It's perhaps a little more complex than you may think.
There may be a role for infection in the story and the lowering of Vitamin D status is a further player.
But the pattern is familiar in several conditions.

Regulated Proteolysis of RAGE and AbetaPP as Possible Link Between Type 2 Diabetes Mellitus and Alzheimer's Disease.

Now who would have guessed there was a similar pattern in Prostate cancers?
Amyloid Formation by the Pro-Inflammatory S100A8/A9 Proteins in the Ageing Prostate

The results provide strong support for the prediction that the generic ability of polypeptide chains to convert into amyloids could lead to their involvement in an increasing number of otherwise apparently unrelated diseases, particularly those associated with ageing.


{beta}-Amyloid, Blood Vessels, and Brain Function.Cerebrovascular disease and Alzheimer disease are common diseases of aging and frequently coexist in the same brain. Accumulating evidence suggests that the presence of brain infarction, including silent infarction, influences the course of Alzheimer disease. Conversely, there is evidence that beta-amyloid can impair blood vessel function. Vascular beta-amyloid deposition, also known as cerebral amyloid angiopathy, is associated with vascular dysfunction in animal and human studies.

I sometimes get the feeling the researchers are beavering away at finding out more minuscule details in their own particular specialty and not seeing that the same pattern of disease response is occurring elsewhere in the system.