From a Clinical Question to a Patient-Level Variable
A clinical question usually describes a benefit in words: less pain, improved function, fewer exacerbations, or longer survival. An endpoint variable makes that question operational for each participant. It specifies what is recorded, when it is assessed, and whether the recorded value is transformed into a clinically interpretable quantity. Without those choices, two analysts could use the same trial data yet analyze different outcomes.
The endpoint variable is one attribute of an estimand, not the estimand itself. It describes the patient-level quantity on which a treatment effect may later be summarized. The population, treatment conditions, and other estimand attributes must also be specified, but the focus here is the outcome variable itself. Choosing the variable does not, by itself, define how to handle every event that might occur after randomization.
Write \(Y_i(t)\) for the measured outcome for participant \(i\) at time \(t\), where \(t\) is measured from a stated origin, such as randomization or baseline. A simple endpoint might be \(Y_i(12)\), a score in points at week 12. A transformed endpoint might be \(Y_i(12)-Y_i(0)\), the change in points from baseline. The notation is useful only if the measurement, time origin, units, and transformation are defined in words as well.
Three Decisions in the Endpoint Definition
A complete definition makes three related decisions. First, it names the measured outcome: for example, a symptom score, a laboratory concentration, or whether a specified event occurred. Second, it states the assessment time or assessment interval. Third, it specifies any transformation from the recorded measurement to the endpoint variable, such as a change score, a responder indicator, or a time-to-event pair.
An assessment time should be more precise than “at follow-up.” If the intended assessment is at week 12, state whether the endpoint is the measurement scheduled at week 12 or a measurement selected from a window around week 12. If a window is needed, specify its boundaries and the rule for choosing among multiple measurements in that window. Otherwise, the same participant’s endpoint could depend on an analyst’s unstated choice.
Transformations also need explicit definitions. A change score must identify the baseline and follow-up measurements and the subtraction order. A responder variable must state its threshold, direction, assessment time, and what happens at the boundary. A time-to-event endpoint must define the event and the time origin, as well as the time horizon or censoring information needed to describe follow-up. These are not cosmetic details: changing them can change the endpoint values and the clinical question.
Specify what is measured or recorded, the scale, and the units. A score of 4 is not interpretable without knowing which score and what its values mean.
State the time origin and the target assessment time, or define an assessment window and a rule for selecting the value.
Write the rule that converts the recorded measurements or event history into one endpoint value, including the scale, units, and direction of benefit.
Worked Examples
Worked Example: Change in a Symptom Score
Hypothetical setting. Participants rate pain on a 0–10 scale, with higher scores indicating worse pain. The clinical question concerns change from baseline to week 12. Suppose one participant has a baseline score of 7.0 points and a week-12 score of 4.5 points. Define the endpoint as follow-up minus baseline:
For this participant,
The endpoint is a 2.5-point decrease in pain score. Because lower scores indicate less pain, a negative change represents improvement. Stating the subtraction order matters: baseline minus follow-up would be \(+2.5\) points and would reverse the sign convention. The variable’s definition should also say whether week 12 means the scheduled week-12 assessment or a value selected by a pre-specified window rule.
Worked Example: Defining a Responder Threshold
Hypothetical setting. A trial measures a symptom score at baseline and week 12; higher scores indicate worse symptoms. Define a responder as a participant whose score has decreased by at least 30% from baseline. For a baseline score \(B_i>0\), let the week-12 score be \(Y_i(12)\). The proportional reduction is \((B_i-Y_i(12))/B_i\), so the endpoint is:
where \(I\{\cdot\}\) equals 1 when the condition inside the braces is true and 0 otherwise. Suppose one participant’s baseline score is 8 points and week-12 score is 5 points. The reduction is
Since \(37.5\%\geq30\%\), this participant has \(R_i=1\), or responder status. For a second participant with baseline 6 points and week-12 score 4.2 points, the reduction is \((6-4.2)/6=0.30=30\%\). Because “at least 30%” includes equality, this participant is also a responder. In this definition, baseline must be positive for the percentage reduction to be defined. The score scale, assessment time, threshold, direction, and inclusion of equality all belong in the endpoint specification.
Worked Example: A Time-to-Event Endpoint at a Fixed Horizon
Hypothetical setting. Consider time from randomization to a first, specifically defined disease-related event, with follow-up through day 180. For a participant whose event occurs on day 74, the event time is 74 days and the event indicator by day 180 is 1. For a participant with no event recorded through day 180, the event indicator is 0 and the recorded follow-up time is 180 days. A useful patient-level representation is the pair \((T_i,\Delta_i)\), where \(T_i\) is observed event or follow-up time in days and \(\Delta_i\) indicates whether the defined event was observed by that time.
For the first participant, \((T_i,\Delta_i)=(74,1)\); for the second, \((T_i,\Delta_i)=(180,0)\). The pair is the endpoint information, not a claim that the second participant experienced an event at day 180. The endpoint definition must state the event, time origin, follow-up horizon, and how event status and follow-up time are recorded. This example defines the patient-level variable; it does not specify an analysis model or a strategy for every event that may occur during follow-up.
Why Transformations Need Justification
A transformation can make an endpoint more directly aligned with a clinical question, but it can also discard information or create interpretive problems. A change score retains a numerical measure of each participant’s difference from baseline. A responder indicator instead groups participants according to a threshold: all reductions beyond the threshold receive the same value. That may make the endpoint easier to interpret clinically, but it loses information about the size of improvement within each group.
The responder definition can be justified directly from its clinical rule. “At least a 30% reduction” means that the reduction divided by baseline is no smaller than 0.30. For a positive baseline value \(B_i\), this condition can be rearranged:
Thus a 30% responder has a week-12 score no greater than 70% of baseline. The derivation depends on \(B_i>0\); if baseline can equal zero, the percentage rule is undefined for that participant and an alternative endpoint definition is needed. The equivalence also relies on the stated direction, with lower scores representing improvement. A threshold should have a clinical rationale and be selected before examining outcome results, rather than chosen after seeing which cutoff produces the most favorable pattern.
Endpoint choices should be examined for internal consistency. Check that the stated direction of benefit agrees with the scale, that the units match the transformation, and that the assessment time matches the clinical question. If a value is taken from a time window, check that the selection rule can be applied consistently. If the endpoint requires a baseline value, check that the definition covers the allowable baseline range. These are definition checks, not substitutes for later checks of data quality or statistical-model assumptions.
Alternatives, Limitations, and Common Mistakes
| Endpoint form | What it records for each participant | Important specification |
|---|---|---|
| Follow-up measurement | Outcome value at a target assessment | Scale, units, time origin, and assessment time |
| Change from baseline | Follow-up value minus baseline value | Which baseline and follow-up values, and subtraction order |
| Responder indicator | Whether a stated threshold is met | Threshold, direction, boundary rule, and denominator conditions |
| Time-to-event pair | Observed time and event status | Event definition, time origin, and follow-up rule |
These forms answer different questions and are not interchangeable by default. A follow-up score describes status at the selected assessment; a change score describes difference from baseline; a responder indicator classifies threshold attainment; and a time-to-event pair records event timing and status. Which is appropriate depends on the clinical question and the measurement process, not on which variable is easiest to compute.
No endpoint definition alone resolves all complications in trial follow-up. For example, when a measurement is unavailable or an event occurs before the target assessment, the endpoint may require additional decisions about how the clinical question should be represented. Those decisions must be stated rather than silently replaced by a convenient observed value. In particular, missing measurements should not automatically be assigned a score such as zero, and an event should not automatically be recoded as a particular endpoint value unless that is part of the defined clinical outcome.
- Leaving the assessment time vague. “Symptom score after treatment” can refer to different visits. State the target time or a complete window-and-selection rule.
- Reversing the change-score direction. Follow-up minus baseline and baseline minus follow-up have opposite signs. Write the formula and state which sign indicates improvement.
- Treating a threshold as self-explanatory. A responder endpoint needs a defined threshold, direction, assessment, and equality rule, as well as a meaningful baseline denominator if the threshold is proportional.
- Confusing a measurement with the endpoint. A laboratory result is a recorded measurement; a change or threshold indicator derived from it is a different patient-level variable.
- Choosing the definition after inspecting results. Selecting a time point or cutoff because it gives a preferred result can make the endpoint data-dependent. Specify the clinical rule in advance.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions.
- A fatigue scale ranges from 0 to 20, with higher scores indicating worse fatigue. A participant scores 13 at baseline and 9 at week 8. What is the week-8 change endpoint if it is defined as follow-up minus baseline, and which direction represents improvement?
- For a positive baseline score, define response as a reduction of at least 25%. Write the responder rule using baseline \(B_i\) and follow-up score \(Y_i(t^*)\), and state the equivalent inequality for the follow-up score.
- Why is “the outcome at follow-up” not a fully specified endpoint definition?
- A participant has a baseline score of 10 and a target-time score of 7.5. Under an “at least 25% reduction” definition, is this participant a responder? Show the calculation and address the boundary.
Solutions. (1) The change is \(9-13=-4\) points. Since higher scores indicate worse fatigue, a negative change represents improvement. (2) The rule is \(R_i=I\{(B_i-Y_i(t^*))/B_i\geq0.25\}\), for \(B_i>0\). Rearranging gives \(Y_i(t^*)\leq0.75B_i\). (3) It does not identify the measurement scale, the assessment time or selection rule, or whether a transformation is intended. (4) The reduction is \((10-7.5)/10=2.5/10=0.25=25\%\). “At least 25%” includes equality, so the participant is a responder.