association

Comparison is what produces one. The CDC's Principles of Epidemiology in Public Health Practice calls comparison the key to epidemiologic analysis: a rate on its own is only a number until it is set beside the rate in another group. A measure of association, the course says, quantifies the relationship between exposure and disease among the two groups, and it uses exposure loosely, to cover not only what people were exposed to but their own characteristics, their activities and the conditions under which they live. The familiar measures are all of this kind, risk ratio, rate ratio and odds ratio among them, and each divides one group's figure by the other's. That is why 1.0 is the number that means nothing separated the groups. A risk ratio of 1.0 indicates identical risk among the two groups, above 1.0 an increased risk for the group in the numerator, and below 1.0 a decreased one.

What the word withholds is direction. The Centre for Evidence-Based Medicine at the University of Oxford describes analytic observational studies as ones in which the researcher simply measures the exposure or treatments of the groups, and says such studies assess associations between exposures and outcomes. Nobody allocated anything, so the association is a fact about how the groups already differed. The centre states the limit of the cross-sectional design in exactly those terms, that it establishes association at most, not causality, and names the standing hazard of the cohort design, that the exposure may be linked to a hidden confounder. An experimental study is the one in which the researcher manipulates the exposure, and it is that allocation, not the size of the number, that lets a design point the arrow.

So an association can be strong, tightly estimated and still leave the question of cause open. Its size says how far apart two groups were, not what moved them apart, and a large association from a cohort and a small one from a randomised trial are not the same kind of claim. The word appears wherever this site reports a cohort, and the sentence beside it is there to say what the design cannot settle.