A Simple Loglinear Model for Haplotype Effects in a Case-Control Study Involving Two Unphased Genotypes

Because haplotypes may parsimoniously summarize the effect of genes on disease, there is great interest in using haplotypes in case-control studies of unphased genotype data. Previous methods for investigating haplotypes effects in case-control studies have not allowed for both of the following two scenarios that could have a large impact on results (i) departures from Hardy-Weinberg equilibrium in controls as well as cases, and (ii) an interactive effect of haplotypes and environmental covariates on the probability of disease. A new method is proposed that generalizes the model of Epstein and Satten to incorporate both (i) and (ii). Computations are relatively simple involving a single loglinear design matrix for parameters modeling the distribution of haplotype frequencies in controls, parameters modeling the effect of haplotypes and covariate-haplotype interactions on disease, and nuisance parameters required for correct inference. Based on simulations with realistic sample sizes, the method is recommended with data from two genotypes, a recessive or dominant model linking haplotypes to disease, and estimates of haplotype effects among haplotypes with a frequency greater than 10%. The methodology is most useful with candidate genotype pairs or for searching through pairs of genotypes when scenarios (i) and (ii) are likely. An example without a covariate illustrates the importance of modeling a departure from Hardy-Weinberg equilibrium in controls.