The gold standard of health insurance studies is the 1982 RAND study, which was a randomized controlled study of health care usage. One of the surprising findings was that when you pushed the cost down, usage went up, but health didn't.

However, Alex Tabarrok points to a major flaw in the study:

Of the 1,294 adult participants who were randomly assigned to the free plan, 5 participants (0.4 percent) left the experiment voluntarily during the observation period, while of the 2,664 who were assigned to any of the cost-sharing plans, 179 participants (6.7 percent) voluntarily left the experiment. This represented a greater than sixteenfold increase in the percentage of dropouts, a difference that was highly significant and a magnitude of response that was nowhere else duplicated in the experiment.

What explains this? The explanation that makes the most sense is that the dropouts were participants who had just been diagnosed with an illness that would require a costly hospital procedure. … If they dropped out, their coverage would automatically revert to their original insurance policies, which were likely to cover major medical expenses (such as hospitalizations) with no copayments.

Who drops out of your study is an important factor that is far too often overlooked, especially by journalists. Weight loss studies are particularly bad for this--the people who aren't losing weight are, naturally, the ones who tend to drop out, which vastly overstates the success figures. But all sorts of medical studies are prone, including, it seems, this one.