Time-to-Event Outcomes & Hazard Ratios

A time-to-event outcome combines two pieces of information: whether a defined event occurred and how much time passed from a defined starting point. The event might be death, recurrence, recovery, device failure, or another prespecified occurrence. The method is often called survival analysis even when the event is not death.[1][3]

This structure lets participants contribute different lengths of follow-up. It also creates interpretive traps. A hazard ratio is not a risk ratio, a censored participant is not known to be permanently event-free, and two separated Kaplan–Meier curves do not by themselves establish a complete or stable treatment effect.[2][3]

Define the outcome before reading the curve

CONSORT 2025 asks reports to identify the measurement variable, participant-level analysis metric, aggregation method, and time point for every outcome. For a time-to-event endpoint, a reader also needs the event definition and the clock that generates the time.[1]

Element	Question to ask	Why it matters
Event	What occurrence counts, and how is it confirmed?	Different definitions can produce different event counts and clinical meanings
Time origin	Does time begin at randomization, enrollment, a procedure, or another milestone?	Misaligned starting points can make groups incomparable
Event time	Is the exact time known, or only an interval between assessments?	The observation schedule affects what can be inferred
Follow-up window	How long could each participant be observed?	Short and unequal follow-up changes the information available
Competing event	Can another event prevent the event of interest from occurring or being observed?	Death, for example, may prevent a later nonfatal outcome
Analysis population	Which randomized participants contribute to the estimate?	Exclusions can change the comparison created by randomization

“Progression-free survival,” “time to recovery,” and similarly compact labels are not self-defining. A report should state event components, adjudication rules, how multiple events are ordered, and what happens after treatment discontinuation or another intercurrent event. These choices determine the question answered; they are not merely software settings.[1][4]

Censoring is partial information, not no event

Under usual right censoring, follow-up ends before the event is observed. The record establishes event-free status only through the last observed time. Survival methods retain that information rather than discarding the person.[3]

Censoring can occur because the study ends, the participant enters late and has less potential follow-up, contact is lost, consent is withdrawn, or another analysis rule stops observation. These reasons are not interchangeable. Administrative censoring at a common study end may be less concerning than loss to follow-up related to worsening prognosis, but neither label removes the need to describe what happened.[2][4]

The analysis relies on assumptions about participants after censoring. If people who disappear from one group are systematically more or less likely to experience the event than otherwise similar people still followed, the curve and model may be biased. A survival method does not manufacture the unobserved event times. It uses the observed event-free intervals under assumptions that should be examined through retention information and, where planned, sensitivity analyses.[2][4]

Report the numbers censored, reasons, timing, and whether patterns differ by assigned group. A single overall “lost to follow-up” percentage conceals whether losses happened early, late, symmetrically, or after events related to prognosis.

Read a Kaplan–Meier curve as an estimate over time

A Kaplan–Meier curve estimates the probability of remaining free of the defined event as follow-up progresses. Each downward step usually marks one or more events; censoring marks the end of observed follow-up for particular participants without causing an event step. The curve becomes less stable as fewer participants remain under observation.[3][6]

Numbers at risk are therefore essential. They show how many participants are still being followed and event-free immediately before selected times. A visually dramatic late separation may rest on only a small fraction of the randomized sample. Confidence bands, when shown, usually widen as information thins.

A complete report should provide, by group:

number randomized and number included in the analysis;
total number of observed events;
numbers at risk at useful time points;
follow-up duration and how it was summarized;
censoring definitions and reasons;
event-free probabilities at prespecified times with uncertainty; and
the between-group effect estimate, uncertainty, and model assumptions.

CONSORT 2025 specifically calls for the number analyzed, number with available data, group results, effect size, and its precision for each outcome. Selectively showing only the most favorable time point or only a curve omits information needed to interpret the comparison.[2]

Hazard, risk, and time summaries are different

Hazard is an instantaneous event rate among participants who remain event-free immediately before a given time. A hazard ratio compares those rates between groups. Under a proportional-hazards model, one ratio summarizes the relative hazards across follow-up.[3]

That ratio is not an absolute probability and should not be translated as though it were one.

Summary	What it compares	What it does not say alone
Hazard ratio	Relative instantaneous event rates over time under the fitted model	The probability that an individual will have the event
Risk ratio at a stated time	Event probabilities by that time	How the difference evolved before that time
Risk difference at a stated time	Absolute percentage-point difference by that time	A constant relative effect across follow-up
Median-time difference	Difference between times when each curve reaches 50%, if both do	The experience of the whole follow-up period
Restricted mean time contrast	Average event-free time accumulated through a specified horizon	Outcomes beyond that horizon

A hazard ratio of 0.75 is commonly described as a 25% lower hazard in the comparison direction. It does not mean 25% fewer participants experienced the event, that every participant’s event was delayed by 25%, or that the median time increased by 25%. Absolute event probabilities depend on baseline hazard and follow-up time. Both relative and time-specific absolute results can be useful.[2][3]

The comparison direction must also be explicit. A ratio for intervention relative to comparator has the reciprocal numerical value of the comparator-relative-to-intervention ratio, even though both encode the same fitted contrast.

Proportional hazards is an assumption, not a visual label

The familiar Cox-model hazard ratio usually assumes that the ratio of hazards is constant over time, although each group’s hazard may itself change. If treatment effects weaken, emerge late, reverse, or otherwise vary materially, one average hazard ratio can conceal the pattern.[3][5]

Crossing curves are an obvious warning but not the only possible departure. Nearly parallel curves do not prove proportional hazards, and visual inspection alone is not a complete assessment. A report should state the model, prespecified checks, and what alternative or time-varying summaries were used when the assumption was not credible.

When effects vary over time, time-specific event probabilities, risk differences, restricted mean time through a prespecified horizon, or explicitly time-varying hazard ratios may answer clearer questions. Restricted mean survival time has been studied as an alternative summary that does not require a constant hazard ratio.[6] These measures are not interchangeable, and choosing one after seeing which looks favorable invites selective interpretation. The endpoint, summary, and analysis should be specified in advance and tied to the scientific question.[1][5]

Competing events change the question

A competing event prevents the event of interest or materially changes its possibility. For example, death can prevent later recovery or recurrence. Treating every competing event as ordinary censoring can answer a hypothetical question that differs from the observed real-world probability of the event.

Methods based on cause-specific hazards and methods based on cumulative incidence target different quantities. A report should name the competing event, explain the chosen strategy, state whether the estimate is a cause-specific or subdistribution hazard ratio when relevant, and present interpretable probabilities where possible. CONSORT’s statistical-methods examples explicitly distinguish a competing-risk cumulative-incidence analysis from a separate cause-specific Cox analysis.[5]

The best method depends on the research question. The important reading rule is simpler: do not treat “competing risks were considered” as a complete description, and do not compare ratios from different models as though they estimate the same effect.

A time-to-event reading checklist

Write down the event definition and every component.
Identify the time origin, follow-up horizon, and assessment schedule.
Record the randomized and analyzed populations and total event counts.
Inspect numbers at risk before interpreting late curve behavior.
Trace censoring reasons and timing separately by group.
Identify competing events and the quantity the chosen method estimates.
Name the effect measure, comparison direction, estimate, and confidence interval.
Check proportional-hazards or other model assumptions and planned alternatives.
Compare the protocol, registry, analysis plan, and reported time points.
Keep the conclusion tied to the studied event, population, and follow-up.

Important limitations

Censoring preserves observed event-free time but does not reveal the later unobserved outcome.
A Kaplan–Meier curve is an estimate, not a participant-level prediction.
A hazard ratio is not a risk ratio, absolute risk difference, or fixed delay in event time.
A single ratio can obscure an effect that changes direction or magnitude over time.
Late curve behavior may be highly uncertain when few participants remain at risk.
Competing-risk methods answer different questions and must be named precisely.
Reporting guidance improves transparency but does not certify an unbiased analysis.
A time-to-event result cannot establish the identity or comparability of a separately sourced material.

Frequently asked questions

Does censoring mean the participant never had the event?

No. It means the event was not observed through that participant’s last usable follow-up time. The person contributes event-free time up to censoring; what happened afterward may be unknown.

Is a hazard ratio the same as a risk ratio?

No. A hazard ratio compares instantaneous event rates among those still event-free. A risk ratio compares event probabilities over a stated period. Their numerical values and interpretations can differ.

Does a hazard ratio of 0.70 mean events occurred 30% later?

No. It describes a 30% lower fitted hazard in the stated comparison direction, under the model. It does not directly give a percentage change in event time or absolute event probability.

What do the numbers at risk under a Kaplan–Meier curve show?

They show how many participants remain under observation and event-free just before selected times. Small late numbers warn that the corresponding part of the curve may be unstable.

Do crossing Kaplan–Meier curves invalidate the study?

Not automatically. They can signal changing effects or non-proportional hazards and make one constant hazard ratio inadequate. The prespecified analysis and time-specific alternatives then matter.

Can loss to follow-up be treated as ordinary censoring without concern?

Only under assumptions that should be justified. If loss relates to prognosis differently across groups, censoring may be informative and bias the estimate; sensitivity analysis can examine, not erase, that uncertainty.

Does a survival result validate a material sold under the same name?

No. The result belongs to the documented intervention, participants, event definition, follow-up, and analysis. It does not authenticate or establish comparability with another material.

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Time-to-Event Outcomes, Censoring, and Hazard Ratios