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.