Bootstrap aggregating of alternating decision trees to detect sets of SNPs that associate with disease

Complex genetic disorders are a result of a combination of genetic and nongenetic factors, all potentially interacting. Machine learning methods hold the potential to identify multilocus and environmental associations thought to drive complex genetic traits. Decision trees, a popular machine learning technique, offer a computationally low complexity algorithm capable of detecting associated sets of single nucleotide polymorphisms (SNPs) of arbitrary size, including modern genome-wide SNP scans. However, interpretation of the importance of an individual SNP within these trees can present challenges. We present a new decision tree algorithm denoted as Bagged Alternating Decision Trees (BADTrees) that is based on identifying common structural elements in a bootstrapped set of Alternating Decision Trees (ADTrees). The algorithm is order nk(2), where n is the number of SNPs considered and k is the number of SNPs in the tree constructed. Our simulation study suggests that BADTrees have higher power and lower type I error rates than ADTrees alone and comparable power with lower type I error rates compared to logistic regression. We illustrate the application of these data using simulated data as well as from the Lupus Large Association Study 1 (7,822 SNPs in 3,548 individuals). Our results suggest that BADTrees hold promise as a low computational order algorithm for detecting complex combinations of SNP and environmental factors associated with disease.