Gene-gene and gene-environment interactions are difficult to detect by traditional parametric computational approaches. Novel nonparametric and model-free strategies, such as the multifactor dimensionality reduction (MDR) algorithm, are thus emerging as practical and feasible methods of analysis to model high-order epistatic interactions, integrating and complementing traditional logistic approaches. With traditional methods of analysis we showed that the interleukin-1 beta (IL-1 beta) C+3962T single nucleotide polymorphism (SNP), along with the Sc70 antibody and the diffuse cutaneous subset of systemic sclerosis, are important risk factors for the development of a severe ventilatory restriction in patients with systemic sclerosis (SSc); however the interactions among these and other genetic and environmental attributes were difficult to model. On the contrary, the MDR analysis detected significant two- or three-way interactions in the presence of nonlinearity. The best model identified by the multifactor dimensionality reduction algorithm included the antibody subset, the IL-1 beta C-511T and the interferon-gamma AUTR5644T SNPs, with a testing accuracy of 85% (p < 0.001) and a cross-validation consistency of 10/10. This model outperformed any one- to-three-way model constructed by considering the three factors with main independent effects identified by traditional computational approaches. Epistatic interactions among IL-1 gene complex SNPs and clinical or environmental factors are more important than the singe attributes in the development of severe ventilatory restriction in SSc patients.