Among the lightest babies, the ones born to smokers somehow do better

Look only at babies born significantly underweight. Among just that group, infants born to mothers who smoked during pregnancy have a lower death rate than equally underweight infants born to non-smokers. Smoking clearly isn't protective for a fetus -- so what's going wrong with this comparison?

Reveal the answer

It's a statistical trap called the low birth-weight paradox, a form of collider bias. Low birth weight has many possible causes. For a non-smoking mother, an underweight baby more often signals something seriously wrong, like a genetic condition or placental problem. For a smoking mother, the same low weight is more often fully explained by the smoking itself, which, once weight is already fixed, adds comparatively little extra risk. Comparing only the lightest babies from each group secretly compares two different risk populations, not the true effect of smoking.

— Wikipedia (statistical phenomenon documented in epidemiology literature), Low birth-weight paradox — Epidemiology; collider/selection bias

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