Tobacco smoke and occupational exposures to chemicals such as polycyclic aromatic hydrocarbons (PAHs) are, aside from alcohol, the major risk factors for development of head and neck squamous-cell cancer (HNSCC). In this study, new statistical methods were applied. We employ new statistical methods to detect genetic interactions perhaps of higher order, that might play a role in developing HNSCC. The underlying study comprises 312 HNSCC cases and 300 controls. Single-nucleotide polymorphisms (SNPs) of PAH metabolizing and repair enzymes, somatic p53 mutations, and tobacco smoke were examined. Key statistical tools for our analysis are methods of unsupervised and supervised learning. In unsupervised learning, one performs cluster analyses based on well-known and new distance measures to find differences in the SNP patterns of cases and controls, and to understand the role of p53. Our main goal in supervised learning was to identify SNPs and SNP interactions that are likely to alter the susceptibility to HNSCC. Logic regression, a classification method well suited for SNPs, was employed as well as a Bayesian generalization that allows for incorporating additional expert knowledge. These methods detected several important interactions, such as an association between CYP1B1, tobacco smokes and p53 mutations and some interactions between CYP1B1 and glutathione S-transferases in smokers, which included a three-way interaction between CYP1B1, CYP2E1-70G>T, and GSTP1 (exon 5).