The Atlantic: Ioannidis [is] ... what’s known as a meta-researcher, and he’s become one of the world’s foremost experts on the credibility of medical research. He and his team have shown, again and again, and in many different ways, that much of what biomedical researchers conclude in published studies—conclusions that doctors keep in mind when they prescribe antibiotics or blood-pressure medication, or when they advise us to consume more fiber or less meat, or when they recommend surgery for heart disease or back pain—is misleading, exaggerated, and often flat-out wrong. He charges that as much as 90 percent of the published medical information that doctors rely on is flawed. His work has been widely accepted by the medical community; it has been published in the field’s top journals, where it is heavily cited; and he is a big draw at conferences. Given this exposure, and the fact that his work broadly targets everyone else’s work in medicine, as well as everything that physicians do and all the health advice we get, Ioannidis may be one of the most influential scientists alive. Yet for all his influence, he worries that the field of medical research is so pervasively flawed, and so riddled with conflicts of interest, that it might be chronically resistant to change—or even to publicly admitting that there’s a problem.

... He first stumbled on the sorts of problems plaguing the field, he explains, as a young physician-researcher in the early 1990s at Harvard. At the time, he was interested in diagnosing rare diseases, for which a lack of case data can leave doctors with little to go on other than intuition and rules of thumb. But he noticed that doctors seemed to proceed in much the same manner even when it came to cancer, heart disease, and other common ailments. Where were the hard data that would back up their treatment decisions? There was plenty of published research, but much of it was remarkably unscientific, based largely on observations of a small number of cases. A new “evidence-based medicine” movement was just starting to gather force, and Ioannidis decided to throw himself into it, working first with prominent researchers at Tufts University and then taking positions at Johns Hopkins University and the National Institutes of Health. He was unusually well armed: he had been a math prodigy of near-celebrity status in high school in Greece, and had followed his parents, who were both physician-researchers, into medicine. Now he’d have a chance to combine math and medicine by applying rigorous statistical analysis to what seemed a surprisingly sloppy field.

... In the paper, Ioannidis laid out a detailed mathematical proof that,assuming modest levels of researcher bias, typically imperfect research techniques, and the well-known tendency to focus on exciting rather than highly plausible theories, researchers will come up with wrong findings most of the time. Simply put, if you’re attracted to ideas that have a good chance of being wrong, and if you’re motivated to prove them right, and if you have a little wiggle room in how you assemble the evidence, you’ll probably succeed in proving wrong theories right. His model predicted, in different fields of medical research, rates of wrongness roughly corresponding to the observed rates at which findings were later convincingly refuted: 80 percent of non-randomized studies (by far the most common type) turn out to be wrong, as do 25 percent of supposedly gold-standard randomized trials, and as much as 10 percent of the platinum-standard large randomized trials. The article spelled out his belief that researchers were frequently manipulating data analyses, chasing career-advancing findings rather than good science, and even using the peer-review process—in which journals ask researchers to help decide which studies to publish—to suppress opposing views. “You can question some of the details of John’s calculations, but it’s hard to argue that the essential ideas aren’t absolutely correct,” says Doug Altman, an Oxford University researcher who directs the Centre for Statistics in Medicine.

...He zoomed in on 49 of the most highly regarded research findings in medicine over the previous 13 years, as judged by the science community’s two standard measures: the papers had appeared in the journals most widely cited in research articles, and the 49 articles themselves were the most widely cited articles in these journals. These were articles that helped lead to the widespread popularity of treatments such as the use of hormone-replacement therapy for menopausal women, vitamin E to reduce the risk of heart disease, coronary stents to ward off heart attacks, and daily low-dose aspirin to control blood pressure and prevent heart attacks and strokes. Ioannidis was putting his contentions to the test not against run-of-the-mill research, or even merely well-accepted research, but against the absolute tip of the research pyramid. Of the 49 articles, 45 claimed to have uncovered effective interventions. Thirty-four of these claims had been retested, and 14 of these, or 41 percent, had been convincingly shown to be wrong or significantly exaggerated. If between a third and a half of the most acclaimed research in medicine was proving untrustworthy, the scope and impact of the problem were undeniable.

... Of those 45 super-cited studies that Ioannidis focused on, 11 had never been retested. Perhaps worse, Ioannidis found that even when a research error is outed, it typically persists for years or even decades. He looked at three prominent health studies from the 1980s and 1990s that were each later soundly refuted, and discovered that researchers continued to cite the original results as correct more often than as flawed—in one case for at least 12 years after the results were discredited.

Carson Chow gives a Bayesian formulation of Ioannidis' argument here (click through to see the equations):

John Ioannidis published a very interesting paper in PLoS Biology in 2005 entitled “Why most published research findings are false.” In it he argued that most affirmative results in biology papers that are based on a statistical significance test (e.g. p-value less than 0.05) are probably wrong. His argument was couched in traditional statistics language but it is really a Bayesian argument. The paper is a wake up call that we may need to look more closely at how we use statistics and even how we do research.

The question he asked was Given some hypothesis, what is the probability that the hypothesis is true given that an experiment confirms the result (up to some level of statistical significance)? ...

In high energy physics (where we don't talk about p values, but rather number of SDs of significance of a result) it has been a common bit of folk wisdom since before I entered the field that at any given time there must be some number of multi-SD anomalies in recent experimental results, but that most (perhaps all) of these will eventually go away. (If you think about it, this is basically Ioannidis' claim.) Fortunately, because we are studying the fundamental laws of Nature (and because everyone in the field understands basic statistics; in medicine it seems almost no one does), these anomalies tend to be revisited, and meta-analyses are always done, so wrong results are not likely to become accepted conclusions for years or decades at a time.