A comparison of two logistic regression approaches for case-control data with missing haplotypes

In a case-control study, subjects are selected according to disease status and their risk factors are determined retrospectively. When risk factors are fully observed for all subjects, maximum-likelihood inference of disease associations may be obtained by applying prospective logistic regression to case-control data as though it were collected prospectively. We investigate the statistical properties of prospective maximum-likelihood (PML) inference of disease associations with risk factors known as haplotypes when haplotype phase is not fully observed in some subjects. We motivate applying PhlL to case-control data and compare PML to an estimating equation (EE) approach developed specifically for such data. We conduct limited simulations of case-control data to investigate the bias of PhlL and EE, both in estimated haplotype risks and in their standard errors. PhlL performed well in the simulation configurations we considered. By contrast, EE gave anticonservative inference when there was marked haplotype ambiguity.