The simple question
If there were no true effect and the statistical assumptions held, how surprising would a result at least this extreme be?
Large samples can make tiny effects significant. Bias can make precise estimates wrong. Read the design, effect size and confidence interval too.
Two estimates being significant separately does not show that the difference between them is significant.
A confidence interval shows effect sizes reasonably compatible with the data and statistical model. Narrower means more precision on the stated scale, not automatic validity.
Difference measures
ARR, spending differences and survival differences use 0 as the no-difference value.
Ratio measures
RR and HR use 1 as the no-difference value.
This supplies more information than HR 0.72 alone. The interval excludes 1, but clinical importance still depends on the outcome and baseline risk.
For corresponding two-sided methods, a 95% CI crossing the null generally agrees with a nonsignificant result at the .05 level. Rounding and differing methods can create exceptions.
20% mortality → 15% mortality
ARR = 5 percentage points. About five fewer deaths per 100 patients treated over the specified five-year horizon.
A positive ARR for a bad outcome favors treatment. Zero means no absolute difference. A negative ARR indicates an absolute increase in risk.
No universal clinical-importance cutoff exists: the outcome, harms, time horizon and burden of treatment matter.
15% ÷ 20% = 0.75
The treatment group has 75% of the control group’s risk.
The comparison needs the same outcome definition and follow-up. RR alone does not tell you the absolute number of patients helped.
For 20% → 15% risk, RR = 0.75 and RRR = 25%.
| Risk change | Relative reduction | Absolute reduction |
|---|---|---|
| 20% → 10% | 50% | 10 percentage points |
| 2% → 1% | 50% | 1 percentage point |
Always ask for baseline risk, the absolute effect and the time horizon.
A hazard ratio compares event hazards over follow-up. HR 0.70 is commonly summarized as about a 30% lower hazard, subject to the model’s assumptions.
| HR | Quick interpretation |
|---|---|
| 1.00 | No hazard difference |
| 0.90 | About 10% lower hazard |
| 0.75 | About 25% lower hazard |
| 0.50 | About 50% lower hazard |
| 1.25 | About 25% higher hazard |
| 2.00 | About twice the hazard |
Read the survival curve, time-specific risks and the paper’s model assumptions. Do not substitute a hazard ratio for a risk ratio in an NNT calculation.
At six years: 72% versus 60% survival.
About 12 more patients out of every 100 are alive at six years in the first group.
At five years, 80% versus 70% would instead be a 10-point difference. These are separate examples, not points on one study’s survival curve.
Its direction depends on which group is listed first. A confidence interval that includes zero includes no survival difference under the model.
ARR 5 percentage points = 0.05
NNT = 1 / 0.05 = 20. Treat about 20 patients to prevent one additional bad outcome over the stated follow-up.
A lower positive NNT generally means a larger absolute benefit for the same outcome and time horizon. It is not a universal quality score.
Harms, costs and patient preferences matter. The point estimate does not supply a confidence interval.
A five-year mortality example: control mortality 20%, treatment mortality 15%. Edit the risks to see how the measures move together.
Use these questions together.
Evidence: read P values and confidence intervals.
Real-world benefit: find absolute risk difference, survival difference and NNT.
Proportional change: interpret RR, RRR or HR.
Time: identify the follow-up.
Baseline risk: determine how much absolute benefit a relative effect implies.
Additional website safeguard: start by checking the study design, who was included, outcome definition, missingness and comparison. No shortcut calculation rescues an invalid comparison.
Adapted from the Blair Compass Clinical Statistics reference, updated September 13, 2026. Website examples use “percentage points” to make absolute versus relative changes explicit. NNH/zero-risk handling and the design-first safeguard are added explanations.