This article extends the Patient Rule-Induction Method (PRIM) for modeling cumulative incidence of disease developed by Dyson et al. (Genet Epidemiol 31:515-527) to include the simultaneous consideration of non-additive combinations of predictor variables, a significance test of each combination, an adjustment for multiple testing and a confidence interval for the estimate of the cumulative incidence of disease in each partition. We employ the partitioning algorithm component of the Combinatorial Partitioning Method to construct combinations of predictors, permutation testing to assess the significance of each combination, theoretical arguments for incorporating a multiple testing adjustment and bootstrap resampling to produce the confidence intervals. An illustration of this revised PRIM utilizing a sample of 2,258 European male participants from the Copenhagen City Heart Study is presented that assesses the utility of genetic variants in predicting the presence of ischemic heart disease beyond the established risk factors.