The medical studies I've read on this issue (not some news journalist's take on the articles, but the actual scientific articles themselves) have generally shown that losing a significant amount of weight leads to a reduction in AHI that in some cases is so dramatic the OSA is effectively cured. It's well established that AHI increases as BMI increases, so why shouldn't AHI decrease as BMI decreases? The reason researchers use gastric bypass/banding/etc. to study this is because those surgeries are the only consistent
methods to significantly reduce body fat; when they do this on a population of OSA patients, the AHI drops as weight drops and some people see such a reduction in AHI that they are no longer diagnosable as having OSA. What's really surprising is that many of these people are still overweight (though not nearly as much as before surgery) which suggests to me that if we all got down to our ideal bodyweights, many of use would not have OSA, or have such a mild case that we don't require therapy.
Maybe later I will post some medical studies on this, though I am sure some of them been posted on this site at one time or another.
One of the few complaints I have with this board is that everyone is so adamant that they are completely powerless to beat OSA when in fact losing enough body fat may very well cure their disease. I personally accept that I have OSA, but until I get down to my ideal body weight, I am not willing to say that this is a lifelong disease. Indeed, this may be merely a consequence of my obesity.
All that said, plenty of OSA sufferers are thin and have no extra weight to lose - the above points do not apply to them.