Hazard Ratio: Meaning, Interpretation, and Reporting

A hazard ratio (HR) compares how fast an event happens in one group versus another. It is the ratio of two hazard rates: the event rate per unit of time among people who have not yet had the event. An HR of 0.70 means the exposed or treated group experiences the event at 70% of the rate of the comparison group at any given time; an HR of 1.50 means a 50% higher rate.

You will meet hazard ratios almost every time a paper analyzes time-to-event data with censoring, usually as the output of a Cox proportional hazards model. This guide explains what the number means, what it does not mean, and how to report it.

What is a hazard?

The hazard at time t is the instantaneous rate of the event among people still at risk at t. Think of it as "how likely is the event in the next short interval, given that it has not happened yet," divided by the length of that interval.

The hazard ratio divides one group's hazard by another's:

HR = hazard in group A / hazard in group B

In a Cox model the HR is assumed to be constant over follow-up (the proportional hazards assumption). That is what lets a single number summarize the comparison. When the assumption fails, the "true" HR changes over time and a single HR becomes an average that may hide important patterns.

How to interpret a hazard ratio

Percent change in hazard is (HR − 1) × 100:

• HR = 0.62 → 38% lower hazard
• HR = 1.26 → 26% higher hazard
• HR = 2.00 → hazard doubled (100% higher)

Hazard ratios live on a multiplicative scale. HR = 2.00 and HR = 0.50 are equally large effects in opposite directions, which is why forest plots use a log scale on the x-axis.

Always read the confidence interval

The 95% confidence interval shows the range of HRs compatible with your data.

• CI excludes 1 (for example 0.45 to 0.85): the result is statistically significant at the 5% level, and the direction of the effect is clear.
• CI includes 1 (for example 0.81 to 1.51): the data are compatible with a lower hazard, no difference, or a higher hazard. Report this as no clear evidence of a difference, not as proof of no effect.
• Width matters: an HR of 0.62 with CI 0.45 to 0.85 is far more informative than an HR of 0.62 with CI 0.20 to 1.90.

The CI is asymmetric around the HR because it is computed on the log scale: exp(ln HR ± 1.96 × SE).

Recovering the SE and p value from a published CI

If a paper reports only the HR and its 95% CI, you can recover the standard error of the log HR, which is useful for meta-analysis:

SE = (ln(upper) − ln(lower)) / 3.92

For HR = 0.62, 95% CI 0.45 to 0.85: SE = (ln 0.85 − ln 0.45) / 3.92 = 0.162, and z = ln 0.62 / 0.162 = −2.95, which gives a two-sided p ≈ .003. Rounding in the published figures makes this approximate.

What a hazard ratio does not mean

Three misreadings are common enough that reviewers flag them:

1. "38% fewer patients died." An HR is a ratio of rates, not of the proportion of people who had the event by a certain date. The difference in cumulative risk depends on how common the event is and how long you follow people.
2. "Patients lived 38% longer." The HR says nothing directly about survival time. Only under a constant hazard (exponential survival) does the ratio of median survival times equal 1/HR; in real data, report the medians from Kaplan-Meier curves instead.
3. "The probability of the event was 0.62 times as high." That describes a relative risk. Close, but not the same quantity.

Hazard ratio vs relative risk vs odds ratio

All three are ratio measures where 1 means no association, but they answer different questions.

A worked comparison

Take a trial with 200 patients per arm and complete one-year follow-up. 30 patients in the treatment arm and 50 in the control arm had the event.

Relative risk. Risk is 30/200 = 0.15 vs 50/200 = 0.25, so RR = 0.15 / 0.25 = 0.60, 95% CI 0.40 to 0.90.

Odds ratio. Odds are 30/170 = 0.176 vs 50/150 = 0.333, so OR = (30 × 150) / (170 × 50) = 0.53, 95% CI 0.32 to 0.88. You can check this with the odds ratio calculator.

Hazard ratio. An HR needs event times, so you would normally fit a Cox model. To see the relationship, assume each arm had a constant hazard. Then the one-year risk is 1 − exp(−hazard), so the hazards are −ln(0.85) = 0.163 and −ln(0.75) = 0.288, and HR = 0.163 / 0.288 = 0.56.

Same data, three answers: RR 0.60, HR 0.56, OR 0.53. With 15% and 25% event risks the three measures already diverge; the OR sits furthest from 1. With rare events they converge: at 4 vs 8 events per 1,000, RR = 0.50 and OR = 0.498. This is why you should never label an OR or HR as a "risk" without qualification, and why you should not pool them carelessly in a meta-analysis.

Odds ratios are the natural measure in case-control studies, where you sample on the outcome and cannot estimate risk directly.

When to use a hazard ratio

Report an HR when:

• The outcome is time to an event.
• Follow-up varies between participants and some are censored.
• The proportional hazards assumption is reasonable (check it with Schoenfeld residuals or log-minus-log plots, as described in the Cox regression guide).

If hazards are clearly non-proportional (for example, Kaplan-Meier curves cross), report time-specific HRs or a restricted mean survival time difference instead of, or alongside, a single HR. The survival analysis primer covers the Kaplan-Meier side.

Unadjusted vs adjusted hazard ratios

An unadjusted (crude) HR comes from a Cox model with one predictor. An adjusted HR comes from a multivariable model and estimates the association holding the other covariates constant. In observational studies, the adjusted HR is usually the primary estimate, but report both so readers can see how much adjustment changed the result. Always list the covariates in the adjusted model.

How to report a hazard ratio in APA 7

Report the HR, the 95% CI in square brackets, and the exact p value. Keep the leading zero for HRs and CIs (they can exceed 1) and drop it for p values.

For a non-significant result:

Clinical journals often prefer: "hazard ratio, 0.62; 95% CI, 0.45 to 0.85; P=0.003." Follow your target journal's style guide.

In Methods, state the model (Cox proportional hazards), the time origin, the event, how censoring was handled, the covariates, and how you checked the proportional hazards assumption.

Common mistakes

1. Reporting the HR without a CI. The CI carries the precision; a bare HR is incomplete.
2. Omitting the reference group. "HR = 2.00 for stage III" means nothing until the reader knows it is relative to stage I–II.
3. Omitting the unit for continuous variables. An HR per year and an HR per 10 years are very different numbers.
4. Interpreting the HR as a risk or survival time ratio. See the misreadings above.
5. Ignoring non-proportional hazards. If the effect reverses halfway through follow-up, a single HR averages away the story.
6. Inverting the direction. HR for treatment vs control and HR for control vs treatment are reciprocals (0.62 vs 1.61). State the comparison explicitly.

FAQ

What is a good hazard ratio?

There is no universal threshold. Whether an HR of 0.80 matters depends on the baseline event rate, the outcome, and the cost or harm of the intervention. Judge it alongside absolute measures such as the difference in survival at a fixed time.

Can a hazard ratio be greater than 1 and still favor treatment?

Yes, if the event is something desirable, such as recovery or discharge. For a "good" event, an HR above 1 means the treated group reaches it faster.

Is a hazard ratio the same as a relative risk?

No. The HR compares event rates over time and uses censored data; the RR compares cumulative probabilities over a fixed period. They are close when events are rare and follow-up is short.

How do I calculate a hazard ratio?

Fit a Cox proportional hazards model in R (coxph), SPSS, Stata, or SAS. The HR is exp(B) for each coefficient, and its 95% CI is exp(B ± 1.96 × SE).

Can I convert a hazard ratio to an odds ratio?

Not exactly without extra information such as baseline risk and follow-up duration. When events are rare, the two will be close, but they should still be labeled correctly.

Getting from data to a draft

If you have time-to-event data in a CSV or Excel file, Data2Paper's Generate Paper can fit Cox models, report hazard ratios with confidence intervals, and draft the Methods and Results sections with tables and a forest plot. The first half of the draft is free to generate and preview; the full paper costs a one-time $19.90. It is an AI-generated draft without expert review, so verify the numbers against your own analysis.