BiostatisticsTier 1Medical Sciences concept

Relative risk reduction / absolute risk reduction calculation

Core concept

Absolute risk reduction (ARR) = risk in control group - risk in treatment group (a simple subtraction of two proportions/incidence rates)
Relative risk reduction (RRR) = ARR / risk in control group (expressed as a percentage) -- describes the proportional reduction, independent of baseline risk
NNT (number needed to treat) = 1 / ARR -- the number of patients who must receive the treatment to prevent one additional adverse event

RRR can look impressively large even when ARR (and clinical benefit) is tiny, if baseline risk is low -- always compute and report both, never RRR alone
- Example pattern: control event rate 2%, treatment event rate 1% -> ARR = 1%, RRR = 50% -- "50% risk reduction" sounds dramatic but the absolute benefit is 1 in 100
Incidence-rate-based calculations use the same ARR/RRR logic but with incidence rates (events per person-time) instead of simple proportions, when follow-up duration varies
NNT must always be quoted with the time period/study duration it applies to (e.g. "NNT to prevent one death over 5 years") -- it is not duration-free

Trap: a drug advertised by its RRR ("reduces risk by 30%") without the baseline risk gives no information about real-world benefit -- always ask for ARR/NNT before judging a treatment's value
NNT calculation from real trial data (e.g. ISIS-2-style large mortality trials): compute ARR from the reported event rates in each arm, then NNT = 1/ARR -- she should be able to do this from raw numbers given in a vignette, not recall a memorised NNT
For harm outcomes, the equivalent calculation is NNH (number needed to harm) = 1 / absolute risk increase

Directly extends Kaplan-Meier interpretation - ARR/NNT can be read off a survival curve at a specified time point using the same formula
RR and RRR are cohort/RCT statistics; case-control data cannot generate them (only OR) -- links back to the study design and OR calculation notes
Same ARR logic underlies absolute risk-based decision thresholds in guidelines (e.g. treating when absolute cardiovascular risk crosses a stated percentage, rather than acting on relative risk reduction alone)

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