To translate hazard ratios and Kaplan–Meier survival results accurately, a translator has to preserve the time dimension behind the statistics. A hazard ratio is not simply a risk ratio with a different name. A Kaplan–Meier curve is not a graph of the percentage of participants who have ever experienced the event. Median survival is not the arithmetic average survival time. Each term belongs to time-to-event analysis, where follow-up length, censoring, risk sets and the timing of events affect what the reported number means.
This guide explains how to translate hazard ratios, survival probabilities, Kaplan–Meier curves, median survival, censoring, number at risk, log-rank comparisons and proportional-hazards language in research papers, clinical reports, technical summaries, public-health material and educational texts. The search intent is specific: how do you translate survival-analysis results without turning an instantaneous relative rate into an absolute risk reduction, a censored observation into a failure, or “median not reached” into “everyone survived”? The safest method is to preserve the event definition, time origin, follow-up rule and model before paraphrasing the statistic.
A reliable translation also separates descriptive survival estimates from model-based comparisons. A Kaplan–Meier curve estimates the survival function over time under its assumptions. A log-rank test compares survival experience between groups in a particular way. A Cox model can estimate hazard ratios while adjusting for covariates. These outputs may appear in one figure or paragraph, but they answer different questions. The translator should identify which sentence describes observed time-to-event patterns and which describes a fitted model.
A fifty-second orientation
Survival analysis is used for time-to-event outcomes, not only death. The event may be recurrence, discharge, failure, recovery, relapse, device breakdown or another defined endpoint. Kaplan–Meier methods estimate the probability of remaining event-free beyond different times while accounting for censoring. Cox proportional-hazards models are commonly used to compare hazards between groups, often expressed as a hazard ratio.
The translation rule follows directly: always ask “time to what event, starting from what time origin, and with what censoring rule?” A phrase such as “survival at twelve months” is incomplete if the event, time origin or population changes elsewhere in the document. Time-to-event terminology is relational. Preserve the relationship, not merely the headline percentage.
1. “Survival” can mean remaining free of any defined event
In everyday language, survival means remaining alive. In statistical time-to-event analysis, the survival function can describe the probability of not yet experiencing any defined event. A machine can have failure-free survival. A patient can have progression-free survival. A participant can have time to withdrawal. A system can have time to first incident.
Translate the endpoint name fully. Overall survival, progression-free survival, disease-free survival, event-free survival, time to recurrence and time to treatment failure are not stylistic variants. They use different event definitions and sometimes different censoring rules.
If the source abbreviates an endpoint after defining it, preserve the full definition at first mention in the target. Do not let the word survival alone suggest death when the statistical event is something else.
2. Time origin is part of the endpoint
Time-to-event outcomes require a starting point. Follow-up might begin at randomisation, diagnosis, surgery, device installation, first treatment, enrolment or another defined origin. Two studies using the same event but different time origins are not measuring exactly the same duration.
Translate “from randomisation,” “since diagnosis,” “post-surgery,” or “from first exposure” with the endpoint. Removing the origin can make a median time or survival probability appear directly comparable with another statistic when it is not.
A useful working note is: “origin = date of randomisation; event = first recurrence; censoring = last known event-free follow-up.” Once those fields are secure, the target sentence can be concise without losing the analysis definition.
3. Censoring is not the same as an event
A censored observation means the exact event time is not observed within the available follow-up under the study’s rule. A participant may still be event-free at the last contact, may leave the study, or may reach the study end before the event occurs. Censoring does not automatically mean the event happened after the recorded time, nor does it mean the person was lost in every case.
Translate censored, lost to follow-up, study end and event-free at last contact as separate ideas. A source may censor at administrative study end even when the participant is fully observed until that date. Calling every censored case “lost” changes the study history.
Do not translate a censor mark on a Kaplan–Meier curve as a death or failure marker. Its role is to indicate the end of observed event-free follow-up for that individual under the stated method.
4. Kaplan–Meier survival probability is conditional through time
The Kaplan–Meier estimator updates survival probability when events occur. At each event time, it considers how many individuals are still at risk immediately before that event and how many events occur. The overall survival estimate is built from these conditional survival proportions.
This is why a Kaplan–Meier curve does not simply divide the number without events by the original sample at every time point. People can be censored and leave the risk set while still contributing information up to their censoring time.
Translate estimated survival probability as an estimate, not a direct raw proportion unless the source explicitly reports a simple proportion. A target phrase such as “the Kaplan–Meier estimate of twelve-month event-free survival was 80%” preserves the method and time point.
5. The number at risk changes over time
Kaplan–Meier figures often include a risk table below the curve. The number at risk at a time point is the number still under observation and event-free immediately before the relevant time definition used in the analysis.
Translate “number at risk” carefully. It does not necessarily mean the number currently exposed to a hazard in ordinary language. It is a statistical risk-set count. A participant can leave the risk set because the event occurred or because follow-up ended through censoring.
A curve based on very few remaining participants near the end may have greater uncertainty. If the source comments on sparse risk sets, preserve that caveat. Do not extrapolate a visually flat tail as evidence that the long-term event rate is zero.
6. A drop in the curve corresponds to an event under the endpoint definition
Kaplan–Meier survival curves are step functions. The estimate drops at event times. Censoring alone does not produce the same downward step, although censoring changes the number at risk for later calculations.
Translate figure captions so readers know what the event is. “Each downward step represents a recurrence event” is different from “each downward step represents a death.” If the endpoint is composite, the source may define several event types that cause a step.
Do not describe a curve as smooth decline if the analysis actually uses a step estimate and the shape itself matters. A stylistic description can unintentionally imply a continuous event process rather than the displayed estimator.
7. Median survival is the time when estimated survival reaches 50%
Median survival is commonly defined as the time at which the estimated survival probability falls to 0.5 or below according to the method and convention used. It is not the arithmetic mean of individual survival times.
If a source reports median progression-free survival of twelve months, translate the endpoint and statistic together. “Average survival was twelve months” is wrong unless the source actually reports a mean.
A median can often be estimated even when some observations are censored because the Kaplan–Meier method uses the survival curve. But if the curve never falls to 50% during observed follow-up, the median may be not reached or not estimable.
8. “Median not reached” does not mean no events occurred
If more than half the estimated population remains event-free throughout observed follow-up, the median event time may not be reached. Events can still have occurred. The curve simply has not crossed the 50% survival level.
Translate “not reached,” “not estimable,” “not attained,” and “not observed” according to the source’s statistical convention. Do not convert “median not reached” into “all participants remained event-free.”
Likewise, do not assign the longest observed follow-up as the median. That would create a statistic the analysis did not estimate.
9. Hazard is an instantaneous event rate concept
The hazard function describes the instantaneous rate at which events occur at time t among individuals who have not yet experienced the event immediately before that time, under the model. It is related to risk but is not the same as cumulative probability.
Translate hazard cautiously. Everyday words such as danger, threat or risk can overstate or distort the statistical concept. In a technical article, retaining hazard as the formal term and explaining it once is often safer.
A hazard can vary over time. Therefore a statement about hazard at a particular time structure should not be rewritten as an absolute probability of the event over the entire follow-up period.
10. Hazard ratio compares hazards, not cumulative risks directly
A hazard ratio compares the hazard in one group with the hazard in another, according to the model. An HR of 0.70 is often described as a 30% lower hazard in the numerator group relative to the reference group under the model interpretation.
Do not translate HR 0.70 as “30% fewer participants experienced the event” or “risk was reduced by 30%” without additional justification. Those are statements about cumulative event proportions or risks, not necessarily the hazard ratio itself.
Keep the reference group explicit. HR = 0.70 for A versus B is equivalent to approximately 1/0.70 = 1.43 for B versus A when the same model contrast is inverted. A translation that swaps group order without inverting the ratio changes the result.
11. “30% lower hazard” is not “30 percentage points lower”
A hazard ratio is a relative measure. HR = 0.70 corresponds to a relative hazard difference of 30% under the simple wording 1 − 0.70. It is not a thirty-percentage-point difference in survival probability.
Suppose twelve-month survival is 80% in one group and 70% in another. The absolute difference at that time is ten percentage points. That time-specific difference cannot be recovered from HR alone without more information about the survival functions and model.
Translate relative and absolute comparisons separately. If the source reports both a hazard ratio and Kaplan–Meier survival percentages, keep both rather than using one as a substitute for the other.
12. Reference category determines the direction of the hazard ratio
Model tables often show one category as reference and report hazard ratios for other categories relative to it. The reference may be marked Ref, 1.00, baseline or another notation.
Preserve the reference label in the target table. If the translator sorts categories alphabetically or reverses column order, the HR interpretation can become unclear unless the reference marker moves correctly.
A sentence such as “Group A had a hazard ratio of 1.5 compared with Group B” means a higher modeled hazard for A under that contrast. Rewriting it as “Group B was 50% safer” changes both terminology and interpretation and should not be done without source support.
13. Hazard ratios can be adjusted or unadjusted
An unadjusted hazard ratio may come from a model with group as the main predictor and no additional covariate adjustment. An adjusted hazard ratio accounts for specified covariates in the model. The two estimates answer related but different conditional questions.
Translate adjusted HR, multivariable-adjusted HR and crude or unadjusted HR distinctly. Do not drop adjusted from a summary because the numerical value still looks plausible.
Also preserve the covariates or adjustment set where the source lists them. “Adjusted for age and stage” is part of the model specification. A target reader should not assume the adjustment included variables that were not in the model.
14. Proportional hazards is an assumption about relative hazard over time
The Cox proportional-hazards model commonly assumes that hazard ratios between groups are constant over time, conditional on the model structure. This does not mean the hazard itself is constant. Both groups’ hazards may change while their ratio remains proportional.
Translate proportional hazards as a model assumption, not as “equal hazards.” The word proportional means the relationship between hazards follows the model’s proportional structure.
If the source reports evidence that the proportional-hazards assumption was violated, preserve that limitation. A single overall HR may then be an incomplete summary of a time-varying relationship.
15. Time-varying hazard ratios need time labels
Some models allow the treatment or group effect to vary over time. A report may provide an HR before six months and another afterward, or present a time-by-group interaction.
Translate the time window with each ratio. “HR 0.6 before six months and 1.1 afterward” should not be simplified to “overall HR 0.6.” The changing effect is the main result.
Likewise, do not describe a time-varying model as proportional hazards without qualification. Preserve the model structure the source actually used.
16. Log-rank test compares survival curves under a different framework
The log-rank test is commonly used to compare survival distributions between groups. Its p-value does not itself estimate the size of the difference. A hazard ratio may be presented alongside it, but the two outputs come from related yet distinct procedures.
Translate “log-rank p = 0.03” as evidence from the curve-comparison test, not as a 3% hazard ratio or 3% probability that the curves are identical. Keep p-value interpretation within the statistical framework explained elsewhere in the translation series.
If curves cross, a standard log-rank comparison may have limited interpretability for some questions. Preserve source caveats about nonproportional effects or alternative tests rather than presenting the p-value as a complete description of the difference.
17. Survival at a time point is not median survival
A source can report “two-year survival 70%” and “median survival 3.4 years” in the same study. The first is an estimated probability at a specified time. The second is a time at which the estimated survival curve crosses 50%.
Do not translate two-year survival as “average survival of two years.” Do not translate median survival of 3.4 years as “3.4-year survival.” The noun order matters because one statistic is a probability and the other is a time.
A translation checklist should classify every survival number as time, probability, ratio, count or p-value before formatting it. This prevents units from migrating between metrics.
18. Confidence intervals for hazard ratios use a ratio scale
A hazard ratio of 0.70 with a 95% confidence interval of 0.50 to 0.98 has an interval entirely below 1.0. Under the fitted model and frequentist interpretation, the interval describes uncertainty around the ratio estimate.
Translate the reference value 1.0 correctly. A ratio of 1 means equal modeled hazards for the compared groups under the contrast. Zero is not the null value for a hazard ratio.
Do not rewrite the interval as “50% to 98% survival.” The endpoints are hazard ratios, not survival probabilities. Keep HR or an equivalent label attached to the interval.
19. Confidence intervals for median survival are time intervals
A median survival estimate may also have a confidence interval, for example 18 months with a 95% interval from 14 to 24 months. Here the interval endpoints are times, not probabilities or ratios.
When several interval types appear in one table, preserve units in every row. “95% CI 0.7–0.9” for an HR and “95% CI 14–24 months” for a median cannot share an unlabeled CI column without context.
A responsive mobile layout can detach units from headings. Translation review should inspect the final rendered table when possible, not only the source spreadsheet.
20. Competing risks change what “event-free” means
In some studies, one event can prevent the event of interest from occurring. Death from another cause can prevent later recurrence, for example. Such competing events require careful analysis and terminology.
Do not translate a cumulative incidence function as ordinary Kaplan–Meier risk without checking the method. Treating competing events as simple censoring can answer a different estimand.
If the source uses cause-specific hazard ratio, subdistribution hazard ratio or cumulative incidence, preserve the full term. These are not interchangeable “risk ratios.”
21. Cause-specific and subdistribution hazards answer different questions
Cause-specific hazard models typically consider the instantaneous event rate among people currently free of the event of interest, treating competing events according to the model framework. Fine–Gray subdistribution models target a different quantity related to the cumulative incidence function.
A translator does not need to derive these models, but must keep their labels distinct. “Subdistribution hazard ratio” should not be shortened to “hazard ratio” in a document that also reports cause-specific HRs.
If the source interprets the model cautiously, preserve that caution. Competing-risk statistics are especially vulnerable to oversimplified public-facing paraphrases.
22. Restricted mean survival time is not median survival
Restricted mean survival time, often RMST, is the area under the survival curve up to a specified time horizon. It can be interpreted as expected event-free time within that restriction under the analysis.
Translate the restriction horizon with the metric. “RMST through 24 months” is different from an unrestricted mean survival time and different from median survival.
If a source reports an RMST difference of two months by 24 months, do not translate that as a two-month difference in median survival. The quantities summarise different aspects of the survival distributions.
23. Landmark analysis fixes a time point before comparing later outcomes
A landmark analysis may include participants who meet specified conditions and are event-free at a chosen landmark time, then analyse subsequent outcomes. The population is therefore conditional on surviving or remaining eligible to the landmark.
Translate “landmark at six months” and the eligibility rule. Do not describe the resulting survival estimate as applying to the original baseline population if the source conditions on reaching the landmark.
Likewise, immortal-time concepts can arise when exposure classification depends on surviving long enough to receive an exposure. Preserve source warnings about such bias rather than simplifying them to generic selection bias.
24. Left truncation and delayed entry change the risk set
Some participants enter observation after the time origin. They are only included in the risk set after their entry time, provided they have remained event-free until then under the study framework.
Translate delayed entry, left truncation and entry time according to the source method. Do not treat them as ordinary right censoring. One concerns when observation begins; the other concerns when observation ends without an event.
A dataset may therefore show “time since diagnosis” larger than “time under study observation.” Preserve both if they are reported. They answer different temporal questions.
25. Left censoring and interval censoring are different again
Right censoring means the event has not been observed up to the last follow-up time. Left censoring can mean the event occurred before the first observation but the exact time is unknown. Interval censoring means the event is known to have occurred between two observation times.
Do not translate all three simply as “missing event time.” Their information structures differ, and specialised methods may be required.
If the source uses an interval-censored analysis, preserve that phrase in methods and results. A target reader should not assume the standard right-censored Kaplan–Meier framework if another model was used.
26. Worked case: hazard ratio versus absolute survival difference
Consider a fictional study comparing Group A with Group B. A Cox model reports HR 0.75 with a 95% confidence interval of 0.60 to 0.94. The Kaplan–Meier estimates at two years are 82% survival in A and 76% in B.
The model result can be described as a 25% lower hazard for A relative to B under the model and reference direction. The two-year survival difference is six percentage points. These are not two ways of saying the same numerical effect.
A flawed target might say, “Group A had 25% higher two-year survival.” That statement is unsupported: 82 versus 76 is not a 25-percentage-point difference and not a 25% relative difference in survival probability. The HR has been incorrectly transferred onto the survival scale.
A repaired translation reports both metrics with their own labels: HR 0.75 for the model-based relative hazard and 82% versus 76% for the two-year Kaplan–Meier estimates. This gives readers two complementary views without mixing scales.
27. Worked case: median not reached
Suppose a fictional trial reports, “Median event-free survival was not reached in Group A and was 18 months in Group B. At 24 months, estimated event-free survival was 62% in A and 45% in B.”
“Not reached” in A means the Kaplan–Meier curve had not fallen to 50% during the relevant observed follow-up. It does not mean no events occurred, and it does not mean median survival is infinite.
The 24-month survival estimate of 62% is consistent with a median not yet reached because more than half remain event-free at that time. Group B’s 45% at 24 months is compatible with a median earlier than 24 months, here reported as 18 months.
A target should preserve “not reached” and the time-point estimates. Do not invent a numeric median for A from the latest follow-up date.
28. Worked case: crossing curves
Imagine two fictional Kaplan–Meier curves. Group A has fewer early events, but after twelve months its curve falls more quickly and crosses Group B. A single proportional-hazards HR is reported, but the methods note says the proportional-hazards assumption was questionable.
A translation should preserve the time-varying pattern and the model caveat. Saying “Group A had better survival” may be too broad because the ordering changes over time.
Likewise, a non-significant log-rank test should not be translated as “the curves are identical.” The curves can differ in ways the test does not summarise well, particularly when effects vary over time.
The target text should let the reader understand that one summary ratio may not capture the full time pattern. This is a place where preserving a limitation is more important than making the prose sound decisive.
29. Practice clinic with explained answers
Practice one: median survival. A Kaplan–Meier curve crosses 50% at 14 months. Median survival is about 14 months under the estimator. Do not call this the mean survival time.
Practice two: median not reached. The curve remains at 65% at the last reliable follow-up. Median survival is not reached. Do not substitute the last follow-up time as the median.
Practice three: HR below one. HR 0.80 for A versus B corresponds to 20% lower modeled hazard for A relative to B under the stated model. It does not automatically mean 20% fewer events by the end of follow-up.
Practice four: HR above one. HR 1.5 for A versus B indicates 50% higher modeled hazard for A under the contrast. If the groups are reversed, the reciprocal ratio is about 0.67.
Practice five: null value. For a hazard ratio, the no-difference reference is 1.0, not zero. Translate confidence intervals and forest plots with that reference line in mind.
Practice six: censoring. A participant followed event-free for ten months and then lost to follow-up is censored at ten months under a simple rule. Do not count the censoring as an event.
Practice seven: risk table. The number at risk falls from 100 to 40 by year three. That does not mean 60 events necessarily occurred; some participants may have been censored.
Practice eight: survival probability. Three-year survival of 72% is a probability estimate at a time point. It is not a median of three years and not an HR of 0.72.
Practice nine: competing risks. A cumulative incidence of recurrence in the presence of death as a competing event should not be relabelled ordinary Kaplan–Meier recurrence risk without checking the method.
Practice ten: RMST. A two-month RMST difference through 24 months is a difference in restricted mean event-free time. It is not necessarily a two-month difference in median survival.
Practice eleven: adjusted HR. If the source says HR adjusted for age and stage, keep adjusted and the covariates. Do not report it as a crude comparison.
Practice twelve: time origin. Time from diagnosis and time from treatment start are different endpoints even if the same event ends both. Preserve the starting point.
30. Frequently asked translation questions
Is a hazard ratio the same as a risk ratio? No. They are different measures. A risk ratio compares cumulative probabilities over a specified period, while a hazard ratio compares modeled instantaneous event rates over time.
Can I call HR 0.7 a 30% reduction in risk? Not without qualification. The safer wording is a 30% lower hazard under the fitted model and reference contrast. Absolute or cumulative risk reduction requires separate information.
Does censoring mean missing data? It means the exact event time is not observed beyond a point under the time-to-event framework. Some censoring is administrative and fully expected. It is not identical to generic missing data.
What does median not reached mean? The estimated survival curve has not fallen to 50% during the observed follow-up in a way that allows the median to be estimated. It does not mean nobody had the event.
Can two groups have the same median but different curves? Yes. Median survival captures one point on each curve. The distributions before and after the median can differ substantially.
What is the best final check? For every number, identify whether it is a time, survival probability, hazard ratio, p-value, confidence interval or risk-set count. Then confirm the event, time origin and comparison group. If those match the source, the time-to-event meaning is likely intact.
31. A release checklist for survival-analysis translation
- Define the event precisely.
- Preserve the time origin.
- Distinguish censoring from events and loss to follow-up.
- Keep number-at-risk tables attached to the correct curves.
- Distinguish Kaplan–Meier survival probability from raw event proportions.
- Preserve median survival as a time, not a mean.
- Keep “median not reached” as a non-numeric result.
- Preserve hazard ratio direction and reference group.
- Do not convert HR directly into absolute risk reduction.
- Distinguish adjusted and unadjusted hazard ratios.
- Preserve proportional-hazards assumptions and violations.
- Keep log-rank tests distinct from effect-size estimates.
- Distinguish competing-risk methods from ordinary survival methods.
- Keep RMST, median survival and fixed-time survival separate.
- Preserve confidence-interval units and null values.
The checklist protects the temporal architecture of the analysis. Time-to-event translation fails when the number is copied but its event, risk set or time reference changes.
32. Continue through the established eduKate translation architecture
This specialist guide belongs under Master Art of Translation. It connects to Probability, Odds, Risk Ratios and Absolute Risk, Confidence Intervals, Standard Errors and Margin of Error, P-Values, Statistical Significance and Effect Sizes, and Incidence, Prevalence, Person-Time and Rates.
The Vocabulary Learning Hub supports precise distinctions between event, hazard, risk, survival, recurrence, censoring and follow-up. How English Works supports temporal clauses, reference phrases, comparison structures and modality. Those language systems matter because a single misplaced “by,” “at,” “from” or “through” can change what a survival statistic refers to.
The final principle is simple: survival analysis is translation across time as much as across language. Preserve the event, starting point, follow-up structure, censoring rule, risk set and comparison model. Then make the target prose clear. The language can change, but the timeline and the statistical question should remain the same.