Machine learning (ML) algorithms can handle complex genomic data and identify predictive patterns that may not be apparent through traditional statistical methods. They become popular tools for medical applications including prediction, diagnosis or treatment of complex diseases like rheumatoid arthritis (RA). RA is an autoimmune disease in which genetic factors play a major role. Among the most important genetic factors predisposing to the development of this disease and serving as genetic markers are HLA-DRB and non-HLA genes single nucleotide polymorphisms (SNPs). Another marker of RA is the presence of anticitrullinated peptide antibodies (ACPA) which is correlated with severity of RA. We use genetic data of SNPs in four non-HLA genes (PTPN22, STAT4, TRAF1, CD40 and PADI4) to predict the occurrence of ACPA positive RA in the Polish population. This work is a comprehensive comparative analysis, wherein we assess and juxtapose various ML classifiers. Our evaluation encompasses a range of models, including logistic regression, k-nearest neighbors, naïve Bayes, decision tree, boosted trees, multilayer perceptron, and support vector machines. The top-performing models demonstrated closely matched levels of accuracy, each distinguished by its particular strengths. Among these, we highly recommend the use of a decision tree as the foremost choice, given its exceptional performance and interpretability. The sensitivity and specificity of the ML models is about 70% that are satisfying. In addition, we introduce a novel feature importance estimation method characterized by its transparent interpretability and global optimality. This method allows us to thoroughly explore all conceivable combinations of polymorphisms, enabling us to pinpoint those possessing the highest predictive power. Taken together, these findings suggest that non-HLA SNPs allow to determine the group of individuals more prone to develop RA rheumatoid arthritis and further implement more precise preventive approach.