The role of low testosterone may increase contracting Alzheimer’s and even type 2 diabetes. Compilation of studies show how testosterone plays a vital role in protecting the brain and is responsible for lowering inflammation and scavenging free radicals.

This study shows that low endogenous testosterone levels were associated with poor cognitive performance in healthy elderly men.
https://www.eurekaselect.com/155570/article
Lower levels of testosterone may be associated with an increased risk of all-cause dementia or AD
https://journals.sagepub.com/doi/10.1177/0891988720933351?url_ver=Z39.88-2003&rfr_id=ori%3Arid%3Acrossref.org&rfr_dat=cr_pub++0pubmed&
“Our findings strongly suggest that normal age-related testosterone depletion is one of the important changes that promote Alzheimer’s disease in men,” said Christian Pike
https://pubmed.ncbi.nlm.nih.gov/30632505/
androgen therapy might be useful in the treatment of neurodegenerative diseases
https://www.sciencedirect.com/science/article/abs/pii/S0149763418309515?via%3Dihub