Why an Endpoint Change Can Change the Question
An adaptive trial may propose changing an endpoint after an interim review. A new measurement may be easier to collect, more reliable, or more clinically informative. But a replacement endpoint does not automatically answer the question the trial originally set out to answer. The essential issue is whether it represents the same target or defines a different treatment effect.
Endpoint compatibility is assessed by comparing what is measured, how it is measured, when it is assessed, which population is summarized, and what population summary is used. A change in units can often be handled by an explicit conversion. A change from symptom burden to a biomarker, from a 12-month outcome to a 24-month outcome, or from a mean difference to a responder proportion generally changes the target, even if the new endpoint is related to the old one.
For a simple mean-contrast target, let \(Y^a(t)\) denote the endpoint value that would be observed at time \(t\) under treatment condition \(a\), and let \(P^*\) denote the specified target population. The treatment effect is
This expression is meaningful only after the outcome, time, population, treatment conditions, and mean summary have been specified. The earlier material on standardizing effects to a fixed population and treatment versions is relevant here: changing an endpoint does not itself authorize changing the target population or what the treatment conditions mean.
A Structured Compatibility Audit
Compare the proposed endpoint with the original one along five dimensions. The goal is not to find a vague resemblance, but to establish which elements are unchanged and whether any difference can be exactly translated without changing the intended clinical interpretation.
| Dimension | Audit question | Warning sign |
|---|---|---|
| Construct | Does the endpoint represent the same clinical concept? | A symptom score is replaced by a laboratory marker that is only associated with symptoms. |
| Measurement and scale | Is the same quantity measured, perhaps in different units or by a documented equivalent instrument? | A score is replaced by a threshold, rank, or transformed quantity with no validated recovery of the original target. |
| Assessment time | Is the outcome assessed at the same time relative to randomization or treatment? | A 12-month endpoint becomes a 24-month endpoint. |
| Target population | Is the summary still over the same defined population? | The endpoint is available only for a selected subset, and that subset becomes the implicit target. |
| Population summary | Is the same summary used, such as a mean difference or a risk difference? | A mean change is replaced by the proportion crossing a threshold. |
A change can be compatible even if recorded numbers look different, provided a fixed, known conversion translates them to the original scale. Conversely, identical units do not establish compatibility: measuring the same quantity at a different time can define a different treatment effect. A high correlation between endpoints is also insufficient. Correlation describes how measurements vary together; it does not show that their treatment contrasts, clinical meanings, or population summaries coincide.
When a Linear Unit Conversion Preserves the Target
Suppose the proposed endpoint is a fixed linear re-expression of the original endpoint, \(Y'=a+bY\), with the same constants \(a\) and \(b\) for every participant and both treatment conditions. Assume the construct, assessment time, target population, and population summary remain unchanged, and that the conversion is applied consistently. Then the treatment contrast on the new scale follows directly from linearity of expectation.
The additive constant cancels, while the contrast is multiplied by \(b\). If \(b>0\), its direction is unchanged; if \(b<0\), the direction reverses because the scale orientation has reversed. The numerical contrast is not generally identical across units. It is a rescaled representation of the same underlying contrast, with units that must be stated. To recover the original contrast when \(b\ne 0\), divide the contrast on the new scale by \(b\).
This argument depends on more than algebra. The conversion must be fixed rather than chosen separately by treatment group or participant in a way that changes the quantity being summarized. The underlying endpoint, time, population, and mean summary must also remain the same. If the proposed change instead applies a nonlinear transformation, such as a logarithm, the mean contrast on that transformed scale is generally a different summary; it does not follow from the linear result above.
Worked Example: Converting a Score Without Changing Its Construct
In a hypothetical trial, the prespecified endpoint is a symptom score in points at 12 weeks, with the mean difference between the same two treatments in the same target population. A revised data system records the identical score in units where 1 new unit equals 0.1 points. The hypothetical treatment means on the original scale are 4.2 points and 3.1 points. Is the change compatible, and what is the contrast in the new units?
The construct, assessment time, population, and mean summary have not changed. The unit definition gives \(1\) new unit \(=0.1\) points, so the numerical value in new units is the value in points divided by \(0.1\) points per new unit. The treatment means are therefore \(4.2/0.1=42\) new units and \(3.1/0.1=31\) new units.
The original treatment contrast is \(4.2-3.1=1.1\) points. The contrast on the new scale is
Equivalently, because one new unit is one-tenth of a point, the numerical contrast is multiplied by 10 when expressed in new units. This is a compatible unit conversion: the contrast is 1.1 points, or 11 new units. Reporting 0.11 new units would reverse the conversion.
Changes That Alter Time, Construct, or Summary
Some changes are not unit conversions. They may still be clinically reasonable, but the treatment effect they target must be described as different. Compatibility should be judged before examining whether a new endpoint gives a more favorable result. The following examples illustrate why.
Worked Example: Moving the Assessment from 12 to 24 Months
Consider a hypothetical trial whose original target is the mean functional score at 12 months. A proposal replaces it with the mean score at 24 months in the same population and on the same scale. Suppose, hypothetically, the treatment and control means are 68 and 62 at 12 months, and 60 and 57 at 24 months.
At 12 months, the target contrast is \(68-62=6\) score points. At 24 months, the contrast is \(60-57=3\) score points. The endpoint construct, scale, and population are unchanged, but the assessment time is different. The 24-month contrast does not become a 12-month contrast by sharing a scale or by being measured in the same participants. It answers a different time-specific question.
The two estimates might both be useful, and the trial could prespecify both with appropriate roles. But replacing the 12-month target with the 24-month target changes the estimand; the protocol should state that change rather than call it a compatible re-expression.
Worked Example: Replacing Symptoms with a Biomarker
Suppose a hypothetical trial originally targets the mean symptom score at 8 weeks. A proposed revision substitutes a blood biomarker at 8 weeks, on a continuous scale, in the same target population. Assume the biomarker and symptom score are positively correlated. Does that establish compatibility?
No. The original construct is symptom burden; the new construct is the biomarker concentration. Positive correlation means that higher values of one tend to occur with higher values of the other in the observed data, but it does not establish that they measure the same clinical outcome or that a treatment effect on one equals a treatment effect on the other.
For example, the hypothetical symptom means could be 10 and 8 points, a treatment contrast of 2 points, while biomarker means are 5.0 and 4.2 units, a contrast of 0.8 units. Those contrasts have different meanings and units. Without a justified measurement relationship that recovers the original target, the proposed endpoint changes the construct and defines a different estimand. The fact that assessment time and population match does not repair that difference.
Worked Example: Replacing a Mean with a Responder Proportion
A hypothetical trial targets the mean improvement in a 0-to-100 scale, with higher improvement being better. A proposed endpoint instead counts participants whose improvement is at least 10 points. Suppose the treatment and control groups have mean improvements of 8 and 6 points, and responder proportions of 0.48 and 0.40.
The mean-difference target is \(8-6=2\) points. The responder risk-difference target is \(0.48-0.40=0.08\), or 8 percentage points. This is not a unit conversion: the first summary uses each participant's improvement, while the second summarizes whether each participant crosses a threshold. Two populations can have the same mean difference but different responder proportions, or vice versa. The proposed endpoint therefore changes the population summary and, in general, the treatment-effect target.
Diagnostics, Alternatives, and Limitations
A practical audit should be written down before adopting the change. List the original and proposed endpoint side by side, then record the construct, instrument or measurement rule, scale and units, assessment time, target population, and population summary for each. For any claimed conversion, write the equation, identify its constants and units, and check it using a concrete value. A conversion that cannot be stated clearly is not yet a demonstrated equivalence.
Look especially for hidden changes: a new instrument may use different items; a new score may reverse direction; a new assessment window may select a different visit; a threshold may turn a continuous measure into a binary outcome; or a new endpoint may be observed only for participants who remain available for follow-up. If the proposed measurement is unavailable for some participants, do not silently treat the observed subset as the original target population.
| Approach | What it means | What must be reported |
|---|---|---|
| Keep the original endpoint | The original construct, time, population, and summary remain the target. | The original definition and measurement procedure. |
| Use a validated re-expression | The recorded scale or instrument differs, but a specified relationship translates it to the original target or a clearly defined scale transformation. | The conversion or validation basis, its assumptions, and the units of the reported contrast. |
| Adopt a new endpoint | At least one target-defining feature changes, so the clinical question changes. | The revised target and a clear explanation that it is not numerically interchangeable with the original one. |
An endpoint that is highly correlated with the original can still be a useful secondary or replacement outcome, but correlation alone is not a conversion rule. A linear transformation preserves a mean contrast up to its known scale factor; a nonlinear transformation, a change in time, or a change in summary generally does not. Even a carefully specified endpoint change has limitations: it may reduce comparability with the original clinical question, depend on assumptions about measurement, or require a new interpretation of the effect.
A common mistake is to reason, “The new endpoint is strongly associated with the old one, so switching endpoints does not change the estimand.” Association is not equality of constructs, treatment effects, or summaries. The correction is to compare the defining features explicitly and show a valid mapping if one is claimed. If no mapping preserves the original target, call the proposal a change of estimand and state the new question plainly.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions below.
- An outcome is recorded in a new unit such that 1 new unit equals 0.1 points. What is a contrast of 1.5 points in new units?
- A mean score at 6 months is replaced by the same score at 18 months. Which compatibility dimension changes, and why is this not merely a re-expression?
- Why does a high correlation between a symptom score and a biomarker fail to prove endpoint compatibility?
- A mean improvement endpoint is replaced by the proportion improving by at least 5 points. Is this a scale conversion or a change of summary?
- Name the features that should be compared in a protocol endpoint audit.
Solutions. (1) Divide by \(0.1\) points per new unit: \(1.5/0.1=15\) new units. (2) The assessment time changes. The target is a time-specific treatment effect, so the 18-month contrast answers a different question from the 6-month contrast. (3) Correlation describes co-variation, not equality of clinical construct or equality of treatment effects; it supplies no mapping that recovers the original target. (4) It is a change of population summary, from a mean to a threshold-based proportion, and generally defines a different estimand. (5) Compare construct, measurement and scale, assessment time, target population, and population summary, while keeping treatment conditions clear.