide range of phenotypic variability within individuals in a single family carrying the mutant allele. A 2-locus epistatic model has been proposed to explain the inheritance of the severe childhood form of ALD and the milder adult-onset adrenomyloneuropathy (AMN). Under a dominant epistatic model, a single M allele at an autosomal modifier locus ameliorates the most severe effects of the disease allele leading to the milder AMN phenotype; only males with genotype mm would have ALD. Under a recessive epistatic model, 2 copies of the M allele would be necessary to have the milder AMN phenotype. Here, we show that recurrence risks for a second affected male depend on the frequency of the protective allele at this modifier locus. Whereas it is most likely that 2 affected brothers will be concordant for their disease phenotypes, discordant pairs of affected brothers are possible at all frequencies of M. Within a narrow range of modifier allele frequencies, the predicted distribution of affected sib pairs (over all families) is consistent with empiric data from a large clinic population. Here we suggest sampling discordant affected sib pairs as a strategy for detecting linkage between a polymorphic DNA marker and a possible modifier gene. Since both epistatic models predict that discordant affected pairs should not share 2 alleles at the modifier locus, we expect that departures from the null distribution could be detected with relatively small numbers of sib pairs.