Two-locus heterogeneity cannot be distinguished from two-locus epistasis on the basis of affected-sib-pair data

The observation of multiple linkage signals in the course of conducting genome screens for complex disorders raises the question of whether distinct genes represent independent causes of disease (heterogeneity) or whether they interact to produce the phenotype of interest (epistasis); and there has been a corresponding interest in statistical methods for detecting and/or exploiting the distinction between these two possibilities. At the same time, researchers are increasingly relying on affected-sib-pair (ASP) data. Here, we demonstrate an apparently unrecognized fact about two-locus (2L) models and ASP data, namely, 2L heterogeneity and 2L epistasis cannot, in general, be distinguished from one another on the basis of ASP marker data, as a matter of mathematical principle and therefore regardless of sample size. By the same token, correlations across ASPs in single-locus LOD scores or other measures also cannot be used to distinguish 2L heterogeneity from 2L epistasis. This raises questions about the measurement of gene-gene interactions in terms of patterns of correlation in marker data. Portions of our results carry over to larger pedigree structures as well, as long as only affected individuals are included in analyses; the extent to which our overall findings apply to general pedigrees (including unaffected individuals) remains to be investigated.