I was reading Andrew Gelman (always a source of interesting statistical thoughts) and I started thinking about p-values in epidemiology.
Is there a measure in all of medical research more controversial than the p-value? Sometimes I really don't think so. In a lot of ways, it seems to dominate research just because it has become an informal standard. But it felt odd, the one time I did it, to say in a paper that there was no association (p=.0508) when adding a few more cases might have flipped the answer.
I don't think confidence intervals, used in the sense of "does this interval include the null", really advance the issue either. But it's true that we do want a simple way to decide if we should be concerned about a possible adverse association and the medical literature is not well constructed for a complex back and through discussion about statistical models.
I'm also not convinced that any "standard of evidence" would not be similarly misapplied. Any approach that is primarily used by trained statisticians (sensitive to it's limitations) will look good compared with a broad standard that is also applied by non-specialists.
So I guess I don't see an easy way to replace our reliance on p-values in the medical literature, but it is worth some thought.