Why the Role of Death Must Be Specified
Death can change what a clinical outcome means. If the endpoint is death, it is the outcome of interest. If the endpoint is a composite that includes death, death is one way for the endpoint to occur. But if the endpoint is a symptom score measured at a fixed visit, a participant who dies before that visit cannot have an observed score there. In that setting, death affects the outcome’s definition or interpretation and must be addressed as an intercurrent event.
These choices answer different clinical questions. A composite endpoint can ask whether treatment changes the chance of experiencing death or a nonfatal event by a specified time. A hypothetical strategy for a symptom score can ask what the score would have been under a specified scenario in which death did not occur. Neither question is automatically more appropriate: the choice must reflect the intended clinical interpretation.
Specify the Endpoint and the Follow-Up Horizon
An estimand is a precise description of the treatment effect being targeted. In the framework introduced in the earlier material on the five attributes of a clinical trial estimand, the endpoint variable and the strategy for each intercurrent event are distinct attributes. For death-related questions, write down both explicitly. A label such as “clinical benefit” is not enough: it does not say whether death counts as an endpoint event, nor what happens to a nonfatal outcome after death.
Let \(a\) denote a treatment condition, and let \(D^a\) indicate whether a participant would die by a specified horizon under that condition. Let \(W^a\) indicate whether the participant would have a specified nonfatal worsening by that horizon. A simple composite endpoint is
Here \(I(\cdot)\) equals 1 when its condition is true and 0 otherwise. The definition must also specify the population, treatment conditions, exact horizon, and what counts as nonfatal worsening. If the endpoint is defined as the first event by day 180, the event categories should be classified consistently through day 180. An event after day 180 does not count in that endpoint.
A composite can also be an ordered outcome, such as a ranking that places death below all nonfatal outcomes. That choice adds a clinical ordering assumption: it declares how death ranks relative to the other outcomes. A binary “death or worsening” endpoint instead records whether either event occurred, without encoding a ranking among people who experience an event. In either case, the endpoint’s construction needs clinical justification.
Worked Example: A 180-Day Mortality Endpoint
Worked Example: A 180-Day Mortality Endpoint
Suppose a hypothetical randomized trial assigns 100 participants to each of two treatments, A and B. The endpoint is all-cause death by day 180. Assume follow-up through day 180 is complete for all 200 participants and death status is ascertained consistently. There are 8 deaths in A and 12 in B.
For this question, death is the endpoint itself, not an intercurrent event. The observed proportions are \(8/100=0.08\) for A and \(12/100=0.12\) for B. The difference, calculated as B minus A, is \(0.12-0.08=0.04\), or 4 percentage points.
The descriptive result is that the observed 180-day death proportion is 4 percentage points higher in B than in A in this hypothetical sample. It is not a symptom-score effect, and it does not say what the effect would be on a composite endpoint. The common horizon and complete ascertainment support the stated comparison; changing the horizon would define a different mortality endpoint and potentially a different estimand.
Worked Example: Death as a Composite Endpoint Component
Worked Example: Death Included With Nonfatal Worsening
In another hypothetical trial, 100 participants are assigned to each treatment. The endpoint is first occurrence by day 180 of either all-cause death or a specified nonfatal clinical worsening. To keep the categories mutually exclusive, a participant who has nonfatal worsening and dies later is counted under the first event, nonfatal worsening. By day 180, A has 8 participants whose first event is death and 22 whose first event is nonfatal worsening. B has 12 whose first event is death and 18 whose first event is nonfatal worsening. Assume all participants’ event status is known through day 180.
For A, the number meeting the composite is \(8+22=30\), so the proportion is \(30/100=0.30\). For B, it is \(12+18=30\), also \(0.30\). The difference in composite-event proportions, B minus A, is \(0.30-0.30=0.00\), or 0 percentage points.
The estimand’s clinical question is whether assignment to B rather than A changes the chance of death or nonfatal worsening by day 180. These data show no difference in the observed composite proportions. They do not show that mortality is the same: the observed death proportions are \(8/100=0.08\) in A and \(12/100=0.12\) in B. Nor do they establish that the nonfatal component alone is unaffected. The endpoint combines distinct outcomes, so its treatment contrast must be interpreted as a contrast on the composite.
Why Composite Effects Can Conceal Different Component Patterns
The arithmetic behind a simple composite helps explain its interpretation. Suppose “death first” and “nonfatal worsening first” are disjoint categories, and either category counts as a composite event. For each treatment condition, the probability of the composite is the sum of the probabilities of those categories. Therefore the treatment contrast in composite probability is the sum of the component-category contrasts.
This equality follows because the two first-event categories are disjoint and together make up the composite event. It does not imply that the component effects have the same direction or clinical importance. Opposing component differences can partly or completely cancel in the total.
Worked Example: A Composite With Opposing Components
Consider a hypothetical trial with 120 participants per treatment and complete event ascertainment through day 180. The endpoint is first occurrence by day 180 of death or nonfatal worsening. In A, 12 participants have death as their first event, 18 have nonfatal worsening first, and 90 have neither. In B, the corresponding counts are 6, 30, and 84.
The composite proportions are \((12+18)/120=30/120=0.25\) for A and \((6+30)/120=36/120=0.30\) for B. The composite difference, B minus A, is \(0.30-0.25=0.05\), or 5 percentage points; the observed composite proportion is higher in B.
For death as the first event, the proportions are \(12/120=0.10\) in A and \(6/120=0.05\) in B, a B-minus-A difference of \(-0.05\), or −5 percentage points. For nonfatal worsening as the first event, the proportions are \(18/120=0.15\) and \(30/120=0.25\), a difference of \(0.10\), or 10 percentage points. The component differences add to the composite difference: \(-0.05+0.10=0.05\).
Thus the composite result is not a summary of a uniform direction of effect across its components. It should be reported alongside the component patterns when those patterns matter clinically. The arithmetic is consistent with the data, but deciding how to weigh the components or what they mean for patients requires clinical judgment, not just the composite calculation.
Death as an Intercurrent Event for a Nonfatal Outcome
Now consider an endpoint that is a symptom score at day 180, with lower scores indicating fewer symptoms. Death before day 180 means that the scheduled score does not exist for that participant. It is therefore not sufficient to write “compare day-180 scores” and then silently remove participants who died. The target question needs a strategy for death.
A hypothetical strategy can specify a counterfactual question, such as the day-180 score under each treatment condition in a clearly defined scenario in which death is prevented. That interpretation requires a meaningful scenario: one must consider what intervention or hypothetical conditions prevent death and whether the resulting symptom score is well-defined. Simply saying “the score the participant would have had if alive” may be inadequate, because different ways of preventing death could lead to different health states and scores.
A composite strategy can instead incorporate death in the endpoint, for example by defining a binary outcome of death or severe symptoms, or by assigning death the worst category in an ordered endpoint. This answers a question about the combined endpoint, not the mean symptom score among people who would be alive. Its validity depends on a defensible definition and, for an ordering, a clinically meaningful ranking.
A treatment-policy strategy includes outcomes regardless of an intercurrent event when those outcomes remain defined and can be measured. But a treatment-policy label does not create a symptom score after death. A principal-stratum estimand, such as one restricted to people who would survive under both treatment conditions, asks about a different target group; membership in that group is generally not directly observed for each participant. These alternatives should not be treated as interchangeable ways to fill in an unavailable score.
Worked Example: A Hypothetical Day-180 Symptom Score
Worked Example: Specifying a Hypothetical Strategy
In a hypothetical trial, 80 participants are assigned to each of A and B. The endpoint is a symptom score from 0 to 10 at day 180, with lower scores better. Four participants assigned to A and 10 assigned to B die before that visit. Among participants alive at day 180, the observed mean scores are 4.2 for A and 3.8 for B.
The survivor means give a descriptive comparison among those alive in each treatment group, but they do not by themselves answer a hypothetical estimand for all randomized participants. The surviving groups may differ because death occurred at different rates, and the scores after death are not observed outcomes.
Suppose, purely for illustration, a prespecified and justified model produces standardized mean scores under a clearly stated hypothetical scenario preventing death of 4.5 for A and 4.1 for B. The hypothetical treatment contrast, B minus A, is \(4.1-4.5=-0.4\) score points. Under that scenario and model, the estimated mean score is 0.4 points lower with B. These stipulated model outputs are not calculated from the survivor means alone; they depend on the hypothetical scenario and the model’s assumptions.
This is a different clinical statement from “B has a lower observed score among survivors.” The scenario must be credible enough to support interpretation, and conclusions should not be extended to a composite endpoint or to mortality without separate estimands.
Assumptions, Diagnostics, and Common Pitfalls
The estimand’s interpretation depends first on the definition, not on which statistical model is later used. Before analysis, verify that the treatment conditions, target population, endpoint, horizon, and death strategy describe the clinical question. Then check that event definitions are applied consistently and that the data distinguish death from nonfatal events in the way the endpoint requires. If participants can experience both, specify whether the endpoint uses first event, any occurrence, a count, or another rule.
- Check the time horizon. Death by day 180 and death by one year are different outcomes. Use the same horizon in the endpoint definition, data summary, and interpretation.
- Check the endpoint construction. If death is part of a composite, confirm that the event rule says how overlapping events are counted and what nonfatal event qualifies.
- Inspect component patterns. A composite can hide opposing effects or be dominated by a more frequent, less serious component. Report components when they are clinically relevant.
- Challenge hypothetical assumptions. If an outcome is undefined after death, ask whether the proposed scenario makes it meaningful and whether conclusions depend on that scenario.
A common mistake is to call death “missing data” and analyze only participants with observed day-180 scores, as though the remaining participants necessarily represent the original target population. The correction is to recognize that death changes the endpoint’s interpretation: specify a clinically coherent strategy, define a composite if that is the intended question, or state a different target group. A second mistake is to say that a favorable composite proves benefit on every component. The correction is to interpret the composite as the combined endpoint and examine its components separately.
Check Your Understanding
Answer each question, then compare with the brief solutions below.
- A trial defines its endpoint as all-cause death by day 90. Is death an endpoint component or an intercurrent event for that estimand?
- A day-180 symptom score is the endpoint, and some participants die before day 180. Why is a comparison restricted to survivors not automatically a treatment-policy estimand?
- In a hypothetical composite, the event proportions are 0.18 for A and 0.23 for B. State the B-minus-A contrast in percentage points and what endpoint it describes.
- Why can a composite result conceal clinically important component differences?
Solutions. (1) Death is the endpoint itself, measured through day 90. (2) A symptom score after death is undefined; including only observed survivors changes the comparison and does not provide outcomes regardless of death. (3) \(0.23-0.18=0.05\), or 5 percentage points higher in B for the specified composite endpoint. (4) Components can differ in frequency, seriousness, or direction of treatment effect; their combined result need not describe the effect on each component.