Statistical properties of the haplotype relative risk

In the haplotype relative risk (HRR) statistic (Rubinstein et al.: Human Immunol 3:384 [abstract], 1981), a disease sample is constructed along with its own internal control by comparing those marker alleles passed from the parents to an affected child with the other parental marker alleles not transmitted. Based on the conditional parental genotype distribution given that they have an affected child, statistical properties of the HRR statistic are derived. It is shown that the HRR is different from 1 only when allelic association is present and the recombination fraction is different from 1/2. Transmitted and nontransmitted marker alleles are shown to be statistically independent only in the absence of either allelic association or recombination.