Broccoli causes lung cancer, or why most science is wrong

Robert Lee Hotz wrote in the Wall Street Journal that most science studies appear to be tainted by sloppy analysis. (My impression here is that "science" means "biomedical science", which is the sort of science that is most reported on by the media, for the simple reason that it is the kind of science which has the most direct effect on people's lives.) I learned about this from Marginal Revolution; NeuroLogica and denialism have picked it up as well; this is all based on some grand meta-analysis by John Ioannidis.

I'd like to share with you an example I made up a few days ago, while I was randomly pontificating. Imagine that for some reason, scientists suspect that there is a link between broccoli and lung cancer. One hundred scientists do one hundred separate studies trying to find this link. Three of them say "there appears to be a positive correlation between broccoli and lung cancer", meaning that they found such a correlation and that it is outside a 95% confidence interval. The media will hear this and will say "look! broccoli causes lung cancer!" and the broccoli industry will be very unhappy. (The elder George Bush will be happy, though.) But if there were no correlation, you'd expect five of the hundred scientists to have found this correlation just by sheer luck! The fact that only three of them found it is evidence towards broccoli not causing lung cancer.

But you'll never hear that on the evening news, because the news people want you to think you're sick, or you're going to get sick. Their audience is aging and their main advertisers are drug companies.

A slightly less toy example can be found in an old Marginal Revolution post.

A bit more seriously, it seems like a lot of people are tinkering with their data too much:

Statistically speaking, science suffers from an excess of significance. Overeager researchers often tinker too much with the statistical variables of their analysis to coax any meaningful insight from their data sets. "People are messing around with the data to find anything that seems significant, to show they have found something that is new and unusual," Dr. Ioannidis said.

But one in twenty things that are "neither true nor false" will appear true. Perhaps it makes sense to require a wider confidence interval for results which are obtained by this sort of "data mining" than for the results which one originally intended to find? It's turning out that a lot of results are not reproducible.

Although I don't presume to be qualified to speak for how medical researchers should do their work, it seems to me that perhaps they need more forums to report negative results. In the broccoli-and-lung-cancer example, I suspect that the researchers publishing the three papers with positive results wouldn't know about enough of the negative results to make them doubt their claim. As Steven Novella points out, the fact that "most published research is wrong" is probably a combination of this lack of such forums and something like my example.

There are growing suggestions that this would even be useful in mathematics, where you'd think we wouldn't need it because we can prove our results beyond a shadow of a doubt. But we don't publicize our negative results -- we don't publish papers saying "I thought proposition X might be true, and here's why, but then I came up with this counterexample", although we might say these things in informal conversation. So there's still probably a tremendous duplication of work. Some duplication of work is probably desirable, even in mathematics; different people will have different perspectives on the same problem. But a lot of people probably have the sense that they are going down an already-explored dead end and it would be nice if they had at least some ability to confirm or refute that. This can only be more important when we're talking about the sort of research where lives are at stake.