The effects of vitamin D supplementation on health are uncertain.   A 2013 review did not find any effect from supplementation on the rates of disease, other than a tentative decrease in mortality in the elderly.  Vitamin D supplements do not alter the outcomes for myocardial infarction , stroke or cerebrovascular disease , cancer, bone fractures or knee osteoarthritis .   Low vitamin D levels may result from disease rather than cause disease. 
It is suggested that bioavailable testosterone represents the fraction of circulating testosterone that readily enters cells and better reflects the bioactivity of testosterone than does the simple measurement of serum total testosterone. Also, varying levels of SHBG can result in inaccurate measurements of bioavailable testosterone. Decreased SHBG levels can be seen in obesity, hypothyroidism , androgen use, and nephritic syndrome (a form of kidney disease ). Increased levels are seen in cirrhosis , hyperthyroidism , and estrogen use. In these situations, measurement of free testosterone may be more useful.
e) In this rodent study , it was noted that the testicular system of rats contains several receptor sites for vitamin A, and that it can be stored in testicular sertoli cells. What’s more interesting is that when the rodents diets were cut off from all vitamin A, testosterone production rapidly decreased (up to the point of where sexual organs literally athropied), and estrogen exposure inside the testes rose rapidly (as humans share nearly identical testicular systems with wistar rats, this becomes very interesting). There’s definitely some evidence that being deficient in vitamin A is not a good thing for your testosterone production or testicular health. And it’s more than likely that men with low vitamin A levels can see significant improvements in their testosterone levels after supplementing with vitamin A or consuming a lot of it in their diets .