Why a Validation Result Has a Domain
A QSP model is not validated for every possible use just because it predicts some observations adequately. A prediction claim always concerns specified conditions: a population, treatment or intervention, endpoint, observation time, and relevant physiological context. Validation evidence supports a claim only to the extent that it is informative about those conditions. Defining the domain of applicability makes that scope explicit before a model is used to inform a new decision.
For example, evidence for an adult population receiving one treatment schedule and assessed on a circulating biomarker does not automatically support a prediction for children, a different schedule, a clinical outcome, or a population with a distinct disease state. The model may still make such a prediction, but its use then involves extrapolation, and the evidence supporting that extrapolation should be identified rather than implied.
The introductory material on selecting validation data and validation across doses, species, laboratories, and populations establishes why validation evidence must be relevant to the intended prediction. Here the task is to synthesize that evidence into a scoped description of where use is supported and where it requires extrapolation. Evidence that was used to calibrate the model is not, by itself, independent predictive validation.
Represent the Claim Before Mapping Evidence
Start by writing the intended prediction in a form that can be compared with the evidence. Specify the target population and its important characteristics; the intervention, dose, route, and schedule; the endpoint and assessment time; and physiological states or concomitant conditions that could change the model’s behavior. Include other context variables when they are relevant to the mechanism or measurement, such as assay, laboratory, species, or background therapy.
A useful representation is a condition vector \(z\), whose components encode these characteristics. The validation record can then be described as a set of conditions \(E\) under which predictions were evaluated. The domain is not necessarily the range of each component considered separately: it depends on which combinations were evaluated and whether the model’s assumptions support extending evidence between them.
For each component, record the values or categories represented in relevant validation data, the prediction performance observed, and any limitations on how well the data represent the target. Distinguish values that were actually studied from values inferred to be covered by interpolation or mechanistic reasoning. A numerical range alone is not evidence that every combination within it is supported.
From Validation Evidence to a Scoped Domain
Mapping requires both empirical evidence and a reasoned account of what that evidence can support. The earlier material on residual diagnostics and structural discrepancy is relevant here: acceptable overall agreement can conceal systematic errors in a subgroup, endpoint, or time window. Therefore, evidence should be considered at the resolution of the intended claim, including relevant subgroups and trajectory features, rather than reduced to a single summary statistic.
A compact way to express the logic is to define \(S(E)\) as the set of conditions for which the validation evidence is relevant and sufficiently informative, and \(A\) as the set of conditions for which the model assumptions and mechanistic structure are considered credible. The supported domain is restricted to conditions satisfying both requirements. This is a logical restriction, not a statistical procedure that automatically supplies a boundary.
The inclusion is deliberately conservative: evidence and assumptions may justify only part of the apparent evidence region. For instance, a study may include a dose but have too little information to evaluate a key endpoint at that dose; or the assay used may not measure the same quantity as the target endpoint. Conversely, mechanistic knowledge may help justify interpolation between well-studied conditions, but it does not turn an unsupported prediction into directly validated evidence.
The reasoning follows from the claim’s structure. A prediction for a target condition depends jointly on its population, intervention, endpoint, and state. If evidence is missing for a feature that could alter the prediction, or if an assumption needed to transfer evidence is not credible, the complete claim is not established by the remaining matching features. Thus the domain should be described as a joint set of supported conditions, not as a Cartesian product of independent minimum-to-maximum ranges unless the study design and scientific rationale justify that product.
Name the target population, intervention and regimen, endpoint and time, relevant physiological states, and context.
For each relevant dataset, record which conditions were represented, what predictions were evaluated, and whether the evidence is independent of calibration.
Look for relevant factor combinations and subgroup or endpoint-specific discrepancies; do not infer coverage from marginal ranges alone.
Describe what is supported, what is interpolated or mechanistically transferred, and what requires extrapolation beyond evidence or assumptions.
Worked Example: Mapping a Dose and Population Range
Hypothetical case. A QSP model predicts a circulating inflammatory marker 24 hours after treatment. Independent validation data include adults aged 18–65 years, baseline marker values from 2 to 8 ng/mL, and doses of 10, 20, and 30 mg, all administered once by the same route. The data include adults across the age and baseline-marker ranges at each dose, and the prediction checks show no material dose- or subgroup-specific pattern in the residuals for this endpoint and time. The stated claim excludes concomitant immunosuppressive therapy.
Consider a proposed prediction for a 52-year-old adult with a baseline marker value of 7 ng/mL receiving 25 mg once by the validated route, without immunosuppressive therapy. The age and baseline value fall within the observed ranges, and 25 mg lies between the tested 20 and 30 mg doses. The evidence also covers the relevant dose-by-population combinations. Under the stated assumption that the model’s response between 20 and 30 mg is adequately represented by its validated dose-response behavior, this use is an interpolation within the mapped domain, not a claim that 25 mg was directly tested.
Now change the target to a 12-year-old receiving the same dose. The numerical dose is in range, but the target age is outside the validated adult population. The prediction therefore requires extrapolation to a different population, even if other features match. The adult evidence alone does not establish that the relevant physiology or treatment response transfers to children.
Worked Example: Marginal Ranges Do Not Establish Joint Coverage
Hypothetical case. A validation program evaluates a model for two baseline disease states, mild and severe, and two regimens, 10 mg once daily and 30 mg once daily. The mild-state cohort receives only 10 mg, while the severe-state cohort receives only 30 mg. The model’s predictions agree with the observed endpoint in both cohorts. A proposed claim concerns severe disease treated with 10 mg once daily.
Across the program, both disease states and both doses are represented. It would be incorrect to conclude that the proposed condition is covered just because “severe” and “10 mg” each appear in the evidence. The observed combinations are mild-plus-10 mg and severe-plus-30 mg; severe-plus-10 mg is not represented. If disease state modifies treatment response, the observed agreement in the two other combinations does not validate this target.
The mapped evidence therefore supports the two evaluated combinations, subject to the endpoint and other study conditions, but does not establish the proposed combination. A further study, or a clearly justified mechanistic argument supported by relevant evidence, would be needed to reduce this gap. Until then, the prediction should be identified as an extrapolation across a joint population-by-regimen condition.
Worked Example: A New Endpoint and Physiological State
Hypothetical case. A model has been independently evaluated for a biomarker at 6 and 24 hours after a single infusion in adults with stable disease. The proposed application is prediction of a clinical response at 7 days in patients experiencing an acute inflammatory flare while receiving a second therapy.
The proposed use changes several claim dimensions: biomarker to clinical response, observed times to 7 days, stable disease to acute flare, and single therapy to combination treatment. Agreement for the biomarker at 6 and 24 hours does not directly validate the clinical response at 7 days. Nor does validation in stable disease establish performance during an acute flare, where baseline processes and treatment effects may differ.
The target therefore lies outside the directly supported domain on endpoint, time, physiological state, and intervention context. A model may still generate the requested prediction, but it should be described as an extrapolative model-based prediction. The validation evidence listed here does not quantify how reliable that prediction is; targeted validation data or additional evidence would be needed to address the identified gaps.
Diagnostics, Alternatives, and Limitations
A domain map is only as informative as its underlying evidence and its level of detail. Inspect validation performance by the factors that could change the intended prediction: dose, regimen, population subgroup, endpoint, time, state, and context. Look for sparse strata, imbalanced combinations, systematic residual patterns, and changes in measurement procedures. If only an aggregate result is available, note that it may not establish performance in a subgroup relevant to the new claim.
The main alternative is to report broad marginal ranges, such as an age interval and a dose interval, and treat any target inside both as covered. This is simple but can conceal missing combinations and interactions. A second alternative is to declare the entire convex hull of validation conditions applicable. That is also unsafe without justification: the hull may include untested combinations or regions where the model’s mechanisms are not credible. A more defensible approach reports observed combinations and separately labels justified interpolation or mechanistic transfer.
- Warning sign: range-only reasoning. A target matches each observed range, but the corresponding joint subgroup or regimen was never evaluated.
- Warning sign: endpoint substitution. Validation for a biomarker is treated as validation for a clinical outcome without evidence supporting the biomarker-to-outcome link.
- Warning sign: hidden context change. Assay, laboratory, species, concomitant therapy, or disease state differs in a way that may affect the model or the observation process.
- Warning sign: pooled agreement masks local failure. Overall prediction performance looks adequate while a clinically important subgroup or time window has systematic error.
The domain is not necessarily a sharp biological boundary. Evidence is often uneven: some conditions are directly studied, some are supported by interpolation, and others rely heavily on assumptions. A useful report preserves these distinctions instead of giving a falsely precise boundary. Domain definitions also depend on the prediction’s purpose and the cost of error; the same evidence may be adequate for exploratory scenario analysis but insufficient for a high-consequence decision.
Finally, defining the domain does not itself decide whether a model qualifies for a particular use or set numerical acceptance thresholds. Those are separate decisions. The domain map supplies the scope and evidence gaps that such decisions must consider; it cannot replace them.
Check Your Understanding
For each question, identify what the evidence does and does not support. Solutions follow the questions.
- Validation includes two doses in adults and two age groups, but each age group received only one dose. Why might a target combining the other age group and dose be outside the supported domain?
- A model is validated for a biomarker at 24 hours. What additional issue arises if the intended claim is a clinical outcome at 7 days?
- Suppose a proposed use matches the validated species, dose, and endpoint but adds a concomitant therapy that changes a pathway represented in the model. How should this condition be classified?
- Why is the convex hull of all validation conditions not automatically the domain of applicability?
- What should be reported when a prediction lies between tested doses but the precise dose was not observed?
Solutions. (1) Marginal coverage does not establish joint coverage: the target age-by-dose combination was not evaluated, and an interaction could affect predictions. It is unsupported unless relevant mechanistic evidence justifies transfer. (2) The endpoint and observation time both differ; biomarker validation does not by itself establish clinical-outcome performance at 7 days. (3) Treat it as an extrapolation in intervention context because the added therapy may alter a represented pathway; matching the other dimensions does not remove that gap. (4) The hull can contain untested combinations or physiologically implausible regions, and evidence may not support interpolation across them. (5) Report that the dose is an interpolation between tested doses, name the tested range and relevant evidence, and state the assumption that response between those doses is adequately represented. Do not describe the precise dose as directly validated.