Capstone: A Causal Claim in the Wild

This capstone takes one health headline and runs the whole unit against it: study design, the rival explanations for a correlation, the sample, the base rate hiding behind a relative risk, and a ranking of what remains.

The headline: daily coffee linked to twenty percent lower risk of heart disease. Start with design. The study is observational, which means nobody assigned who drank coffee, so Mill's method of difference was never available — the groups differ in whatever else led people to drink coffee. Now run the rivals for any correlation. Reverse causation: could healthier hearts cause coffee drinking rather than the other way round? Plausible, since people with cardiac symptoms are told to cut caffeine, which removes them from the coffee group and leaves it healthier by selection. Common cause: employment, income, and sleep all track both coffee consumption and heart health. Coincidence: with a large enough sample this is unlikely, though it depends on how many outcomes were tested. Interrogate the sample. Volunteers who complete a decade-long dietary questionnaire are not the general population, and the healthy-volunteer effect runs in the same direction as the finding. Now the base rate behind the relative risk. Twenty percent lower is a relative figure. If the underlying ten-year risk is five in a hundred, a twenty percent reduction moves it to four in a hundred — one person per hundred over ten years. Rank the explanations. The correlation is real. The most likely account combines reverse causation with a common cause, and a genuine protective effect remains possible but unproven. Verdict: the study licenses an association worth further study; the headline claims a benefit it cannot support.