Why Measure Outcomes After an Intercurrent Event?
An intercurrent event can change what happens between treatment assignment and the planned outcome assessment. A participant might discontinue assigned treatment, start rescue medication, or switch to another therapy. If the endpoint is still meaningful after that event, an assessment taken afterward describes the participant’s outcome under the care actually received. Whether that value belongs in the treatment effect of interest depends on the chosen intercurrent-event strategy.
For a treatment-policy strategy, the target is the effect of assignment to each treatment, regardless of whether the specified event occurs. A meaningful endpoint collected after the event can therefore contribute directly to the target outcome. For another strategy, such as a hypothetical or while-on-treatment strategy, the post-event value may describe a different outcome from the one the estimand targets. It should not be treated as interchangeable simply because it is observed.
This distinction is not the same as the distinction between an event and missing data. An event describes what happened to a participant; missingness describes the absence of an outcome measurement that the study intended to obtain. A participant can have an event and a measured post-event outcome, or an event and a missing post-event outcome. If the endpoint is not defined after an event—for example, a measurement that cannot exist after death—the issue is not simply an unrecorded value. The endpoint and strategy must be defined accordingly.
When Post-Event Measurements Enter the Target
Let \(A\) denote randomized treatment assignment, with \(A=1\) for the active treatment and \(A=0\) for control. Let \(Y\) be a fixed-endpoint outcome, such as a functioning score in points, with larger values indicating better functioning. Under a treatment-policy strategy, \(Y\) is the endpoint at the planned assessment whether or not the specified nonfatal intercurrent event occurred, provided the endpoint is meaningful after it.
Write \(Y^a\) for the outcome that would be observed under assignment \(a\), with subsequent events and care handled according to the treatment-policy strategy. A mean-difference estimand is \(E[Y^1]-E[Y^0]\). In a randomized trial, the observed arm means estimate these assignment-specific means when the endpoint is defined and ascertained for all relevant participants, treatment assignment is implemented as specified, and the observed outcome corresponds to the assigned strategy. Randomization supports comparison by assignment; it does not make missing endpoint values observed.
In this calculation, each participant’s endpoint value is used according to assignment. If an endpoint was measured after rescue medication, discontinuation, or another specified event, it remains in the arm mean for a treatment-policy estimand. The measurement is not “adjusted back” to the value that might have occurred without the event. The estimand includes outcomes under the actual subsequent course of care covered by the strategy.
Worked Example: Including Measurements After Rescue Medication
In a hypothetical randomized trial, the endpoint is a functioning score at 12 weeks, measured in points; higher scores indicate better functioning. Rescue medication is a specified intercurrent event. Each of five participants per arm has a measured 12-week score, including participants assessed after rescue medication. The scores are:
Active assignment: 8, 9, 6 (after rescue), 7 (after rescue), 10.
Control assignment: 7, 6, 8 (after rescue), 5, 9.
Check the conditions for this calculation. The example defines the endpoint at 12 weeks for all ten participants, including those who used rescue medication, and gives a measured value for each. The endpoint is therefore usable after this nonfatal event, and the treatment-policy calculation includes those values.
The active-assignment mean is \((8+9+6+7+10)/5=40/5=8.00\) points. The control-assignment mean is \((7+6+8+5+9)/5=35/5=7.00\) points. Thus the estimated treatment-policy mean difference is \(8.00-7.00=1.00\) point in favor of active assignment.
This is a contrast by randomized assignment that includes outcomes after rescue medication; it does not isolate the effect of treatment received without rescue. If one instead removed the two active-arm and one control-arm post-rescue values, the resulting means would be \(27/3=9.00\) and \(27/4=6.75\) points, respectively. Their difference, 2.25 points, is not the treatment-policy contrast: it compares selected participants with no post-rescue measurement included and answers a different question.
Why Other Strategies May Not Use Those Values as the Target Outcome
A post-event measurement remains useful information, but it does not automatically answer every estimand. Under a hypothetical strategy, the target concerns an outcome in a scenario where the specified event did not occur. The observed post-event value was measured after the event and under the subsequent care that actually took place. It is not the unobserved outcome in the hypothetical no-event scenario. Excluding the observed value from a calculation does not, by itself, identify that hypothetical outcome.
Under a while-on-treatment strategy, the target is tied to a defined period on assigned treatment. A measurement after treatment discontinuation may fall outside the target outcome definition even if it is recorded. For a composite strategy, the event may itself be incorporated into a composite outcome, or may determine how the outcome is summarized; the post-event measurement is used only if the composite definition says it contributes. Thus a study can collect a post-event value for safety, description, or another analysis without making it part of a particular estimand.
Worked Example: The Observed Value Is Not the Hypothetical Value
Suppose, hypothetically, that the target is the 12-week functioning score that would have been observed had participants not started rescue medication. Four participants assigned active treatment have measured scores of 8 and 7 without rescue, and 4 and 3 after rescue. The event is rescue use, and larger scores mean better functioning.
The observed mean among all four participants is \((8+7+4+3)/4=22/4=5.50\) points. The mean among the two who did not use rescue is \((8+7)/2=7.50\) points. Neither calculation is automatically the mean score that all four would have had without rescue. The two observed post-rescue scores of 4 and 3 are outcomes under rescue, not measurements of their no-rescue outcomes; and the two participants without rescue need not represent the two who used it.
The hypothetical target is therefore not obtained by simply including the post-rescue scores, nor by discarding them and averaging the remaining scores. A method for estimating the unobserved no-rescue outcomes would require additional assumptions and a suitable analysis. The observed post-event values can still describe actual outcomes after rescue and help the study characterize what happened.
The same logic applies if a treatment-policy estimand is the target but some post-event assessments are not obtained. A missing post-event value is not a reason to redefine the treatment-policy strategy as “exclude everyone with an event.” It is an outcome that the target calls for but that was not observed. The distinction between an event and missing data is established in the earlier material on Missing Data, while the choice of strategy determines which outcome the study is trying to estimate.
Specify Post-Event Collection Before the Trial
A study intended to estimate a treatment-policy effect should plan for endpoint collection after relevant events when the endpoint remains meaningful. The protocol and data-collection plan should make clear what is collected, from whom, and how the measurement will be interpreted. At minimum, specify:
- Which events matter: define the events whose occurrence changes treatment, subsequent care, or endpoint interpretation.
- What outcome is measured: identify the endpoint, instrument or measurement method, units, and the planned assessment window.
- Who is followed: state whether endpoint follow-up continues after discontinuation, rescue use, or treatment switching, subject to consent and feasibility.
- What context is recorded: retain event status and relevant treatment or subsequent-care information so that a post-event value can be understood.
- How nonmeasurement is distinguished: record whether an assessment was not obtained and, where available, why; do not code an unmeasured value as if it were an event or a numerical endpoint.
These details are part of making the estimand operational. If follow-up routinely stops after discontinuation, for example, a study may be unable to observe the treatment-policy outcome for many participants. Conversely, collecting a post-event outcome does not commit every analysis to use it as the target endpoint. The estimand specifies the question; the collection plan should preserve the information needed to answer that question and to describe other relevant outcomes.
Worked Example: Auditing Post-Event Outcome Collection
In a hypothetical two-arm study, ten participants in each arm are assigned treatment. The plan calls for a 12-week symptom score after rescue medication, but after the trial begins the team finds that four participants in each arm used rescue medication; scores were obtained for three of those four in each arm. All six participants without rescue in each arm have scores.
In either arm, the post-rescue measurement rate is \(3/4=0.75\), or 75%. The total endpoint measurement rate is \((6+3)/10=9/10=0.90\), or 90%. The missing post-rescue score in each arm is not a zero score and is not evidence that the event did not occur. Each participant had the event, but the endpoint was not measured.
For a treatment-policy target, the team should report the gap between the intended collection and what was observed, retain the event and measurement-status information, and use an analysis that addresses the unobserved endpoint under stated assumptions. The complete-case mean from the nine measured participants does not automatically equal the mean for all ten assigned participants. The audit also points to a design improvement: maintain endpoint follow-up after rescue and record reasons for any missed assessment.
Derivation, Diagnostics, and Limitations
The treatment-policy sample-mean calculation follows directly from the randomized assignment and the outcome definition. With complete measurement, consistency (the observed outcome under the received course of care corresponds to the potential outcome for the assigned treatment-policy strategy), and random assignment, the mean among those assigned \(a\) estimates the mean outcome under assignment \(a\). The sample contrast subtracts these two arm-specific estimates:
This justification requires that \(Y\) actually be defined under the strategy being compared and that the relevant outcomes be observed for the calculation. Randomization does not remedy systematic loss of post-event measurements. If outcomes are missing, the simple mean contrast may no longer estimate the intended population means without additional assumptions and an appropriate missing-data analysis. The later material on missing data within a defined estimand addresses that separate problem.
Useful diagnostics begin with the data flow: compare the number of events, attempted assessments, and obtained endpoint values by assigned arm and event status. Check that post-event values are not silently dropped, coded as zero, or treated as pre-event measurements. Check whether the endpoint instrument retains the same meaning after the event. Large differences in post-event measurement rates between arms or event groups warrant investigation because they can make the observed values an unrepresentative subset.
There are also limits to what post-event measurement can achieve. A value measured after an event does not reveal what would have happened in a counterfactual scenario without that event. A treatment-policy contrast describes assignment effects including the subsequent care covered by the strategy; it does not by itself isolate pharmacologic effects or the causal effect of the event. And if an endpoint is undefined after an event, collecting a value may be impossible or conceptually inappropriate. The endpoint and event strategy must then be specified consistently rather than treating undefined outcomes as ordinary missing measurements.
| Strategy | Role of a meaningful post-event measurement | Key caution |
|---|---|---|
| Treatment policy | Included as the endpoint under assigned treatment, regardless of the event | It must be measured and remain meaningful after the event |
| Hypothetical | Describes the observed course after the event, but is not the no-event outcome | Excluding it does not identify the counterfactual target |
| While on treatment | May be recorded but may fall outside the target period or outcome definition | Follow-up and analysis must reflect the defined on-treatment target |
| Composite | Contributes only as specified by the composite outcome definition | Do not assume a separate post-event score replaces the event component |
A common mistake is to reason, “The participant had an intercurrent event, so the post-event score should be excluded.” That rule confuses an event with a strategy. Under treatment policy, an observed score after a meaningful nonfatal event is part of the target outcome. Under another strategy, it may not be. The correction is to name the estimand strategy first, define the endpoint under that strategy, and then decide how each measured value is used.
Check Your Understanding
Answer each question using the stated strategy and endpoint definition.
- A participant uses rescue medication and has a 12-week score that remains meaningful and is measured. Under a treatment-policy strategy, should the score be included in the assigned-arm outcome?
- For a hypothetical no-rescue estimand, why can the observed score after rescue not be substituted for the score the participant would have had without rescue?
- In one arm, 12 participants are assigned, 5 use rescue, and post-rescue scores are obtained for 4. What is the post-rescue measurement rate, and how many participants have a missing post-rescue score?
- Name two kinds of information a study should preserve to interpret post-event measurements and missing post-event assessments.
Solutions. (1) Yes. If the endpoint is defined and measured after rescue, treatment policy includes it in the outcome under assigned treatment. (2) It is an observed outcome under rescue; the hypothetical no-rescue outcome is counterfactual and is not directly measured by that value. (3) The rate is \(4/5=0.80\), or 80%; one participant who used rescue has no post-rescue score. (4) For example, preserve event status and relevant subsequent-treatment information, and record whether the assessment was obtained and why it was missed.