The following figure highlights the exposure scheme in the three published vitamin D / allergy clinical trials so far: Grant 2016, Litonjua 2016 and Chawes 2016.
None of them found anything important, maybe due to the design flaw in all these studies?
All three studies have been designed with the assumption of a beneficial vitamin D effect.
They are dose finding studies that do not allow to prove or disprove any vitamin D effect.