Synopsis
Calculate and interpret core measures of frequency, association, effect and uncertainty, while separating statistical evidence from bias, clinical importance and causal inference.
- Define the population, unit, time horizon, numerator and denominator before calculating prevalence, risk, rate or an effect measure.
- Risk ratio compares probabilities; odds ratio compares odds; risk difference gives absolute change; number needed to treat is the reciprocal of a non-zero absolute risk reduction.
- A confidence interval expresses precision under model assumptions; it is not the probability that this one fixed interval contains the true value.
Reasoning priorities
Expose event and non-event counts in intervention or exposure and comparison groups.
Calculate risks, odds and absolute differences from the cells; sparse cells create unstable estimates and continuity corrections can materially affect results.
Worked reasoning
Inputs: over two years, 18 of 300 control participants and 9 of 300 intervention participants experience the outcome; calculate risks, RR, ARR and NNT.
- Calculate control risk: 18 divided by 300 equals 0.06, or 6%; intervention risk: 9 divided by 300 equals 0.03, or 3%.
- Calculate risk ratio: 0.03 divided by 0.06 equals 0.50, corresponding to a 50% relative risk reduction.
- Calculate absolute risk reduction: 0.06 minus 0.03 equals 0.03, or 3 percentage points over two years.
- Calculate NNT: one divided by 0.03 equals 33.33, rounded upward to 34 people treated for two years to prevent one additional outcome, assuming the estimate applies.
- State outcome with both scales: risk fell from 6% to 3%, RR 0.50, ARR 3 percentage points and NNT 34 over two years; uncertainty requires confidence intervals not supplied here.
- Verify with counts: treating 300 people produced nine fewer events, and 300 divided by nine equals 33.33, agreeing with the reciprocal calculation before upward rounding.