Why Nonadherence Needs an Explicit Estimand
Participants may reduce a dose because of tolerability, interrupt treatment temporarily, miss doses, or take less than prescribed. These events can affect the outcome and may be related to a participant’s health. The central question is not simply whether to keep or discard measurements collected after a dose change. It is which clinical question should the treatment comparison answer? The answer determines whether post-event outcomes are part of the outcome being compared, are replaced by a counterfactual outcome under a different treatment condition, or are excluded by a specifically defined outcome summary.
A dose modification is not automatically an intercurrent event. First specify the intervention: for example, whether protocol-permitted reductions are part of the assigned treatment regimen. A permitted adjustment may be part of the treatment condition itself. A reduction that departs from the defined regimen may instead be an intercurrent event. The protocol should give an operational definition, including the event threshold, start time, duration, and handling of temporary interruptions.
For a treatment-policy question, write \(Y^a\) for the outcome that would occur under assignment \(a\), with adherence and dose changes following their natural course under that assignment. The outcome includes measurements after the event. For a hypothetical question, \(Y^{a,\mathrm{maintain}}\) denotes the outcome under assignment \(a\) in a hypothetical setting where the specified adherence event does not occur. These are different potential outcomes and generally represent different questions.
Retaining Outcomes: The Treatment-Policy Strategy
A treatment-policy estimand asks about the effect of assignment to the treatment strategies as they are implemented, including the dose changes and interruptions that occur after randomization. If larger \(Y\) is better, one possible contrast is the difference in population means:
Here, a participant’s outcome after reducing or interrupting assigned treatment remains part of the outcome under that assignment. The treatment-policy question may be relevant when the decision concerns offering the treatment strategy in practice, where some participants will not maintain the intended dose. It does not isolate the biological effect of continuous full-dose exposure.
Worked Example: Retaining Outcomes After Dose Changes
Hypothetical data. In a small randomized trial, the endpoint is a symptom score at week 12, measured in points, with lower scores indicating fewer symptoms. Three of six participants assigned to the experimental regimen reduced or interrupted their dose. Their week-12 scores were still collected. The six scores in the experimental arm are 8, 10, 7, 12, 9, and 6 points; the six control scores are 5, 6, 8, 7, 4, and 6 points.
For a treatment-policy comparison, use all week-12 scores in their randomized groups. The experimental-arm mean is \((8+10+7+12+9+6)/6=52/6=8.667\) points. The control-arm mean is \((5+6+8+7+4+6)/6=36/6=6.000\) points. Thus the estimated contrast, experimental minus control, is \(8.667-6.000=2.667\) points.
The result describes the difference in mean week-12 scores under assignment to the two treatment strategies, including the dose changes that occurred. It is not an estimate of the effect among participants who maintained their full dose. The calculation assumes the week-12 outcomes are observed for all 12 participants; if some are missing, the estimand remains the same, but this simple calculation no longer estimates it directly without further assumptions or methods.
Randomization gives a simple justification for the treatment-policy contrast when outcomes are completely observed. Under random assignment, consistency, and no interference, \(E(Y\mid A=a)=E(Y^a\mid A=a)\). Randomization makes \(A\) independent of the potential outcome \(Y^a\), so \(E(Y^a\mid A=a)=E(Y^a)\). Therefore:
This argument does not require participants to adhere perfectly: their post-randomization dose changes are part of the outcome process under assignment. It does require the observed outcome to correspond to the defined endpoint and, for the direct equality above, to be observed for everyone. Randomization alone does not make incomplete outcomes harmless.
Changing the Treatment Condition: Hypothetical Estimands
A hypothetical strategy asks what the outcome contrast would be if the specified event did not occur. For example, it may target the mean difference under sustained use of the assigned full dose:
The word “maintain” must be made precise. It could mean no dose reduction, no interruption, or adherence above a stated threshold. The hypothetical treatment condition should also specify what happens to participants for whom maintaining the regimen would not be feasible. This estimand does not retain their actual post-event outcomes as the outcomes of interest; it targets outcomes under a counterfactual treatment condition.
Worked Example: Defining a Sustained-Dose Question
Hypothetical illustration. Suppose a trial’s week-12 symptom score is measured in points, with lower scores better. The clinical question is the mean difference if all participants in each arm had remained on their assigned starting dose through week 12. This defines a hypothetical estimand, not a treatment-policy estimand. Assume a prespecified analysis has produced hypothetical mean scores of 9.4 points under sustained experimental treatment and 7.1 points under sustained control treatment.
The target contrast is \(9.4-7.1=2.3\) points, experimental minus control. Under the stated hypothetical conditions, the experimental regimen has a 2.3-point higher mean symptom score. The arithmetic is straightforward; the substantive difficulty is that these means concern outcomes under sustained doses, which are not necessarily the outcomes observed after actual dose changes.
These hypothetical means are stipulated model-based results for illustration, not values that can be obtained by simply averaging the observed outcomes of adherent participants. To support such an analysis, the assumptions and method must make the unobserved counterfactual outcomes credible. For instance, the analysis must address whether measured history adequately accounts for why participants changed dose and whether there are comparable participants who continued treatment at relevant histories. If those conditions are implausible, the hypothetical contrast may not be reliably identified from the trial data.
The distinction matters: a treatment-policy estimand describes outcomes under the actual pattern of adherence after assignment, whereas a hypothetical estimand changes the treatment condition by imagining that a specified event did not occur. The latter can be clinically useful, but its interpretation depends on a counterfactual scenario and assumptions beyond randomization.
Excluding Post-Event Measurements: Define the Outcome First
A while-on-treatment strategy can be appropriate when the question concerns outcomes while participants receive the assigned treatment. It must define an outcome summary that ends at, or is otherwise restricted to, the time the participant stops receiving that treatment. For example, a study might define each participant’s outcome as the average of scheduled symptom scores collected while receiving the assigned regimen through week 12. The treatment contrast then compares the population summaries so defined.
That definition is not equivalent to deleting post-event records from an analysis while leaving the original week-12 outcome unchanged. If the target remains the week-12 score, excluding a score because it was measured after a dose reduction does not turn the missing week-12 value into a while-on-treatment outcome. It may instead produce a selected comparison of participants with available pre-event measurements. The event timing and the rule for constructing the outcome must be explicit, including what happens if a participant has no eligible measurement.
Worked Example: A Defined While-on-Treatment Summary
Hypothetical data. Scores are measured at weeks 4, 8, and 12, in points, with lower scores better. Define each participant’s outcome \(Q\) as the arithmetic mean of their scheduled scores obtained while receiving the assigned regimen, through week 12. This example assumes every participant has at least one eligible score. A score after the participant stops the assigned regimen is not included in \(Q\).
In the experimental arm, participant 1 has eligible scores 4 and 6, then interrupts treatment before week 12, giving \(Q_1=(4+6)/2=5\). Participant 2 has scores 5, 7, and 8 while on treatment, giving \(Q_2=20/3=6.667\). Participant 3 has scores 6 and 8 before stopping treatment, giving \(Q_3=14/2=7\). The experimental mean is \((5+6.667+7)/3=6.222\) points, using the unrounded mean \(20/3\) in the calculation.
In the control arm, suppose the corresponding participant summaries are 6, 7, and 8 points. Their mean is \((6+7+8)/3=7.000\) points. The contrast is \(6.222-7.000=-0.778\) points. For this defined summary, the experimental arm has a 0.778-point lower mean score while participants receive their assigned regimen.
This result is not a week-12 treatment-policy contrast or an effect of maintaining full dose. The summaries may average different numbers of visits and cover different treatment durations. Those features are part of this particular outcome definition, so they must be judged clinically. If the intended question instead concerns a common fixed-time endpoint, this construction does not answer it.
Compare Strategies and Check the Definition
| Strategy | Outcome after nonadherence | Question represented | Important caution |
|---|---|---|---|
| Treatment policy | Retained in the outcome under randomized assignment | What is the effect of assignment when adherence changes naturally? | Does not isolate sustained-dose efficacy. |
| Hypothetical | Replaced by the outcome under a specified no-event condition | What would the contrast be if the specified event did not occur? | Counterfactual outcomes require assumptions and an appropriate analysis. |
| While on treatment | Excluded from a specifically defined summary once outside the treatment condition | What is the contrast for the defined outcome while treatment is received? | Different follow-up durations or visit counts can affect the summary. |
| Composite | The event is incorporated into the outcome, such as by assigning an event category or score | What is the effect on a combined outcome that includes both clinical status and the event? | The event’s ordering or assigned score needs clinical justification. |
A composite strategy is another option when the dose event itself is important to the clinical question. It does not simply discard post-event outcomes: the event becomes part of the defined outcome, possibly alongside the clinical measure. The construction and interpretation of a composite must be stated; an arbitrary penalty for dose reduction can change the clinical meaning of the result.
Before interpreting an analysis, check that the operational event definition matches the assigned treatment conditions, that the outcome and its time horizon are specified, and that the chosen strategy answers the intended clinical question. A useful diagnostic is to tabulate reductions and interruptions by arm, timing, reason, and severity, then show how many outcome measurements fall before and after each event. Large differences in event frequency or timing can make strategies answer markedly different questions. Also investigate whether participants without eligible measurements are concentrated among those with early events. Such checks can reveal a mismatch between the estimand and the analysis, but they do not establish that the assumptions for a hypothetical or restricted-outcome analysis hold.
Common mistake: “We want the effect of full-dose treatment, so we will remove everyone who reduced their dose and compare the remaining participants.” This is not, by itself, a valid hypothetical comparison. Adherence is determined after randomization and may be related to prognosis; restricting to adherent participants can therefore destroy the comparability provided by randomization. The correction is to define the target explicitly—treatment policy, hypothetical, while-on-treatment, or another strategy—and use an analysis aligned with that target. In particular, deleting post-event observations is a data-handling choice, not a complete estimand definition.
Check Your Understanding
Answer each question, then compare with the brief solutions.
- A trial asks about the effect of assignment when participants may reduce their doses, and it collects the endpoint after a reduction. Which strategy retains those outcomes, and what does its contrast mean?
- Explain why the mean among participants who maintained full dose does not automatically estimate a hypothetical sustained-dose effect.
- A researcher removes all post-interruption scores but continues to describe the endpoint as the week-12 score. What needs to be clarified or changed?
- A protocol allows a lower dose after a specified safety trigger. Why must the intervention definition be checked before labeling every lower-dose period as nonadherence?
Solutions. (1) The treatment-policy strategy retains the measured post-reduction outcomes and compares outcomes under randomized assignment with adherence evolving naturally. (2) Full-dose adherence occurs after randomization and may depend on participants’ health or prognosis, so adherers need not remain comparable across arms; the hypothetical effect concerns counterfactual outcomes under sustained doses. (3) The estimand must say whether it targets a defined while-on-treatment summary or the fixed week-12 outcome. Excluding post-event scores alone does not define a replacement outcome or establish a valid analysis. (4) If the lower dose is part of the assigned regimen under the protocol, it is not a departure from that regimen; the event definition must distinguish permitted dose adjustment from the nonadherence event of interest.