Comparison of prospective and retrospective methods for haplotype inference in case-control studies

We compare bias and power of three methods for haplotype inference on disease risk using unphased genotype data from a case-control study. We examine the prospective score test of Schaid et al., a novel modification of the prospective estimating equations of Zhao et al. and the retrospective likelihood of Epstein and Satten. We find that all three approaches are roughly comparable when the haplotype effect on disease odds follows a multiplicative model. However, for dominant and recessive models of haplotype effect, the retrospective-likelihood method has increased efficiency with respect to the prospective methods. As all three methods assume haplotype frequencies are in Hardy-Weinberg Equilibrium (HWE), we compare the robustness of each procedure to departures from HWE. We find the prospective methods are robust to departure from HWE, while the retrospective-likelihood method is biased for dominant and recessive models of haplotype effect. To remedy this limitation of the retrospective-likelihood method, we propose a modification that allows for a non-negative fixation index (common to all haplotype pairs) and show it dramatically reduces the bias of the retrospective likelihood when HWE is violated.