Correlation vs Causation
Correlation describes how two variables move together in observed data, while causation is a claim about what would change if one were intervened upon, and only the second supports a treatment decision.
An association is a property of the joint distribution of what was observed. A causal claim is counterfactual: it states what would have happened to the same people under a different exposure, a quantity never observed in anyone. Four routes produce association without causation, none of them exotic. Chance. Reverse causation, where the outcome drives the exposure. Confounding by a common cause of both. And selection or collider effects created by who ended up in the dataset.
Beta-carotene is the cleanest cautionary case. Cohort after cohort found that diets and blood levels rich in it went with lower lung cancer risk. Two randomised trials then tested supplementation directly, ATBC in Finnish male smokers and CARET in smokers and asbestos-exposed workers, and both found lung cancer incidence higher in the supplemented arms; CARET was stopped early. Beta-carotene had been a marker of a diet and a way of living, not the agent doing the work.
What upgrades an association is structure: a clean temporal window, a dose-response gradient, replication in populations whose confounding differs, negative controls, natural experiments, Mendelian randomisation, and ultimately randomisation itself. Magnitude carries some weight too, since a hazard ratio of 1.1 in a cohort is within reach of residual confounding while a tenfold association is much harder to produce that way.
In peptide discussion the error usually runs from a dish to a person. A compound raises collagen output in cultured dermal fibroblasts, or raises serum IGF-1, and the marketing describes tissue repair, which is a chain of associations between an assay and a hoped-for outcome with no demonstrated causal link at either joint. The mirror error is using the slogan to dismiss observational work wholesale, discarding the only evidence that will ever exist for rare harms and long-latency outcomes.