We studied eight polymorphisms within APOE, PRNP, PRND, and CYP46 genes in 213 Polish late-onset patients with Alzheimer's disease (AD) and 171 non-demented elderly controls. A latent classification approach, grade-of-membership analysis, was taken to identify three extreme pure type risk sets defined by the probabilities of being affected with AD and for genotypes found at the examined genes. Sets I and II represented high intrinsic risk, having a higher density of various genotypes compared to set III, at low intrinsic risk. A gradient of onset age depending on membership in the risk sets was also observed. Logistic regression analysis showed that the highest risk for AD was found for individuals who co-inherited APOE epsilon4 allele, PRNP codon 129 homozygosity, PRND codon 174 Thr allele, and CYP46 rs754203 g allele. AD can be influenced by genetic profiles leading to appearance of the disease, composed of genes which separately evoke a little or unnoticeable effect. Moreover, there may be multiple sufficient risk sets for AD. Looking at multiple genes together rather than analyzing them individually, may improve identification of risk alleles.