The risk of Alzheimer's disease (AD) increases rapidly with age. It is not clear whether this increase continues at the very oldest ages. A slowing of the rate of increase in risk could result from heterogeneity associated with genetic or other risk factors. This study models explicitly the effect of heterogeneity of risk on the age pattern of incidence of AD. The model is fitted to published data from five prevalence studies and nine studies of AD risk by genotype for the apolipoprotein-E (APOE) gene. The model suggests that the prevalence of AD among white males at age 100 is 41.5%. Heterogeneity in the risk of AD causes the incidence rate to level off at about 11.7% per year at age 102. Some of the heterogeneity of risk is due to differences by APOE genotype. The model estimates that at age 80, the epsilon3/4 genotype is associated with an incidence rate 3.40 times that of those with the epsilon3/3 genotype. The epsilon4/4 genotype is associated with a relative risk of 9.4. Carriers of the epsilon2 allele have a risk that is only 43% of the risk among the epsilon3/3. There is substantial variation in risk associated with unobserved risk factors. Within each APOE genotype, the coefficient of variation of risk is about 1.09. In addition, the model estimates that about 0.20% of the population carries genes that cause AD at very early ages, through mechanisms that are not associated with the APOE genotype.