Haplotype relative risks: an easy reliable way to construct a proper control sample for risk calculations

An alternative to Woolf's (1955) relative risk (RR) statistic is proposed for use in calculating the risk of disease in the presence of particular antigens or phenotypes. This alternative uses, as the control sample, the parental antigens or haplotypes not present in the affected child. The formulation of a haplotype relative risk (HRR) thus eliminates the problems of sampling from the same homogeneous population to form both the disease sample and an appropriate control. We show that, in families selected through a single affected individual, where transmission of the four parental haplotypes can be followed unambiguously, the mathematical expectation of the HRR is identical to that of the RR. Since the sample formed from the 'non-affected' parental haplotypes is clearly from the same population as the disease sample, the HRR thus provides a reliable alternative to the RR. A further advantage obtains when family data are being collected as part of a study since the control sample is then automatically contained in the family material. Data from studies of patients with insulin dependent diabetes mellitus (IDDM) are used to obtain an estimate of the risk to those with HLA antigens or phenotypes associated with IDDM using the HRR statistic. A comparison of the HRR's and RR's for these data is also presented.