Why a Treatment-Policy Estimand Includes Outcomes After an Event
A participant may stop assigned treatment, start rescue medication, or otherwise experience an event after randomization that affects how the endpoint should be interpreted. The outcome can still be measured after that event. A treatment-policy estimand uses that outcome: it asks about the effect of assigning one treatment condition rather than another when outcomes are assessed regardless of whether the event occurs. This makes the consequences of the event part of the treatment effect being targeted.
The event is not simply ignored. Its timing and consequences may matter clinically, and the trial still needs to collect the endpoint after it occurs. The defining choice is that event occurrence does not change which outcome is summarized: the endpoint is measured at the specified time for participants whether or not they discontinued treatment or used rescue medication.
Formalizing the Target
Suppose participants come from a target population, and \(a=1\) and \(a=0\) denote two treatment conditions assigned at randomization. Let \(Y_i(a)\) be the endpoint value for participant \(i\) at the specified assessment time under assignment to condition \(a\), with the trial's subsequent care taking place as it would under that assignment. If a participant discontinues assigned treatment or receives rescue medication, \(Y_i(a)\) is still the endpoint after that event. For a continuous endpoint, one possible population-level treatment-policy estimand is
Here, the expectation is over the target population. The scale and direction depend on the clinical question: for an endpoint where smaller values are better, a negative \(\Delta_{\mathrm{TP}}\) favors assignment to condition 1. For a binary endpoint, the corresponding treatment-policy contrast might instead be a risk difference, risk ratio, or another population-level summary.
The definition requires the treatment conditions, target population, endpoint, assessment time, population-level summary, and strategy for the event to be clear. These are the attributes used to specify an estimand; the earlier material on population-level summaries of treatment effects provides the relevant options for the summary. Here, the central point is that the outcome under each assigned condition includes the post-event outcome. The estimand is not restricted to people who remain on treatment or avoid the event.
A treatment-policy estimand is often aligned with the effect of randomized assignment, but it is not synonymous with an analysis set or a particular estimator. For example, analyzing only participants who completed assigned treatment would generally change the population being compared and would not, by itself, estimate this target.
Why the Post-Event Outcome Belongs in the Summary
The population mean under an assigned condition includes outcomes from all event pathways. For a simple binary event indicator \(E_i(a)\), the mean can be written as a weighted average of the means among those who do and do not experience the event:
This identity follows by partitioning the population into the two mutually exclusive event groups and adding their contributions to the overall expectation. It shows why the event rate and the outcomes after the event both contribute to the treatment-policy mean. The groups defined by event status can differ between assigned conditions; the estimand compares the two overall means, not the event groups as if they were interchangeable.
Randomization supports comparison of assigned conditions in the target population, provided treatment assignment is implemented as planned and outcomes are obtained and analyzed appropriately. The interpretation also depends on clearly specified treatment conditions and endpoint, and on consistency: each participant's observed outcome under the condition assigned corresponds to the outcome defined for that condition. The usual no-interference condition is also relevant: one participant's assignment should not determine another participant's endpoint. Most importantly for this strategy, the endpoint must remain meaningful and be collected after the event.
Worked Example: Treatment Discontinuation With Follow-Up Outcomes
Consider a hypothetical randomized trial comparing an active treatment with control. The endpoint is a symptom score at week 12, in points, with lower scores better. Six participants per group have week-12 scores, including the scores of participants who discontinued assigned treatment. In the active group, two participants discontinued; their scores are 12 and 17. The active-group scores are 8, 10, 12, 14, 15, and 17. In control, the scores are 10, 12, 13, 15, 16, and 18. The treatment-policy target is the difference between the population mean week-12 scores under assignment to active treatment and control, regardless of discontinuation.
The observed active-group mean is
The control-group mean is
The estimated difference, active minus control, is \(12.67-14.00=-1.33\) points. In this hypothetical sample, the mean score is 1.33 points lower under assignment to active treatment. Because lower scores are better, the direction favors assignment to active treatment. This is a sample estimate of the treatment-policy contrast, not a statement that every participant benefits or that the population contrast is known exactly.
The discontinuers remain in the calculation because the endpoint was collected after discontinuation. Removing their scores would change the analysis and could select participants based on a post-randomization event.
Rescue Medication: Include the Outcome, Not Just the Event History
When rescue medication is permitted, its use may change the endpoint that follows. Under a treatment-policy strategy, that post-rescue endpoint contributes to the assigned group's outcome distribution. The target therefore includes both how often rescue is used and the outcomes that occur in the presence of rescue. The clinical interpretation is the effect of assignment in the setting where rescue medication is available and used according to the trial's specified care.
Worked Example: A Continuous Endpoint After Rescue Medication
In a hypothetical pain trial, the week-8 pain score is measured in points, with lower values better. Among 10 participants assigned active treatment, 4 use rescue medication and have a mean week-8 score of 3 points; the other 6 have a mean of 5 points. Among 10 control participants, 2 use rescue medication and have a mean score of 4 points; the other 8 have a mean of 6 points. Assume the week-8 score is obtained for everyone, including rescue-medication users.
The treatment-policy mean for active assignment combines both event groups:
The corresponding control mean is
Thus the estimated treatment-policy difference is \(4.20-5.60=-1.40\) points. The sample mean is 1.40 points lower under active assignment. This contrast includes outcomes after rescue medication; it does not isolate the effect of the assigned treatment in the absence of rescue.
Comparing only the mean scores among rescue users, 3 points versus 4 points, would answer a different question. Rescue use occurs after randomization, and the people who use it in one group need not be comparable to those who use it in the other. That subgroup comparison is not the overall treatment-policy contrast.
Specification and Estimation in Practice
Before data collection, a protocol should make the event and outcome strategy operational. For a discontinuation example, it should specify how the week-12 endpoint will be sought after participants stop assigned treatment. For a rescue-medication example, it should specify whether the endpoint will be measured after rescue use and under what follow-up schedule. If post-event outcomes are not collected, the intended treatment-policy estimand may still be defined, but the observed data alone do not supply the outcome values needed to calculate it.
In a randomized trial, the difference between observed arm means can estimate a continuous treatment-policy contrast when the endpoint is observed for all relevant participants and the analysis matches the specified population and summary. In a Bayesian analysis, the model and prior govern the uncertainty assigned to the target using the observed data; they do not redefine the target. The treatment-policy choice is part of the estimand, while the statistical model is part of the method used to learn about it.
Worked Example: A Binary Response After Discontinuation or Rescue
Suppose a hypothetical trial defines response at week 16 as a score improvement meeting a prespecified threshold. Response status is recorded for every randomized participant, including those who discontinued assigned treatment or used rescue medication. There are 20 participants per group. Twelve participants assigned active treatment respond, and 8 assigned control respond. These counts include participants with either event.
The estimated response risks are
On the risk-difference scale, active minus control, the estimated treatment-policy contrast is
In this hypothetical sample, the response risk is 20 percentage points higher under assignment to active treatment. The calculation uses all randomized participants with recorded response, irrespective of event status. If the protocol instead defined response using a different rule for participants who discontinued or used rescue, that would alter the endpoint definition or event strategy and would need to be stated explicitly.
Diagnostics, Alternatives, and Limitations
The main practical diagnostic is whether the outcome is actually observed at the planned time after the event. A treatment-policy strategy is not achieved merely by retaining a participant's name in an analysis dataset. If discontinuers are not followed, or rescue users have no endpoint assessment, their outcomes are missing. An intercurrent event and missing outcome data are distinct: the event is part of the clinical course; missingness describes the absence of an outcome measurement. The introductory material on intercurrent events and missing outcome data is relevant to keeping those concepts separate.
Review follow-up rates by randomized group and by event history, check whether endpoint timing and measurement remain comparable after the event, and document why any outcome is unavailable. Large or imbalanced amounts of missing follow-up can make the treatment-policy target poorly supported by observed data. Any model-based treatment of unavailable outcomes requires assumptions; the treatment-policy definition itself does not supply those missing values.
Treatment-policy, hypothetical, composite, and while-on-treatment strategies can target different clinical questions. A hypothetical strategy asks about an outcome under a specified scenario in which an event does not occur; a composite strategy incorporates the event into the endpoint; a while-on-treatment strategy focuses on outcomes while assigned treatment continues. These are alternatives, not interchangeable labels for the same contrast. The treatment-policy choice is useful when the question concerns assignment in the real trial setting, including event-related consequences, but may be uninformative if post-event outcomes are not clinically meaningful or cannot be measured.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions.
- A trial measures a continuous endpoint at week 24. What makes its strategy treatment-policy if participants may stop assigned treatment before week 24?
- In a hypothetical trial, each arm has 50 participants. There are 30 responses in the active group and 20 in control, including responses after rescue medication. Calculate the risk difference, active minus control, and interpret it.
- Why is comparing outcomes only among participants who discontinued treatment not generally the treatment-policy contrast?
- A participant uses rescue medication, but no week-12 endpoint is recorded. Is rescue use itself missing outcome data? What is missing?
- Name one design or follow-up feature that supports estimation of a treatment-policy estimand.
Solutions. (1) It is treatment-policy when the week-24 endpoint is used regardless of discontinuation, so outcomes after stopping assigned treatment remain part of the assigned-group summary. (2) The risks are \(30/50=0.60\) and \(20/50=0.40\); the risk difference is \(0.60-0.40=0.20\), or 20 percentage points higher under active assignment in this hypothetical sample. (3) Discontinuation occurs after randomization, and conditioning on it selects post-randomization subgroups that may differ between arms; their contrast is not the overall assigned-group contrast. (4) Rescue use is the intercurrent event. The week-12 endpoint is missing. (5) Continue to seek and measure the endpoint at the planned time after discontinuation or rescue use, with follow-up procedures specified in advance.