The aim of this work is to solve the problem of the ranking of genes relative to their importance in the process of nucleation and development of a genetic disease, in particular, Alzheimer's disease. As a biological value of the relevance index used to determine the "power" of genes, we will consider a modified Shapley vector. Analyzed gene databases of patients with a diagnosis of Alzheimer's disease, as well as patients with other types of dementia. Identified genes with a high index of "activity", which can play a key role in the pathogenesis of Alzheimer's disease. The influence of some of the genes obtained is confirmed by modern scientific publications. In addition, genes have been identified, the influence of which has not yet been considered.