This paper addresses the computational challenge fac- ing association analysis of case-control studies ? search- ing an enormous amount of possible gene interactions. A complex risk factor (RF) is proposed to be modeled as close (weighted) match to a diplotype (e.g., no more than k mismatches) and the optimization formulation asks for RF with the maximum odds ratio. We have applied and cross-validated previously known and two proposed search methods for finding basic RF's with large odds ratios on 5 real case-control studies. New proposed methods find RF's that are statistically significant on all data including two datasets where no significant RF's were found before. The found RF's explain 1.5-4 times more cases than previ- ously known RF's. The new methods also have significantly higher leave-half-out cross-validation rate.