Survival curves, hazard ratios and non-inferiority trials
Read a Kaplan–Meier curve, interpret a hazard ratio correctly, look critically at composite end-points, and decide whether a non-inferiority trial proves what it claims.
Reviewed and kept current
Last editorial review: 28 September 2026 · Next scheduled refresh: March 2027.
Clinical vignette
Begin with the patient. Read the case, weigh the options, then work through the unit.
Mr J has heart failure. His cardiology letter suggests a new drug. He has read the trial summary. It reports a hazard ratio for cardiovascular death or hospitalisation of 0.75 (95% CI 0.65 to 0.86) compared with placebo.
He asks: “Does that mean I will live 25% longer?” He already takes several tablets. He wants to know whether one more is worth it.
The outcome combines two events of very different weight: death and a hospital admission. The hazard ratio is a relative measure.
Options to weigh
- Tell him that he will live 25% longer.
- Explain that, at any point during follow-up, treated patients had a 25% lower rate of the combined outcome than patients on placebo.
- Check which component of the combined outcome drove the result before discussing benefit.
- Derive an absolute benefit from the trial’s control event rate or its Kaplan–Meier curves, with its time frame.
- Tell him that his absolute risk falls by 25%.
Reflect
How would you explain this hazard ratio so that Mr J can decide about the drug, and what would you be careful not to say?
What this unit covers
Pocket-sized and self-contained: three AKT-style questions, the answers explained, an expanded discussion with hyperlinked guidance, a decision algorithm and a certificate.
By the end of this unit you will be able to
Five steps, in order
Answer first, then learn. Each section unlocks as you progress, and your progress is saved in this browser.
1Three single best answer questions
Commit to an answer for all three single best answer questions, then submit. Sections 2–4 open on submission; your certificate opens at 2/3 or better.
Question 1 of 3
A heart-failure trial reports a hazard ratio for cardiovascular death or hospitalisation of 0.75 (95% CI 0.65 to 0.86) with the new drug compared with placebo.
Which interpretation is most accurate?
Question 2 of 3
A Kaplan–Meier curve shows the proportion of patients free from stroke over five years. Small vertical tick marks appear on each curve.
What do the tick marks represent?
Question 3 of 3
A trial tests whether a new oral anticoagulant is non-inferior to warfarin for preventing stroke in atrial fibrillation, using a pre-specified non-inferiority margin for the hazard ratio of 1.38. The result is HR 0.88 (95% CI 0.75 to 1.03).
What is the correct conclusion?
2Answers explained
Question 1
Correct answer D. At any point during follow-up, treated patients had a 25% lower rate of the outcome than placebo patients
A hazard ratio compares the instantaneous event rates (hazards) in the two groups over the whole follow-up, assuming the ratio is roughly constant (proportional hazards). HR 0.75 = a 25% relative reduction in the hazard at any given time.
It is a relative measure — it says nothing about absolute risk (option A) or survival time (option C). The CI excludes 1, so the result is significant.
Question 2
Correct answer A. Censored participants
Each downward step on a Kaplan–Meier curve is an event. The tick marks show censored participants — people who left observation without having the event (end of study, lost to follow-up, or died of another cause if that is not the outcome). They contribute information up to that point and then leave the “number at risk”.
Always read the “number at risk” table beneath the curve: the right-hand end of a curve, based on few patients, is imprecise.
Question 3
Correct answer A. The new drug is non-inferior to warfarin
Non-inferiority is shown when the upper limit of the CI lies below the non-inferiority margin (1.03 < 1.38). Superiority is not shown, because the CI includes 1.
A CI crossing 1 makes a superiority trial inconclusive, but that is not the question a non-inferiority trial asks — option E is the trap.
3Expanded discussion, worked examples & guidance
1. Time-to-event data and censoring
Many outcomes (death, stroke, admission) are about when, not just whether. Survival analysis uses everyone’s follow-up time, even people who leave the study early (censoring), assuming censoring is unrelated to prognosis.
- Kaplan–Meier curve — the proportion event-free over time. Steps = events; ticks = censoring.
- Median survival — the time at which the curve crosses 50% (0.5).
- Log-rank test — compares whole curves (gives a p-value).
- Cox proportional hazards regression — gives an (adjusted) hazard ratio.
Worked example 1 — reading a curve
A Kaplan–Meier curve shows that 50% of patients on standard care have died by 18 months, and 50% of those on the new treatment by 27 months. At 24 months, 60% on the new treatment and 42% on standard care are alive.
- Median survival: 27 vs 18 months — a 9-month gain.
- Absolute difference in survival at 24 months = 60% − 42% = 18 percentage points.
- NNT to keep one extra patient alive at 24 months = 1/0.18 = 5.6 → 6.
Answer. NNT ≈ 6 over 24 months — the Kaplan–Meier curve lets you derive absolute effects that the HR alone hides.
2. Hazard ratio vs relative risk
The RR compares cumulative risk at one time point; the HR compares event rates throughout follow-up. They are often similar in value. Both are relative measures, so derive the absolute benefit from the curves or the event rates.
Worked example 2 — HR to absolute benefit
Control event rate over 3 years = 20%; HR = 0.75.
- Approximate treated event rate ≈ 20% × 0.75 = 15% (reasonable when event rates are modest).
- ARR ≈ 5%; NNT ≈ 20 over 3 years.
Answer. About 20 patients treated for 3 years to prevent one event.
3. Composite end-points
Cardiovascular trials often use composites (e.g. “CV death, MI or stroke” — MACE; “CV death or HF hospitalisation”). They increase event numbers and therefore power, but:
- the components may differ greatly in importance (death vs a hospital admission);
- the effect may be driven by the least important component — check the individual components table;
- components should share a common mechanism.
Example: in the SGLT2-inhibitor heart-failure trials, much of the benefit in the primary composite came from fewer heart-failure hospitalisations.
4. Superiority, non-inferiority and equivalence
| Design | Question | Conclusion rule (for a ratio where <1 favours new) |
|---|---|---|
| Superiority | Is new better? | Whole CI below 1 |
| Non-inferiority | Is new not unacceptably worse? | Upper CI limit below the pre-specified margin (e.g. 1.38) |
| Equivalence | Are they the same within limits? | Whole CI within both margins (e.g. 0.8–1.25) |
Why do non-inferiority trials? The new treatment may be cheaper, safer, or easier (e.g. DOACs vs warfarin with no INR monitoring). Appraisal points: Was the margin justified clinically before the trial? Was the comparator given at its best (warfarin time in therapeutic range)? Do ITT and per-protocol analyses agree? (Sloppy trials drift towards “no difference”, which favours non-inferiority.)
- An HR < 1 means fewer events only if the outcome is bad (death); for “recovery” an HR > 1 is good.
- Non-inferiority can be declared even when the point estimate is slightly worse than the comparator.
- Superiority may be tested after non-inferiority is shown (hierarchical testing).
References and further reading
Guidance checked at the last editorial review (28 September 2026). Always use the current version.
4Decision algorithm
Interpreting a trial with a hazard ratio
Start
Identify the outcome (single or composite), the follow-up period and the trial type.
Decision
Is it a non-inferiority trial?
Decision
Is the outcome a composite?
Action
Convert to absolute terms using the Kaplan–Meier curve or control event rate: ARR and NNT over the stated time.
Outcome
Check the number-at-risk table, censoring, and whether the curves separate early (plausible mechanism) or late.
Revision summary; apply clinical judgement and local pathways.
5Certificate of completion
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