Why Put an Estimand in a Table?
A clinical protocol may say that a treatment should “improve symptoms at 12 weeks,” while leaving important questions unresolved. Which patients define the target? Does the question concern assignment to treatment or treatment received? What counts as the symptom outcome, and what happens to the treatment-effect question if a patient discontinues, starts rescue medication, or dies? Different answers can define different estimands, even when they arise from the same trial.
An estimand specification table is a compact way to record the choices that define the treatment-effect question. It is not an analysis-results table and does not, by itself, identify an estimand from observed data. Its purpose is to make the question explicit: readers can see the target population, treatment conditions, outcome variable, handling strategy for each relevant intercurrent event, and population-level summary in one place.
These components answer related but distinct questions. The population says for whom the effect is defined; the treatment conditions say what is compared; the variable specifies what outcome is summarized and when; event strategies say how specified post-baseline events enter the question; and the summary says how outcomes are aggregated and contrasted. This structure builds on the earlier material on translating protocol language into estimands.
What Each Row and Column Should Make Clear
A practical table has one column for each estimand component and a row for each estimand under consideration. If the clinical question includes several intercurrent events, list each event and its strategy explicitly, either in the same cell or in separate event-and-strategy rows. A vague entry such as “use all available data” does not say what treatment effect is being defined.
| Component | What to record | Useful level of detail |
|---|---|---|
| Population | The patients to whom the treatment effect pertains | Eligibility characteristics and the target trial population, not just “patients” |
| Treatment conditions | The interventions or treatment conditions being compared | Include assignment, dose, background care, or other features needed to distinguish conditions |
| Variable | The outcome definition and assessment occasion | Scale, direction, time point, and any rule for deriving the outcome |
| Intercurrent events and strategies | Each relevant event and how it enters the estimand | Name the event and state the strategy for that event specifically |
| Population-level summary | How the outcome distribution is summarized and compared | For example, a difference in mean change or a difference in response probabilities |
The event strategy is not a generic property of the trial; it is a choice made for a particular event within a particular estimand. For example, a treatment-policy strategy asks about outcomes regardless of whether rescue medication is started, whereas a hypothetical strategy defines the outcome that would be expected under a specified scenario in which an event did not occur. A composite strategy can incorporate an event into the outcome itself, and a while-on-treatment strategy focuses on outcomes up to a defined event or discontinuation. A principal-stratum strategy defines the target through a subgroup characterized by potential event status under treatment conditions. These strategies answer different questions; the table should not leave the intended one to be inferred.
Missing outcome data require separate attention. A missed week-12 assessment is not automatically an intercurrent event: it is an absence of an observed value for the variable at the planned assessment. By contrast, treatment discontinuation or initiation of rescue therapy may be an intercurrent event because it changes the clinical course relevant to the treatment question. A table should specify event strategies without implying that a strategy alone solves the missing-data problem.
Worked Example: Symptom Change With Rescue Medication
Suppose a hypothetical randomized trial compares a new symptom-relief drug with placebo in adults with moderate chronic pain. The intended question concerns the effect of assignment to either treatment over 12 weeks, including outcomes after patients start rescue medication or stop assigned treatment. Construct the table row, stating the choices rather than assuming them.
| Population | Treatment conditions | Variable | Intercurrent events and strategies | Population-level summary |
|---|---|---|---|---|
| Adults meeting the trial’s moderate chronic pain eligibility criteria and randomized in the trial | Assignment to the new drug regimen versus assignment to placebo, with the protocol’s usual background care | Change from baseline to week 12 in the prespecified pain score; lower scores indicate less pain | Starting rescue medication: treatment-policy strategy. Discontinuing assigned treatment: treatment-policy strategy. | Difference between treatment conditions in mean week-12 change from baseline, new drug minus placebo |
The table’s entries fit together. The specified variable is measured at week 12, so outcomes after rescue medication or discontinuation must still correspond to the week-12 pain score for this treatment-policy question. “Treatment-policy” does not mean that the event is ignored in data collection; it means the question concerns outcomes regardless of its occurrence. If week-12 scores are missing for some participants, the table still defines the target outcome, but additional assumptions and methods are needed to handle those unobserved values.
The summary’s direction is also explicit. If the mean change is −3 points under the new drug and −1 point under placebo, then the estimated contrast is \( -3 - (-1) = -2 \) points. A negative contrast favors the new drug because lower pain scores indicate improvement. This arithmetic illustrates the contrast implied by the table; it does not establish that the estimate is unbiased or that the estimand is identified from the available data.
Deriving the Contrast From the Table
Once the table states a variable, event strategy, and treatment conditions, the population-level summary can be written in terms of potential outcomes. Let \(Y^{a,s}\) denote the outcome under treatment condition \(a\), interpreted according to the stated strategy \(s\) for relevant intercurrent events. For a mean-difference estimand in a target population, the contrast for conditions \(a=1\) and \(a=0\) is:
This expression follows directly from the table’s choices. The variable determines what \(Y\) represents; the population determines the expectation; the treatment conditions set \(a=1\) and \(a=0\); and the event strategy determines the interpretation of \(Y^{a,s}\). If any of these choices changes, the potential outcomes being averaged—or the population over which they are averaged—may change, and so may \(\Delta\). A table is therefore more than a formatting convenience: it shows the ingredients needed to state the target contrast unambiguously.
The notation does not claim that every potential outcome is observed or that the contrast is automatically identifiable. Those are separate questions about the trial, assumptions, and data. In particular, a fully specified estimand can still be difficult to estimate if outcomes are missing or the assumptions required for an event strategy are unsupported.
Worked Example: A Hypothetical Treatment Strategy
Consider a hypothetical randomized trial of a maintenance treatment for a chronic condition. The clinical question is the mean symptom score at week 24 that would be seen if participants did not discontinue assigned treatment before that time. Participants who start rescue therapy remain under follow-up, and the question is about outcomes regardless of rescue therapy. Specify the table and explain the meaning of its event choices.
| Population | Treatment conditions | Variable | Intercurrent events and strategies | Population-level summary |
|---|---|---|---|---|
| Eligible adults randomized in the hypothetical maintenance-treatment trial | Assignment to maintenance treatment versus assignment to control, each with protocol-specified background care | Symptom score at week 24, with lower scores indicating fewer symptoms | Discontinuing assigned treatment: hypothetical strategy, defining the outcome under the specified scenario of no discontinuation. Starting rescue therapy: treatment-policy strategy. | Difference in mean week-24 symptom score under the two treatment conditions, treatment minus control |
The row has two event entries because discontinuation and rescue therapy are not being handled identically. The hypothetical strategy defines a scenario in which assigned treatment is not discontinued; it does not mean that the trial physically prevents discontinuation. The treatment-policy strategy for rescue therapy retains outcomes after rescue therapy begins. If the mean score under treatment for the stated estimand were hypothetically 8.2 points and the mean under control were 10.0 points, the contrast would be \(8.2-10.0=-1.8\) points. In this score, the negative contrast indicates a lower average symptom burden under treatment.
The example also shows why the event strategy must be recorded alongside the variable and summary. A week-24 outcome under the hypothetical no-discontinuation scenario is not simply the observed score among participants who happened not to discontinue. The latter is a selected group, and its observed mean does not by itself equal the mean defined by the hypothetical strategy.
Making Event Choices Visible
A table should be specific enough that another analyst could restate the clinical question without filling in unstated choices. In particular, name each intercurrent event in clinically meaningful terms, then record the strategy applied to it. If an event has more than one possible definition—such as discontinuation for lack of efficacy versus discontinuation for an unrelated reason—state the event definition or make clear that the strategy applies to all discontinuations.
Likewise, “change in outcome” is usually insufficient as a variable entry. Specify the outcome measure, the baseline reference if change is used, the assessment time, and the direction of better outcomes where relevant. For a binary response, state the response criterion and time point. The table need not reproduce every operational detail in the protocol, but it should point to definitions that make the outcome reproducible.
Worked Example: Response With Death Included in the Outcome
Suppose a hypothetical trial compares two treatments for a serious condition. The clinical team wants a week-24 binary outcome that counts a participant as a responder only if the participant is alive and meets a prespecified symptom-improvement threshold. Death before week 24 is therefore incorporated into the outcome as nonresponse. The table entry is:
| Population | Treatment conditions | Variable | Intercurrent events and strategies | Population-level summary |
|---|---|---|---|---|
| Eligible adults randomized in the trial | Assignment to treatment A versus assignment to treatment B, with the same protocol-defined background care | Week-24 response: alive at week 24 and meets the prespecified symptom-improvement threshold | Death before week 24: composite strategy, with death classified as nonresponse. Treatment discontinuation: treatment-policy strategy, with response assessed at week 24 regardless of discontinuation where the outcome is available. | Difference in week-24 response probabilities, treatment A minus treatment B |
For illustration, suppose 54 of 120 participants assigned to treatment A and 42 of 120 assigned to treatment B meet this defined response outcome. The estimated response proportions are \( \hat{p}_A=54/120=0.450 \) and \( \hat{p}_B=42/120=0.350 \). The estimated risk difference is \(0.450-0.350=0.100\), or 10.0 percentage points in favor of treatment A for this outcome definition.
Death is not being treated as a missing week-24 symptom score in this table; it is explicitly part of the outcome definition. However, if a participant is alive but has no observed symptom assessment, the response status may still be unavailable unless the protocol has an outcome rule that determines it. The composite strategy for death does not automatically resolve missing assessments among living participants.
How to Use and Review the Table
A useful construction process begins with the clinical question, not with a preferred statistical model. Write down who the question concerns and the treatment conditions, define the outcome and assessment time, enumerate relevant intercurrent events, assign a strategy to each, and then state the population-level summary in a directionally interpretable form. Finally, read across the row: each entry should contribute to the same clinical question.
Name the population and the two treatment conditions precisely enough to distinguish the question from other possible trial questions.
Record the measure, time point, derivation rule, and direction of better outcomes where relevant.
For every relevant intercurrent event, state the event and the strategy chosen for that event. Do not treat missingness as though a strategy name alone determines its solution.
Specify the population-level quantity and the order of subtraction or other comparison, then verify that its sign has a clear interpretation in context.
Ask what outcomes the question requires after events and at the stated assessment time. This reveals data-collection and estimation needs without changing the estimand after seeing the data.
The table also helps distinguish the estimand from nearby alternatives. A protocol narrative describes the trial’s rationale and conduct, but may leave the treatment-effect question implicit. An analysis plan describes an estimator or model, which may or may not align with the intended estimand. A results table reports estimates and uncertainty. None of these substitutes for explicitly defining the target contrast. Conversely, completing an estimand table does not select a model, prove identification, or guarantee that the necessary outcomes were collected.
Common Pitfalls and Limitations
- Using “intention-to-treat” as the entire estimand. This label alone does not specify the outcome, event strategies, time point, or population-level summary. State those components directly.
- Giving one strategy for all events without checking the question. Rescue therapy, treatment discontinuation, and death can have different clinical meanings and may require different strategies within one estimand.
- Confusing an event strategy with a missing-data method. A treatment-policy strategy defines the question about outcomes regardless of an event; it does not supply an unobserved outcome when follow-up is missing.
- Leaving the summary scale or direction unclear. A “treatment difference” is incomplete unless the table says which summary is contrasted and in which order. State units or, for probabilities, whether the contrast is in percentage points.
- Assuming a complete table settles estimation. The table defines the target. Estimation still depends on the data, design, and assumptions needed to connect observed information to that target.
The central limitation is deliberate: an estimand table makes choices transparent; it does not establish that those choices are clinically appropriate or that the target can be recovered from the observed data. That separation is useful. It prevents an analysis method from silently defining the question and makes later evaluation of assumptions more focused.
Check Your Understanding
For each item, identify or revise the relevant table component. Solutions follow the questions.
- A protocol says “compare average function at six months.” Name two details needed to make the variable entry more precise.
- Participants may start rescue therapy. The scientific question concerns outcomes regardless of rescue therapy. Which strategy belongs in the table, and what does it mean?
- Explain why “missing week-12 score” and “discontinued assigned treatment” should not automatically be entered as the same kind of event.
- In a binary-outcome trial, 36 of 90 participants in one arm and 27 of 90 in the other meet the defined response criterion. Calculate the estimated risk difference in the order first arm minus second arm.
- What does a completed estimand specification table establish, and what does it not establish?
Solutions. (1) State the function measure and exactly how it is assessed or derived; also specify the six-month time point precisely, such as the scheduled visit or a defined day window. If the outcome is a change score, name the baseline reference. (2) Use a treatment-policy strategy for rescue therapy: the target concerns outcomes regardless of whether rescue therapy is initiated, so post-rescue outcomes remain relevant to the question. (3) Discontinuation is a possible intercurrent event that may alter how the treatment effect is defined. A missing score is an unobserved value of the outcome and needs a missing-data approach; it is not, by itself, an event strategy. (4) The proportions are \(36/90=0.400\) and \(27/90=0.300\), so the estimated risk difference is \(0.400-0.300=0.100\), or 10.0 percentage points. (5) The table states the treatment-effect question through its population, conditions, variable, event strategies, and summary. It does not prove that the estimand is identifiable, that assumptions are satisfied, or that a particular estimator is valid.