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.

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A method is presented for the preliminary ordering of loci on a chromosome using pairwise linkage data. The method is based on the biologically reasonable assumption that the "true" order of a set of linked loci will be the one that minimizes the total length of the chromosome segment. Here the "length" is defined as the sum of adjacent recombination fractions. The method searches for the optimal order, represented by a minimum distance map (MDMAP), even when it is not possible to examine the n!/2 possible distinct orders for n loci. A computerized approach, using the simulated annealing algorithm of Kirkpatrick et al. [1983], forms the basis of the method. It can be applied to data from radiation hybrid experiments as well as that from conventional family linkage studies. The technique is applied to several sets of published data to illustrate how it performs in practice. The advantages and the disadvantages of the method are discussed so that it will be clear under what conditions it is likely to work well. When data sets are "complete," in the sense that all possible pairwise recombination fractions have estimates, and when no large clusters of extremely tightly linked loci are present, the method produces ordered sets of loci that agree well with those generated by other, more complex methods. Any discrepancies that occur are likely to be with respect to the orientation of nearest-neighbor loci, where relative order cannot be reliably established by any method. The method thus provides a simple, rapid means of obtaining a preliminary order for a set of loci known to be in the same linkage group.