Nonparametric methods of linkage analysis (3)

Analysing affected sib pair data

If IBD information is available then one can test whether the observed counts of pairs sharing 0, 1 or 2 alleles IBD differ from the expected counts assuming probabilities of 0.25, 0.5 and 0.25. A simple chi- squared test can be used to compare observed and expected counts, bearing in mind that the proportion of pairs sharing 2 alleles should be greater than 0.25.

Alternatively, one can test whether overall more alleles are shared than not shared, again with a chi-square test.

If only IBS information is available then the expected counts depend on the allele frequencies since pairs are more likely to be IBS for a common allele than a rare one.

To appropriately use all information, the likelihood of observing the sample assuming allele sharing probabilities z0, z1 and z2 of 0.25, 0.5 and 0.25 can be calculated. This is then compared with the likelihood for unconstrained values. 2ln(LR) forms a chi-squared statistic.

The power of the likelihood method for sib pairs can be enhanced by constraining the allele-sharing probabilities to lie within the "possible triangle", bounded by z1=0.5, z1+z2=1, 3z1+z2=1.

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