Likelihood-Based Inference on Haplotype Effects in Genetic Association Studies

Abstract

A haplotype is a specific sequence of nucleotides on a single chromosome. The population associations between haplotypes and disease phenotypes provide critical information about the genetic basis of complex human diseases. Standard genotyping techniques cannot distinguish the two homologous chromosomes of an individual, so only the unphased genotype (i.e., the combination of the two homologous haplotypes) is directly observable. Statistical inference about haplotype–phenotype associations based on unphased genotype data presents an intriguing missing-data problem, especially when the sampling depends on the disease status. The objective of this article is to provide a systematic and rigorous treatment of this problem. All commonly used study designs, including cross-sectional, case-control, and cohort studies, are considered. The phenotype can be a disease indicator, a quantitative trait, or a potentially censored time-to-disease variable. The effects of haplotypes on the phenotype are formulated through flexible regression models, which can accommodate various genetic mechanisms and gene–environment interactions. Appropriate likelihoods are constructed that may involve high-dimensional parameters. The identifiability of the parameters and the consistency, asymptotic normality, and efficiency of the maximum likelihood estimators are established. Efficient and reliable numerical algorithms are developed. Simulation studies show that the likelihood-based procedures perform well in practical settings. An application to the Finland–United States Investigation of NIDDM Genetics Study is provided. Areas in need of further development are discussed.