Estimation of the association between haplotypes and disease from a case-control study is considered. Assuming a single ``disease haplotype'' leads to the increased risk, attention focusses on the relative risks associated with a single copy, or two copies of the disease haplotype, relative to individuals with no copies. In this setting, case frequencies of the haplotype pairs are in Hardy-Weinberg Equilibrium (HWE) only if the combined influence of the two copies of the disease haplotype on risk is multiplicative. Thus, imputation cannot rely on the assumption of HWE for cases. A method is presented for obtaining estimates of the relative risks, making use of the EM algorithm and the assumption of HWE only for controls. The method accounts for the additional variation in the estimates due to the imputation of expected frequencies of haplotype pairs from ambiguous genotypes. A simulation study shows that the resulting confidence intervals have nominal coverage, and that the methods based on the assumption of HWE for both cases and controls can lead to bias.
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