Someone asked me about small relative risk. It was only 1.12, but because of the large sample size, it was still statistically significant. This person wanted to discount the relative risk because anything less than 2 is unreliable.
This is a point of controversy. I don't think that you should disregard a relative risk less than 2.0, but I do think you need to hold it to a higher level of scrutiny.
Hill published nine criteria for causation in 1964, and these were intended as general criteria, and not to be interpreted too literally. One of the nine criteria was "strength of association" and a relative risk less than 2 fails to meet this criteria. But if other criteria (such as replication, dose response, biological plausibility) are met, then you can put a lot of faith in that result.
If your small relative risk was unreplicated, you couldn't come up with a plausible mechanism, and so forth, then don't trust that finding. That doesn't mean you don't publish. But you publish with a lot of cautions and reservations. The final sentence should read, "The results of this research should be replicated, so someone please give me a nice fat research grant."
You can find an earlier version of this page on my original website.