Genetically modified mice characterized by one or more symptoms or signs associated with expression of human APOE4p and mouse Trem2p and relevant to non-familial late-onset Alzheimer's disease are provided wherein the genome of the mouse includes: 1) a DNA sequence encoding a human APOE4 protein (APOE4p) operably linked to a promoter; and 2) a DNA sequence encoding a mouse Trem2 protein having a mutation p,R47H (Trem2p) operably linked to a promoter, such that the mouse expresses human APOE4p and mouse Trem2p. Methods ace provided for screening for a compound for use in the treatment of Alzheimer's disease using such genetically modified mice.