The sib-pair problem. I. Affected pairs with parents. Constant penetrance models

Affected sib pairs with typed but unaffected parents, conveniently termed foursomes, have become a major source of information on genetic susceptibility to common disease. So far most methods of analysis have been based on extensions of the single locus analyses developed, and successfully applied, to the mendelian disorders. However, unifactorial methods are not suited to multifactorial disorders. The power of methods of detecting linkage in the presence of more than one locus with one or more susceptibility alleles is considered. The relevance of familial clustering to predicting the presence of loci with susceptibility or resistance alleles sufficiently frequent and effective to have an appreciable influence on population incidence is discussed. The mathematical problem of clustering due to numerous alleles of small effect was resolved by Pearson in 1901 in relation to claims that the mendelian model of an allele at a single locus determining a distinct phenotype was necessary to explain the familial concentrations that had been observed in several species. The apparent inconsistency between the mendelian and polygenic models was resolved by Fisher's demonstration in 1918 that there was no essential difference between these two extreme forms of phenotypic determination. Although constant penetrance models are unrealistic, and no longer necessary since Pearson's analysis, the assumption is implicit in most recent analyses and has the advantage of simplicity in providing a lower limit on the sample sizes necessary.