Why Assessment Timing Is a Design Choice
A longitudinal endpoint can show a different treatment effect at different times. An assessment scheduled before an effect develops may underestimate a later benefit; an assessment scheduled near a transient peak may overstate what is sustained. The design question is not simply, “When is the effect largest?” It is, “Which feasible assessment time or schedule best measures the treatment effect defined by the endpoint and estimand?”
The introductory material on estimands establishes that the target treatment contrast must be specified in context. Here, the aim is to use expected response trajectories and visit constraints to compare assessment options for that target. A planned assessment time should not be chosen after examining unblinded trial outcomes just because it produces a larger observed contrast.
The trajectory used for planning is an expectation, not a promise that every participant follows the same path. It may come from prior data, pharmacologic understanding, or a justified model. For a useful comparison, specify the time origin, treatment-effect direction, likely onset and duration, and clinically important scale. Also state which times are feasible given the trial’s visit schedule and allowable windows.
Compare Candidate Times Against the Target
A practical first comparison is a table or plot of expected treatment and control means, or of \(\Delta(t)\), at feasible candidate times. Compare both the size and the timing of the expected contrast. A large effect at one time may be less attractive than a slightly smaller effect that is more durable, easier to measure consistently, or more representative of the intended clinical question.
If the protocol’s primary estimand is a contrast at a particular time, that time defines the primary endpoint. Other assessments may support interpretation or describe the trajectory, but they do not replace the primary time-specific contrast. If the endpoint instead summarizes several times, its definition must specify how those assessments contribute. A schedule by itself does not determine an endpoint contrast.
Worked Example: Comparing Candidate Single Assessment Times
Hypothetical data. Consider a lower-is-better symptom score. Planning assumptions give the following expected mean differences, with \(\Delta(t)=\mu_T(t)-\mu_C(t)\). Candidate times are feasible unless noted.
| Week | Expected \(\Delta(t)\), score points | Interpretation |
|---|---|---|
| 4 | -2.0 | Early, modest expected benefit |
| 8 | -4.5 | Largest expected benefit |
| 12 | -3.5 | Smaller but sustained expected benefit |
| 16 | -2.5 | Benefit is waning |
By expected magnitude alone, week 8 is the strongest candidate. But the choice depends on the endpoint’s purpose: week 8 targets the anticipated peak, whereas week 12 assesses a later, still substantial effect. Suppose the planning team also wants a simple standardized separation index for an equal-allocation design with 60 participants per group and a common outcome standard deviation of 5.5 points. Under independent groups and the stated common-standard-deviation assumption, the standard error of a difference in means is
At week 8, the standardized expected separation is the absolute expected contrast divided by this standard error:
The calculation uses the unrounded standard error in the ratio. Rounding \(SE\) to 1.004 first would slightly change the result. This index is a planning comparison under the stated assumptions, not an observed test statistic or a stand-alone power conclusion. It does not account for uncertainty in the trajectory, visit-window variation, or departures from the assumed variability. If week 12 is the prespecified primary time, its expected contrast remains the primary target even though week 8 has a larger expected separation.
Visit Windows and Uncertain Assessment Times
A nominal visit time is not always the time at which an assessment occurs. A protocol may allow a window around the target, and scheduling constraints may produce assessments at different actual times. If the treatment effect changes appreciably across that window, treating every observation as if it occurred exactly at the nominal time can be misleading. One planning summary is the average expected effect over the window, provided the assumed distribution of actual assessment times is relevant.
For a window from \(a\) to \(b\), if actual assessment times are expected to be uniformly distributed across the window, the average expected contrast is
This is a planning summary of the trajectory over the window. It is not automatically the estimand for the trial: the protocol may instead define an assessment at a nominal visit, with a specified rule for handling the actual visit date. The assumed distribution of visit times matters; uniform timing is not appropriate when visits cluster near one edge of the window.
Worked Example: Comparing Two Visit Windows
Hypothetical data. Suppose the benefit is defined as \(B(t)=\mu_C(t)-\mu_T(t)=-\Delta(t)\), so positive values favor treatment. The expected benefits are 3.0 points at week 6, 4.5 at week 8, and 4.0 at week 10. Assume linear change between these times and uniform actual visit timing within each candidate window.
For the week 7–9 window, linear interpolation gives \(B(7)=3.75\), \(B(8)=4.50\), and \(B(9)=4.25\) points. The two trapezoid areas are \(1(3.75+4.50)/2=4.125\) and \(1(4.50+4.25)/2=4.375\) point-weeks. Therefore,
Suppose a second feasible window is weeks 10–12, with expected benefits of 4.0 points at week 10, 3.8 at week 11, and 3.5 at week 12, again interpolated linearly. Its area is \(1(4.0+3.8)/2+1(3.8+3.5)/2=3.9+3.65=7.55\) point-weeks. Its average is \(7.55/2=3.775\) points. Under these assumptions, the week 7–9 window has the larger average expected benefit. The comparison would need to be reconsidered if actual visit times are not uniform, the trajectory is not approximately linear within the windows, or the prespecified endpoint is defined at a nominal time rather than as a window average.
Schedules Must Match the Endpoint Definition
A schedule can be compared by first writing down how its visits enter the endpoint. For example, an endpoint defined as the equally weighted mean of two assessments has an expected contrast equal to the mean of the two time-specific contrasts. An endpoint defined only at week 12 does not become a two-visit average simply because week 8 is also measured. Additional visits can help describe onset or durability, but they also require participant and site time.
The following comparison assumes that the endpoint is explicitly defined as an equally weighted average of the two listed assessments. All values are hypothetical benefits in score points, with higher values favoring treatment.
Worked Example: Comparing Two Feasible Assessment Schedules
Suppose expected benefits are 3.0 points at week 6, 4.5 at week 8, 4.0 at week 10, and 3.5 at week 12. Schedule A assesses at weeks 8 and 12; Schedule B assesses at weeks 6 and 10. Assume both visits are feasible, there are no missing assessments for this comparison, and the endpoint gives the two visits equal weight.
For Schedule A, the expected endpoint contrast is \((4.5+3.5)/2=4.0\) points. For Schedule B it is \((3.0+4.0)/2=3.5\) points. Schedule A therefore has the larger expected contrast for this particular two-visit average. This does not establish that Schedule A is preferable in every respect: it spans a later period and may impose different logistical demands. If the primary endpoint were instead the week-12 contrast, both schedules would need an eligible week-12 assessment to measure that endpoint; the week-8 value could not be substituted without changing the endpoint definition.
The equal-weight calculation is not a universal rule for combining visits. Weights, time points, and the intended clinical interpretation belong to the endpoint definition. Choosing weights after inspecting trial results can bias the reported treatment effect. For planning, evaluate the prespecified endpoint under each feasible schedule, rather than selecting a schedule solely because it creates the largest calculated average.
Assumptions, Diagnostics, and Alternatives
A timing recommendation is only as credible as the trajectory and feasibility assumptions behind it. Check whether the expected onset and duration are supported by relevant evidence, whether the endpoint scale and direction are consistent across time, and whether the modeled trajectory represents the population and treatment regimen of interest. For window calculations, check the interpolation and actual-visit-time assumptions. For a standardized separation such as the one above, also check the assumptions used for the variability and group sizes.
Useful diagnostics include plotting treatment and control trajectories with the candidate times and windows marked; checking whether conclusions change under plausible faster, slower, or less durable responses; and confirming that proposed windows fit operational constraints. If small plausible changes in onset move the apparent best time substantially, report the recommendation as sensitive rather than treating one time as definitively optimal. If a candidate time lies outside the period supported by data or a defensible model, extrapolation should be made explicit.
Alternatives depend on the planning question. A single time-specific contrast is clearest when the clinical question is about benefit at that time. A prespecified multi-time summary can represent benefit over a period, but its weights must be clinically justified. A full trajectory assessment can describe onset and persistence, but it is not interchangeable with a single-time endpoint. These choices target different summaries; they should not be ranked as though they measured an identical quantity.
- Do not optimize only for the peak. A short-lived maximum may not reflect the intended clinical benefit.
- Do not assume the nominal time is the actual time. A steep trajectory within a wide visit window can materially change the expected assessment.
- Do not treat more visits as automatically better. Additional visits may add burden without improving the endpoint relevant to the decision.
- Do not ignore trajectory uncertainty. A precise calculation based on a poorly supported curve can give a misleadingly confident recommendation.
These comparisons have limits. Expected trajectories may be uncertain, operational constraints may vary across sites, and a planning summary does not by itself quantify all uncertainty in a treatment-effect estimate. Nor does the largest expected contrast establish clinical importance or guarantee a successful trial. The recommendation should be tied to the endpoint’s purpose, the supporting evidence, and the assumptions that make the selected assessment feasible and interpretable.
Check Your Understanding
Answer each question using the stated assumptions. Brief solutions follow the questions.
- A lower-is-better endpoint has expected treatment-minus-control contrasts of \(-1.5\) points at week 4 and \(-3.0\) at week 8. Which time has the larger expected benefit, and what must be checked before choosing it?
- Under a uniform visit window from week 5 to week 7, a benefit trajectory is linear from 2.0 points at week 5 to 4.0 points at week 7. Calculate the average expected benefit over the window.
- An endpoint is prespecified as the equally weighted mean of weeks 8 and 12. Expected benefits are 4.0 and 3.0 points, respectively. What is its expected contrast? Does measuring at week 6 change that contrast?
- Why can a uniform-window average be inappropriate when actual visits cluster near the beginning of the window?
Solutions: 1. Week 8 has the larger expected benefit because its treatment-minus-control contrast is more negative on a lower-is-better scale. Before choosing it, check that week 8 fits the clinical purpose, is feasible, and is supported by a credible trajectory. 2. For a linear trajectory, the average is the mean of its endpoint values: \((2.0+4.0)/2=3.0\) points. 3. The expected contrast is \((4.0+3.0)/2=3.5\) points. A week-6 assessment does not change this prespecified two-time average unless the endpoint definition is changed. 4. A uniform average gives equal probability to all times in the window. If visits cluster near the beginning, the appropriate expected contrast weights early times more heavily; use the actual-time distribution or report the uniform assumption as a limitation.