In genome-wide association studies, the primary task is to detect biomarkers in the form of single nucleotide polymorphisms (SNPs) that have nontrivial associations with a disease phenotype and some other important clinical/environmental factors. However, the extremely large number of SNPs compared to the sample size inhibits application of classical methods such as the multiple logistic regression. Currently, the most commonly used approach is still to analyze one SNP at a time. In this article, we propose to consider the genotypes of the SNPs simultaneously via a logistic analysis of variance (ANOVA) model, which expresses the logit transformed mean of SNP genotypes as the summation of the SNP effects, effects of the disease phenotype and/or other clinical variables, and the interaction effects. We use a reduced-rank representation of the interaction-effect matrix for dimensionality reduction, and employ the L1-penalty in a penalized likelihood framework to filter out the SNPs that have no associations. We develop a majorization–minimization algorithm for computational implementation. In addition, we propose a modified BIC criterion to select the penalty parameters and determine the rank number. The proposed method is applied to a multiple sclerosis dataset and simulated datasets and shows promise in biomarker detection.
- MM algorithm
- Penalized Bernoulli likelihood
- Simultaneous modeling of SNPs
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty