Associating single nucleotide polymorphisms (SNPs) with binary traits

Association mapping uses statistical analyses to test for relationships between genomic markers that are called single nucleotide polymorphisms (SNPs) and traits. A statistically significant association between a SNP and a trait suggests that there exists a biological association between a nearby genomic region and the trait. This research focuses on the use of logistic regression to assess the additive, dominance, and epistatic effects when investigating associations between SNPs and binary traits. A very specific phenomenon, called quasi-separation of points (QSP), can arise in association mapping data, resulting in infinite maximum likelihood estimates (MLEs) of logistic regression parameters. One solution to this problem is to use Firth's MLE, which provides finite estimates in the presence of QSP. Simulation studies are conducted to investigate the use of Firth's MLE in a QSP setting, and to assess the similarity between Firth's MLE and the traditional MLE when QSP is not present. Two published association mapping studies in humans are reanalyzed to demonstrate the implementation of Firth's MLE in real data settings.