I unfortunately can't find the source either, but I read something about you having to take vitamin D suppliments for a while before the change could be detecte

I unfortunately can't find the source either, but I read something about you having to take vitamin D suppliments for a while before the change could be detected in the body, ie. if you are already sick it does not matter to take suppliments where you only see the benefit after weeks or months. This seems to support what you read.