Why Estimand Alignment Comes First
A treatment-effect estimate is meaningful only in relation to the question it answers. Two regional trials may use the same drug and report a number called a “treatment effect,” yet that number could refer to different patient groups, outcome measurements, follow-up times, or approaches to events such as rescue medication. Comparing the numbers before clarifying these features can produce an apparently precise answer to the wrong question.
In a bridging analysis, the source trial provides information intended to support a decision in a target region or population. Defining the source and target is not enough: the treatment-effect questions in the evidence being bridged must also be compared. Alignment does not guarantee that a result can be transported, but material misalignment can show that a direct comparison is not justified.
An intercurrent event is an event occurring after treatment initiation that affects either the interpretation or existence of the outcome. Examples include treatment discontinuation, use of rescue medication, switching therapy, or death before an outcome can be measured. The question is not simply whether such events occurred, but what treatment effect is intended in light of them.
The Attributes to Compare
For each trial, write the estimand in words before comparing its reported result with another trial. Record the details that determine what the contrast means, not just the label in a protocol or publication.
- Population: Who is the target group for the effect? Specify clinically relevant eligibility features and whether the question concerns all randomized participants, a subgroup, or another defined group.
- Treatment conditions: Which interventions are compared? Include dose, regimen, duration, comparator, and relevant background care. “Drug versus control” may conceal differences between placebo and active standard care.
- Outcome and assessment time: What variable is measured, in what units, by what instrument or definition, and at what time? For a change-from-baseline endpoint, specify the baseline and follow-up measurements.
- Intercurrent-event strategy: How does the estimand handle each event that matters? Common strategies include treatment policy (use outcomes regardless of the event), hypothetical (consider outcomes under a specified scenario in which it did not occur), composite (incorporate the event into the outcome), while-on-treatment (focus on outcomes before the event), and principal stratum (focus on a defined subgroup characterized by potential event status).
- Summary measure: How are outcomes summarized and contrasted across the population? Examples include a mean difference, risk difference, risk ratio, odds ratio, or a time-to-event contrast.
The same event can be handled differently for different estimands. Under a treatment-policy strategy, outcomes after rescue medication remain part of the outcome being summarized. Under a hypothetical strategy, the question concerns outcomes that would have been observed under a specified no-rescue scenario. The latter generally requires assumptions or a model because outcomes under that unobserved scenario are not directly recorded for participants who received rescue.
Worked Example: Endpoint and Assessment-Time Mismatch
Consider two hypothetical randomized trials of the same treatment for symptom severity, where lower scores indicate fewer symptoms. In the source trial, the outcome is change from baseline at week 12. Mean scores are 12 at baseline and 4 at week 12 for treatment, and 11 at baseline and 6 at week 12 for control. In the target-region trial, the reported outcome is the absolute score at week 16: 14 for treatment and 16 for control. Assume the means are calculated for the same randomized population within each trial, the endpoint is measured for all participants, and both trials use the same score instrument.
For the source trial, change is follow-up minus baseline:
The estimated treatment contrast in mean change is therefore:
For the target trial, the reported contrast in absolute week-16 scores is \(14-16=-2\) score points. These values are not direct estimates of the same estimand: one is a week-12 contrast in change and the other is a week-16 contrast in absolute score. In the target trial, its baseline means are 20 for treatment and 21 for control, so its contrast in change would be \((14-20)-(16-21)=-6-(-5)=-1\) score point. That still differs from the source trial’s week-12 change contrast, and it is measured at a different follow-up time. The shared instrument and treatment name do not establish endpoint alignment.
A valid comparison would require a clearly defined common outcome and assessment time, plus data and an analysis that support that definition. The summary statistics given here do not justify converting a week-12 effect into a week-16 effect.
When Differences Change the Treatment Question
Not every difference in trial conduct changes the estimand. A different analysis method can sometimes estimate the same estimand, while identical methods can estimate different estimands if the outcome or event strategy differs. The key test is whether the difference changes the population-level treatment effect being asked for.
Population differences matter when the treatment contrast is not constant across the groups represented. To see why, suppose a population has two subgroups, with treatment effects \(\tau_1\) and \(\tau_2\), measured on the same scale. If subgroup 1 has proportion \(w\), the population mean treatment effect is:
For source and target populations with subgroup-1 proportions \(w_S\) and \(w_T\), the difference between their population effects is:
Thus, if subgroup effects differ and the population proportions differ, the population-level effects need not be the same. If subgroup effects are equal, this particular composition difference does not change the effect on this scale. This algebra explains why the population is part of the estimand; it does not establish that subgroup effects are equal or provide a method for transporting an effect.
Worked Example: Intercurrent-Event Strategies
Suppose a hypothetical 12-week pain trial measures improvement in pain score, in points, with larger values indicating greater improvement. There are 40 participants per arm. Rescue medication is used by 8 treatment-arm participants and 16 control-arm participants. The mean observed improvements, including outcomes after rescue medication, are 6 points for treatment and 4 points for control. Assume complete outcome follow-up and that the reported means use all randomized participants.
With a treatment-policy strategy for rescue medication, the estimated treatment contrast is:
This contrast answers a question that includes the consequences of rescue use as it occurred under each assigned treatment. Now suppose a separate analysis reports a model-based hypothetical-strategy estimate of 1.5 points, for the scenario in which no participant used rescue medication. That is a different estimand, even though the treatment, trial population, and pain scale are unchanged. The 1.5-point result cannot be derived from the observed means of 6 and 4 alone: estimating outcomes under no rescue requires assumptions about the unobserved outcomes for participants who did receive rescue.
If a source trial’s estimate uses the hypothetical strategy and the target trial’s estimate uses treatment policy, comparing 1.5 with 2 as though they represented the same treatment effect would be unjustified. Alignment would require a common event strategy and suitable data and assumptions to estimate it. Complete follow-up supports use of the observed outcomes for the treatment-policy question, but does not by itself validate the hypothetical estimate.
A summary measure can also change the numerical treatment effect even when the population, event strategy, and binary endpoint are aligned. For example, risk difference and odds ratio are distinct population-level summaries. They are not interchangeable without information about the underlying risks.
Worked Example: Risk Difference and Odds Ratio
In a hypothetical trial, 30 of 100 treatment participants and 20 of 100 control participants meet the same binary response definition by week 12. Assume response status is observed for all participants and the same population and event strategy are used for both arms.
The estimated risk difference is:
This is a 10-percentage-point higher response proportion in the treatment arm. The estimated odds ratio is:
The risk ratio is \(0.30/0.20=1.5\), another distinct summary. To see why the odds ratio alone does not determine the risk difference, consider a second hypothetical population with a control response risk of 0.10 and the same odds ratio of 1.714. Control odds are \(0.10/0.90=0.1111\). Treatment odds implied by the odds ratio are \(0.1111\times1.714=0.1904\), corresponding to treatment risk \(0.1904/(1+0.1904)=0.1600\). The risk difference in this population is \(0.1600-0.1000=0.0600\), or 6 percentage points. Therefore, the same odds ratio can accompany a different risk difference. A proposed bridge must specify which summary is the target, rather than treating the measures as equivalent.
A Practical Alignment Check
A comparison is most defensible when the estimands are the same in every attribute relevant to the decision. If they are not, identify the exact mismatch and determine whether the available data and assumptions can support a common estimand. A difference should not be dismissed merely because both trials use similar terminology.
For source and target, record population, treatment conditions, outcome and time, intercurrent-event strategies, and summary measure.
Check operational definitions, units, assessment windows, comparator and background care, as well as how events and missing outcomes were handled.
Decide whether it changes the treatment-effect question, can be resolved by analyzing suitable data under stated assumptions, or cannot be reconciled with the available evidence.
Describe an aligned comparison as a comparison of the specified estimand, not as proof that all trial differences are irrelevant. If a mismatch remains, explain why the proposed comparison is limited or unsupported.
When estimands are not directly aligned, the main options are not interchangeable. Reanalysis of individual-level data may allow a common endpoint, time point, event strategy, or summary measure to be estimated, if the needed measurements and assumptions are available. A model-based analysis may address differences that cannot be removed by simple reanalysis, but it adds assumptions that need evaluation. If the needed outcomes were not collected or the assumptions are not credible, the appropriate conclusion may be that the proposed bridge is not supported by that comparison.
| Situation | Interpretation for a proposed bridge | Appropriate response |
|---|---|---|
| Same estimand; different valid estimation procedures | Estimates may address the same treatment-effect question, though precision or bias may differ. | Compare methods, assumptions, and data quality before interpreting differences. |
| Different but harmonizable outcome or summary | A direct comparison is not yet aligned. | Use suitable data to estimate a prespecified common quantity and explain the assumptions. |
| Different event strategies with unobserved outcomes needed for reconciliation | The results answer different questions; reconciliation may rely on untestable assumptions. | Show sensitivity to those assumptions or avoid claiming direct comparability. |
| Material mismatch with insufficient data to resolve it | The evidence does not identify a common treatment effect for the proposed bridge. | State the limitation and do not interpret the numerical contrast as a like-for-like effect. |
Diagnostics, Limitations, and Common Mistakes
The most useful diagnostic is an estimand table completed from protocols, statistical analysis plans, and trial reports. Investigate discrepancies in endpoint wording, instrument versions, visit windows, rescue-use rules, discontinuation handling, and analysis populations. A difference between a prespecified estimand and a reported analysis is also important: the reported estimate may not answer the stated question. Missing outcomes require particular care, because an analysis procedure’s label does not, by itself, specify or justify the assumptions about those outcomes.
- Pitfall: “Both trials report a mean treatment effect, so the effects are comparable.” A mean difference in change at week 12 and a mean difference in absolute score at week 16 are different quantities. Name the variable and time point before comparing numbers.
- Pitfall: “Rescue medication is just a protocol detail.” If one analysis includes post-rescue outcomes and another estimates a no-rescue scenario, the event strategies differ. State the strategy and assess whether the data can support a common one.
- Pitfall: “The odds ratio and risk difference are two ways to write the same effect.” They summarize effects on different scales. As the worked example shows, the same odds ratio can correspond to different risk differences.
- Pitfall: “Matching estimands proves the bridge is valid.” Alignment removes one obstacle; it does not prove that the treatment effect applies to the target population or that trials are otherwise comparable. The bridge still depends on the quality of the evidence and the assumptions of the analysis.
Estimand alignment is a necessary discipline, not a universal guarantee of comparability. Some questions cannot be made identical because trials collected different outcomes or because a desired intercurrent-event scenario is not observed. In those cases, the limitation is substantive: a model cannot make missing information appear without assumptions. A transparent account of what each estimate means is more useful than a single pooled number whose target question is unclear.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions below.
- A source trial estimates a week-24 response risk difference under a treatment-policy strategy. A target trial estimates a week-12 odds ratio after excluding participants who discontinued. Name at least three estimand attributes that differ or may differ.
- In a hypothetical trial, treatment and control mean improvements are 5 and 3 points. What is the estimated treatment-policy contrast if all observed outcomes, including those after rescue, are included? What additional information is needed to estimate a no-rescue hypothetical contrast?
- Two populations have subgroup treatment effects of 2 and 5 units, and subgroup-1 proportions of 0.25 and 0.75. Calculate each population effect using the weighted-mean formula. Why does this matter for alignment?
- A trial reports response risks of 0.40 under treatment and 0.20 under control. Calculate the risk difference and risk ratio. Are these interchangeable summaries?
- Both trials use the same drug and endpoint name, but one assesses the outcome at week 8 and the other at week 16. Is the bridge automatically aligned? State a defensible next step.
Solutions. (1) The assessment time differs (week 24 versus week 12), the summary measure differs (risk difference versus odds ratio), and the event strategy or analysis population may differ: treatment policy includes outcomes regardless of discontinuation, whereas excluding discontinuers changes the population or handling of that event. (2) The treatment-policy contrast is \(5-3=2\) points of mean improvement. A no-rescue hypothetical contrast requires data and assumptions or a model for outcomes under no rescue among participants who received it. (3) The effects are \(0.25(2)+0.75(5)=4.25\) units and \(0.75(2)+0.25(5)=2.75\) units. Different subgroup compositions yield different population effects when subgroup effects differ, so the target populations must be specified. (4) The risk difference is \(0.40-0.20=0.20\), or 20 percentage points; the risk ratio is \(0.40/0.20=2\). They are distinct summaries, not interchangeable. (5) No. The assessment time differs, so the estimands are not automatically aligned. Determine whether suitable data support estimation at a common time point; otherwise report the mismatch and do not present the estimates as direct comparisons.