The Math Behind Misleading Headlines
"Cancer Risk Cut in Half!" reads the headline. The study shows a drug reduces cancer incidence from 2% to 1% in a five-year period. Technically, risk fell by 50%—but only one person per 100 was actually prevented from developing cancer. The relative risk reduction (50%) and absolute risk reduction (1%) tell opposite stories.
Relative risk reduction (RRR) divides the risk difference by the baseline risk. Formula: (2% - 1%) / 2% = 50%. It's mathematically correct but contextually incomplete. News outlets prefer relative numbers because they sound more impressive. Pharmaceutical marketing similarly emphasizes RRR when promoting drugs.
Absolute risk reduction (ARR) simply subtracts: 2% - 1% = 1%. This answers the real question patients ask: "How many people actually benefit?" An ARR of 1% means you must treat 100 people to prevent one case—the number needed to treat (NNT).
Consider a real example: A meta-analysis of statins for primary prevention (people without prior heart disease) showed they reduce cardiovascular events by roughly 30% relative reduction over five years. Sounds excellent until you examine absolute numbers. In low-risk populations, this translates to preventing 1-3 events per 100 people treated. The NNT ranges from 50-100, meaning you treat many asymptomatic people for years to prevent one event.
Medias rarely distinguish these measures. When a study shows "vitamin D reduces respiratory infection by 40%," journalists dutifully report dramatic relative reductions. Baseline infection rates matter hugely. If you're in a community where 20% develop respiratory illness, a 40% reduction prevents 8 per 100 people. If baseline is 2%, the same 40% reduction prevents only 0.8 per 100—changing the benefit-harm calculus entirely.
Baseline risk is everything. Understanding your population's pre-test probability (background risk) is essential for interpreting any risk reduction. A 50% reduction in rare disease differs vastly from 50% reduction in common disease.
Converting between measures helps clarify. If you know RRR and baseline risk, calculate ARR: ARR = baseline risk × RRR. If a drug shows 30% RRR and baseline risk is 5%, then ARR = 5% × 30% = 1.5% absolute reduction.
Alternatively, some studies report odds ratios (OR) rather than risk ratios (RR). These diverge when baseline risks are high. An OR of 0.5 doesn't equal a 50% relative risk reduction—the relationship is more complex. Critically appraising research requires converting all measures to absolute terms for meaningful comparison.
Better health reporting specifies both measures and baseline risk transparently. NNT communication ("one patient benefits per 100 treated") should accompany claims of benefit. Until media outlets standardize this practice, readers must translate headlines themselves.