The problem with your idea is that Alzheimer's disease is not easy to study.
1) There is no good diagnostic test for Alzheimer's outside of a brain biopsy (although Lilly just got a diagnostic approved). Today, it's usually diagnosed by a process of elimination (i.e. you don't have any signs that it's another organic brain disease, thus it must be Alzheimer's).
2) The time of onset to the time of death for Alzheimer's is often measured in decades. You'd have to run a REALLY long study to be able to capture that data.
The other issue is that analyzing data from studies retrospectively (studies that weren't designed to test your given hypotheses) are generally regarded as "lower quality". It may support your hypotheses, but it's pretty weak support.
1) Lilly's diagnostic is about beta amyloid plaques, not Alzheimer directly. There is some questions whether amyloid plaques are good indicators of Al Zheimer or not, and this will need to be validated in the future.