THE HAPLOTYPE-RELATIVE-RISK (HRR) METHOD FOR ANALYSIS OF ASSOCIATION IN NUCLEAR FAMILIES

One major problem in studying an association between a marker locus an d a disease is the selection of an appropriate group of controls. Howe ver, this problem of population stratification can be circumvented in a quite elegant. manner by family-based methods. The haplotype-relativ e-risk (HRR) method, which samples nuclear families with a single affe cted child and uses the parental haplotypes not transmitted to that ch ild as a control individual, represents such a method for estimating t he relative risk of a marker phenotype. In the special case of a reces sive disease, it was already known that the equivalence of the HRR met hod with the classical relative risk (RR) obtained from independent sa mples holds only if the probability theta of a recombination between m arker and disease locus is zero. We extend this result to an arbitrary mode of inheritance. Furthermore, we compare the distribution of the estimators for HRR and RR and show that, in the case of a positive lin kage disequilibrium between a marker and disease allele, the distribut ion of the estimator for HRR is (stochastically) smaller than that for RR, irrespective of the recombination fraction. The practical implica tion of this result is that, for the HRR method, there is no tendency to give unduly high risk estimators, even for theta > 0. Finally, we g ive an expression for the standard error of the estimator for HRR by t aking into account the nonindependence of transmitted and nontransmitt ed parental marker alleles in the case of theta > 0.