I just read Antidepressants: Bad Drugs... Or Bad Patients, linked by wallowinmaya in a discussion post and based on the journal articles Antidepressant Clinical Trials and Subject Recruitment: Just Who Are Symptomatic Volunteers? and Failure Rate and "Professional Subjects" in Clinical Trials of Major Depressive Disorder (paywalled). The authors of the latter paper "were told anonymously by trial sponsors that duplicate subjects in some protocols have been as high as 5%", and write "we believe that failure rates are rising due to the increase in "professional subjects," who go from site to site, learning inclusion and exclusion criteria and collecting stipends."
Aha! No wonder so much antidepressant research is crap. How many people do you suppose there are, who sign up for lots of trials at once? They'd have to defraud the researchers, of course; no one would allow a patient like that into their study knowingly. What do you suppose that sort of person would do, and how would it be reflected in the data? What other types of studies are affected? And how would we find out? (Dietary studies look vulnerable, and their results have been conspicuously unreliable. On the other hand, lots of people want to lose weight, so legitimate subjects are probably plentiful and drive down the percentage).
Let's start with some speculative modeling. First, to be clear: we're talking about people who participate in multiple studies, and lie about it. That means defrauding researchers, and they know it. If they're doing so rationally, then a lot of their responses are going to be lies, designed to maximize the chance they get paid, and minimize the chance they get caught. Now, if you were defrauding researchers anyways, there's no reason to actually take all the drugs, and good reasons not to (other drugs they denied taking could interact, for example). Instead, you'd start by figuring out whether you were in the placebo group or not. This isn't very hard; you can either try the pills and see if there's any effect at all (real drugs have perceptible effects, even if they're only side effects), or break one open and taste it, or even do a proper chemical test. If in the placebo group, you'd answer all questions in a manner consistent with getting no effect: no side effects, no change in status, etc. This could be even more placebo-like than a real placebo; normal subjects on placebo sometimes report unrelated things as side-effects, but fraudsters probably wouldn't. If in the experimental group, on the other hand, you'd try to match the experimenters' expectations, to avoid attention. This would mean claiming that it helped. So in a drug trial with a goal that's unverifiable, you'd expect people who got into the study fraudulently to systematically bias the study towards showing effectiveness.
One of the papers repeated an anonymous claim of finding up to 5% duplicate subjects in some studies. Those are subjects who used the same name each time, but there could be more, who use aliases. Since one fraudster can participate in many studies, a small number of them can have a big impact. Since many studies end with small effect sizes, but we count significance rather than size, their effect is magnified further.
The main obstacle to preventing this kind of fraud is confidentiality; medical records are supposed to be kept secret, which means it's hard to get at other studies' patient lists to cross-check. But it's certainly not impossible, and I think some auditing is called for. Another strategy is to conduct a "study on study fraud" - advertise it like an antidepressant study, conduct it like one, pay well, and give everyone placebos in a special bottle that logs the time and the weight of its contents whenever it's opened. A similar strategy for dietary studies is to include a food with distinctive metabolites, and test for those metabolites.