Most studies about vitamin D and Alzheimer's have focused on the correlation between D deficiencies and the development of the disease. One 2010 study investigated the relationship between vitamin D levels, cerebrovascular disease, and various forms of dementia. They found that "Vitamin D insufficiency and deficiency was associated with all-cause dementia, Alzheimer's disease, stroke (with and without dementia symptoms), and MRI indicators of cerebrovascular disease", all of which point to vitamin D having an important protective role in the brain. The same year, another group of researchers published a paper regarding vitamin D levels and age-related cognitive impairment and dementia. In their six-year study, they found that low levels of vitamin D were associated with "substantial cognitive decline".
Other studies have looked at lowered vitamin D levels as a risk factor for the development of cognitive issues. A review paper published in 2012 investigated the association between dementia, cognitive function, and vitamin D, concluding that "...lower vitamin D concentrations are associated with poorer cognitive function and a higher risk of AD [Alzheimer's]". Two years later, another study of over 1,500 patients looked at whether low vitamin D levels increase the risk of age-related cognitive issues. The researchers found that vitamin D deficiency substantially increased the risk of developing dementia and Alzheimer's.