Why Dose-Response Questions Need an Estimand
A dose-response result is interpretable only when its clinical question is explicit. “The higher dose improved the endpoint” is incomplete if the target population, comparator, endpoint definition, assessment time, or handling of rescue treatment is unclear. Two analyses can use the same trial data and produce different answers because they target different questions, not because one calculation is necessarily wrong.
This matters across development phases. A Phase 2 trial may compare several doses over a short interval, while a Phase 3 trial may compare selected regimens over longer follow-up and allow additional care. A dose-response estimate from one phase informs another only to the extent that the intended population, treatment contrast, outcome, time point, and intercurrent-event strategy are understood and clinically relevant.
An intercurrent event is an event occurring after treatment starts that affects either the interpretation of an outcome or whether it can be observed. Examples include stopping assigned treatment, starting rescue medication, switching treatment, or receiving a prohibited concomitant therapy. An intercurrent event is not automatically the same as ordinary missing data: the event can change what outcome should count for the clinical question.
Specify Each Component Before Comparing Doses
The population describes whose treatment effect is targeted. It may be defined by disease characteristics, prior treatment, baseline severity, eligibility criteria, or another clinically meaningful set of characteristics. The target need not be identical to every trial participant, but an estimate for a narrower trial population should not be silently interpreted as the effect in a broader population.
The treatment contrast states which regimens are compared. A regimen includes the dose and any relevant schedule, route, background therapy, or titration rule. “High versus low dose” is not sufficient if multiple doses or schedules could fit those labels. The contrast can be a difference, ratio, or another summary of outcomes under the specified regimens.
The endpoint identifies the outcome variable and how it is summarized. For a continuous endpoint, specify the scale and direction; for a binary endpoint, specify the response definition and denominator. The time point is also essential: a mean difference at Week 8 is not necessarily the same clinical quantity as a mean difference at Week 24.
For each intercurrent event, specify the strategy that determines how outcomes after that event contribute to the estimand. Common strategies include:
- Treatment policy: use outcomes regardless of whether the event occurred. This targets the effect of assignment to the regimens in a setting where subsequent care can occur as observed.
- Hypothetical: target the outcome that would have been observed had the event not occurred, such as if rescue treatment had not been started. This requires assumptions and methods to infer an outcome that is not directly observed after the event.
- Composite: incorporate the event into the endpoint itself, for example defining rescue treatment before the assessment as treatment failure.
- While-on-treatment: use outcomes up to the event and define the target around the period before it. The resulting quantity concerns outcomes while on treatment, not necessarily the outcome at a common later time.
- Principal stratum: target a group defined by the intercurrent-event status that would occur under specified treatment conditions. This can be clinically useful, but membership is generally not directly observable for each participant under both regimens.
Different events may require different strategies. For instance, a treatment-policy strategy for discontinuation does not determine how rescue medication is handled. Specify the event and its strategy together, rather than assigning one vague label to all post-randomization events.
Worked Example: A Treatment-Policy Contrast for a Continuous Endpoint
Suppose a hypothetical Phase 2 trial randomizes adults with moderate disease to 10 mg or 30 mg once daily. The endpoint is change from baseline in a symptom score at Week 12; a more negative change indicates greater improvement. Rescue medication is permitted. The target population is the randomized population meeting the stated disease and eligibility criteria, and the rescue-medication strategy is treatment policy: Week 12 outcomes count regardless of rescue use.
Assume Week 12 scores are collected for every participant, including those who used rescue medication. For illustration, the mean changes are \(-3.2\) points among \(n=80\) participants assigned 10 mg and \(-5.0\) points among \(n=82\) assigned 30 mg. Define the contrast as the mean change with 30 mg minus the mean change with 10 mg:
The estimated contrast is a 1.8-point greater mean reduction at Week 12 for assignment to 30 mg rather than 10 mg, under the treatment-policy strategy for rescue medication. It is not an estimate of the effect that would have occurred if nobody had used rescue medication. A confidence interval and its uncertainty would also be needed to assess how precisely this hypothetical trial estimated the contrast.
The interpretation depends on the stated endpoint direction and comparator order. Reversing the subtraction would yield \(+1.8\) points, representing the same difference with the opposite sign. The strategy is justified here only if the clinical question concerns assignment to the dose regimens with rescue available and the outcomes can be meaningfully interpreted after rescue.
Deriving Why the Components Change the Answer
An estimand can be represented as a contrast between population-level summaries of outcomes under specified regimens and event strategies. Let \(Y^{a,s}(t)\) denote the outcome at time \(t\) in the target population under regimen \(a\), interpreted according to the specified strategy \(s\). For a continuous endpoint, one possible estimand is the difference in population means:
The notation is only a compact statement of the question: \(a_1\) and \(a_0\) are the two regimens, \(t\) is the assessment time, and \(s\) specifies how the relevant intercurrent event is handled. The target population is implicit in the expectations and must still be stated in words.
The difference between treatment-policy and hypothetical strategies can be seen by separating outcomes according to rescue use. Let \(R^a\) indicate whether rescue would be used under regimen \(a\). Under treatment policy, outcomes after rescue remain part of the regimen-specific outcome distribution. Under a hypothetical no-rescue strategy, the target instead concerns outcomes under the condition that rescue does not occur. Unless rescue has no effect on the endpoint, or the two strategies happen to produce the same outcome distribution, these targets need not be equal. Therefore, changing the event strategy changes the target quantity rather than merely changing a technical detail of the analysis.
This also explains why the estimator must follow the estimand. If post-rescue outcomes are included, excluding those participants would generally discard outcomes that belong to a treatment-policy target. If the target is hypothetical, simply analyzing observed outcomes before rescue does not generally recover the hypothetical Week 12 contrast: the people who receive rescue may differ in prognosis from those who do not. Additional assumptions and a suitable estimation method are required.
Worked Example: A Composite Endpoint for Rescue Use
Consider a hypothetical Phase 3 comparison of 20 mg and 40 mg at Week 24. The endpoint is a binary response, defined as at least a 30% improvement from baseline. The estimand uses a composite strategy for rescue: any participant who starts rescue treatment before Week 24 is classified as a nonresponder, whether or not the Week 24 score meets the improvement threshold.
Suppose 54 of 100 participants assigned 20 mg and 63 of 100 assigned 40 mg meet the composite response definition. The response proportions are \(54/100=0.54\) and \(63/100=0.63\). Define the risk difference as the response proportion with 40 mg minus that with 20 mg:
The estimated difference is 9 percentage points in favor of 40 mg for the probability of being a Week 24 responder without prior rescue, according to this composite definition. It is not the difference in response among participants who avoided rescue, because the analysis keeps all randomized participants in the denominator and counts rescue as failure.
The composite strategy is defensible when rescue before Week 24 is itself considered a clinically relevant failure. It would be misleading if rescue were routine and not evidence of inadequate response, or if the decision to rescue differed substantially between treatment groups for reasons unrelated to response. The endpoint definition and the clinical meaning of rescue must support the chosen composite.
Phase 2 and Phase 3: Maintain Meaning, Not Just Labels
A useful development plan distinguishes an estimand that is intentionally carried forward from one that changes for a stated clinical reason. For example, Phase 2 may target mean symptom-score change at Week 12 under treatment policy for discontinuation, while Phase 3 targets Week 24 response with rescue counted as failure. Both can be informative, but they answer different questions. A difference in results cannot be attributed to dose alone without considering the change in endpoint, time, and event strategy.
When the intended question is comparable across phases, define the components in compatible terms. This does not require identical trial designs or identical populations. It does require stating any population differences and explaining whether the Phase 2 result is intended to inform the Phase 3 target. A Phase 2 estimate in a selected population is not automatically the Phase 3 estimate for a broader population.
The treatment contrast should also be explicit across phases. A 30 mg versus placebo contrast in Phase 2 does not directly equal a 30 mg versus 10 mg contrast in Phase 3. Likewise, a titration regimen reaching 30 mg is not necessarily the same treatment condition as starting at 30 mg. Clear regimen descriptions prevent dose labels from concealing clinically meaningful differences.
Worked Example: A Hypothetical No-Rescue Estimand
Suppose a hypothetical Phase 2 trial compares 15 mg and 30 mg at Week 16. Rescue medication is sometimes started before Week 16, and the target is the mean symptom-score change that would occur if rescue were not started. This is a hypothetical strategy, not a treatment-policy strategy.
Assume a prespecified model uses baseline severity and symptom measurements collected before rescue to predict Week 16 outcomes under no rescue. In this hypothetical illustration, the model-based estimated means are \(-4.1\) points for 15 mg and \(-5.6\) points for 30 mg. The estimand contrast is:
Under the stated hypothetical strategy, the estimated 30 mg regimen produces a 1.5-point greater mean reduction than 15 mg at Week 16 if rescue had not occurred. This is not a direct comparison of observed Week 16 means among only those who avoided rescue. That subgroup is selected after randomization and may have a different prognosis.
The estimate relies on assumptions: the model must adequately relate measured history to Week 16 outcomes; relevant predictors of rescue and outcome must be captured; there must be sufficient information to estimate outcomes for participants with the histories observed before rescue; and the model must be appropriate for the target population. These assumptions cannot be verified merely by computing the difference. Diagnostics should examine model fit, prediction performance where outcomes are observed, patterns of rescue by treatment and baseline characteristics, and sensitivity to plausible alternative assumptions. If key predictors are unmeasured or no comparable participants remain for some histories, the hypothetical contrast may be weakly identified.
Diagnostics, Alternatives, and Common Pitfalls
Before interpreting a dose-response estimate, check that the data and analysis correspond to every component of the estimand. Confirm the dose regimen and comparator; verify endpoint coding, units, direction, and assessment window; and report how many participants experienced each intercurrent event by treatment group. For treatment-policy targets, check whether outcomes after the event were collected and included as intended. For hypothetical targets, examine the prediction or censoring models and assess how conclusions change under plausible alternative assumptions.
The strategies are alternatives because they answer different clinical questions, not interchangeable methods for producing a preferred result. A treatment-policy estimand asks about outcomes under assigned regimens with post-randomization care occurring as it does in the trial. A hypothetical estimand asks what would have happened under a specified condition that did not occur for everyone. A composite estimand treats the event as part of the endpoint. A while-on-treatment estimand focuses on an interval ending at the event. Choosing among them requires clinical justification, not selecting whichever gives the largest apparent dose effect.
Important limitations remain even when the estimand is carefully specified. An estimand does not guarantee that the target is identifiable from the observed data, that assumptions are met, or that the estimate is precise. Nor does a well-defined treatment contrast establish that a result applies to patients outside the target population. The estimand clarifies the question; design, data quality, analysis, and uncertainty determine how credibly it can be answered.
- Pitfall: treating “on treatment” as a neutral default. Excluding outcomes after discontinuation can change the target and select participants who tolerate or respond to treatment. State the intended strategy and assess whether the data support it.
- Pitfall: calling a hypothetical result “the observed treatment effect.” A no-rescue outcome is not observed after rescue has occurred. Label it as hypothetical, state the assumptions and method, and avoid presenting it as a directly measured contrast.
- Pitfall: comparing estimates with different endpoints or times as if they were the same quantity. A Week 12 mean change and a Week 24 response proportion have different scales and clinical meanings. Describe the distinction before drawing conclusions across phases.
Check Your Understanding
For each question, first identify the relevant estimand component. Solutions follow each prompt.
- A trial reports a mean difference at Week 12 but does not say how rescue medication is handled. What is missing, and why does it matter?
- In a treatment-policy estimand, should a participant’s Week 24 outcome after discontinuing assigned treatment be included if it is observed? Explain.
- A hypothetical no-rescue analysis predicts Week 16 outcomes for participants who started rescue at Week 8. Name one assumption needed to interpret its estimate.
- Phase 2 compares 10 mg with placebo on Week 8 mean change, while Phase 3 compares 10 mg with 30 mg on Week 24 response. Are the numerical dose effects directly interchangeable? Why or why not?
- In a composite endpoint, rescue before the assessment is defined as nonresponse. What does the resulting response proportion describe?
Solutions. (1) The intercurrent-event strategy for rescue is missing. Including outcomes after rescue, predicting outcomes without rescue, or counting rescue as failure targets different quantities. (2) Yes. Treatment policy includes outcomes regardless of discontinuation, provided the outcome is observed and defined after discontinuation. (3) For example, measured participant history must adequately capture information needed to predict the no-rescue outcome; the model and assumptions must support extrapolation to those who received rescue. (4) No. The comparator, endpoint, and time point differ, so the contrasts have different meanings and scales. (5) It describes the probability of meeting the response definition by the assessment time without having started rescue before then, under the specified regimen and target population.