A replicative association analysis of Alzheimer's disease (AD) was carried out for 15 genetic markers that have been associated with cognitive disorders in genome-wide association studies. In the Russian population, AD was associated with CSMD1 rs2616984 (OR = 1.50, 95% CI 1.07 - 2.09, p-value = 0.018) and, potentially, with NOTCH4 rs313296 (OR = 1.53, 95% CI 0.98 - 2.39, p-value = 0.06) and NRIP1 rs2229741 (OR = 1.35, 95% CI 0.99 - 1.85, p-value = 0.061). Combinations of epistatically interacting genes (CSMD1 and NRIP1; NOTCH4, CSMD1, and NRIP1; and TLR4, CSMD1, and NRIP1) were identified, along with their genotype combinations that showed a significant association with AD and the highest predictive values. Possible molecular mechanisms of the gene involvement in AD pathogenesis are discussed. A bioinformatics analysis of the biological processes, molecular functions, and protein-protein interactions for the AD genes indicated that the genes may play a modulating or modifying role, acting together in various regulatory and signaling pathways involved in AD.