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.