Discrete Methods for Association Search and Status Prediction in Genotype Case-Control Studies

Recent improvements in high-throughput genotyping technology make possible genome-wide association studies and status prediction (classification) for common complex diseases. This paper addresses three challenges commonly facing such studies: (i) searching an enormous amount of possible gene interactions, (ii) validating reproducibility of associations and (iii) reliably predicting disease status. These challenges have been traditionally addressed in statistics while here we apply computational approaches -optimization and cross-validation. A complex risk factor is modeled as a subset of SNP´s with specified alleles and the optimization formulation asks for the one with the maximum odds ratio. When searching for disease associated risk factor, we show that greedy heuristics are much faster and lead to significantly better solutions than exhaustive heuristics in a reasonable amount of time. We propose a novel randomized complimentary greedy search method that is advantageous to the previously best search method. To measure and compare ability of search methods to find reproducible risk factors, we propose to apply a cross-validation scheme usually used for prediction validation. The proposed heuristic association search methods promise better reproducibility than exhaustive searches. We then show that k-fold cross-validation is more reliable than leave-one-out cross-validation for disease status prediction methods since it captures overtraining effect. We have applied known search methods with proposed enhancements as well as status prediction methods (based on these search methods) to real case-control studies for several diseases (Chron´s disease, autoimmune disorder, tick-born encephalitis, lung cancer, and rheumatoid arthritis). 2-and 3-fold cross-validations show that the new methods find strongly associated risk factors and reliably predict disease status for considered case-control studies.