The multiple polymorphisms contributing to Alzheimer disease (AD) have been difficult to identify. Three essentially sufficient risk sets were found using a fuzzy latent classification statistical model; that is, grade-of-membership analysis, and genotypes for APOE, APOCI, LDLr, cystatin C, and cathepsin D (180 cases, 120 controls). These were: (a) CST3:GA and CTSD:CT; (b) APOE44 and LDLr8:GG and LDLr13:TT; and (c) APOE34 and LDLr13:TC. Consonance with one of the groups and high aggregate membership carried >800-fold elevated risk for AD. The absence of these combinations defined low risk. APOE3/- with heterozygous promoter and receptor genotypes predicted long life without dementia.