THE SIB-PAIR PROBLEM .1. AFFECTED PAIRS WITH PARENTS - CONSTANT PENETRANCE MODELS

Affected sib pairs with typed but unaffected parents, conveniently ter med foursomes, have become a major source of information on genetic su sceptibility to common disease. So far most methods of analysis have b een based on extensions of the single locus analyses developed, and su ccessfully applied, to the mendelian disorders. However, unifactorial methods are not suited to multifactorial disorders. The power of metho ds of detecting linkage in the presence of more than one locus with on e or more susceptibility alleles is considered. The relevance of famil ial clustering to predicting the presence of loci with susceptibility or resistance alleles sufficiently frequent and effective to have an a ppreciable influence on population incidence is discussed. The mathema tical problem of clustering due to numerous alleles of small effect wa s 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 ob served in several species. The apparent inconsistency between the mend elian and polygenic models was resolved by Fisher's demonstration in 1 918 that there was no essential difference between these two extreme f orms 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 .