The distribution of Q: a powerful sibship test of association

Non-random inheritance of the two parental haplotypes among siblings affected by certain diseases has long been used to provide evidence of the presence of disease susceptibility genes. The distribution of a powerful test, called Q, based on haplotype concordance and discordance, is derived under the null hypothesis of random inheritance of haplotypes by affected siblings. The presence of a disease gene possibly linked to one of the haplotypes causes a change in the distribution of these haplotypes in the affected siblings. This distribution is found to be that of the sum of two independent variates contributed by the two parents in all parental types except one where both parents are heterozygous for the disease allele; which is dealt with separately. For comparison, the tables showing the powers of the test along with those of another well-known test, the N-test of haplotype concordance, are given. This is because Q is a modification of N to deal with the case when information on unaffected siblings is also available.