A double-blind, randomized, placebo-controlled trial of the short-term effect of vitamin D3 supplementation on insulin sensitivity in apparently healthy, middle-aged, centrally obese men

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Trouble with this study is they didn't persue the supplementation for long enough.
They ended up after six weeks at 25(OH)D (nmol/l) 36.5 ± 14.55nmol/l

Don't these people understand that you need to at least meet your body's daily vitamin D requirement before there is any spare to deal with inflammation. So as we know the body uses 3000~5000iu/daily and needs to reach 100 nmol/l before we get a basic balance between Vitamin D3 and Circulating calcidiol.
To deal with inflammation or infection or other challenge we need a store of D3 available to ensure the body's response is effective.
So we find the least incidence of chronic disease at levels above 55NG thats 137.5nmol/l CONSIDERABLY higher than these study participants got anywhere near.

We evolved from a species that lived outdoors virtually naked. We know that if we nowdays take off our clothes and spend time in the sun we attain and maintain a level between 40ng 100nmol/l and 80ng 200nmol/l
We find that human breast milk flows replete with vitamin D3 around 50~60 ng. So the sweet spot, that achieves both the lowest incidence of chronic illness and human breast milk replete with D3 is 55ng 137.5. and guess what.
That is also around the level at which we achieve peak muscle performance.

But you cannot achieve it in six weeks, mostly at intakes around 5000iu/daily it takes 3 months to get up to that level. You can check your 25(OH)D status here