Why Map Validation Evidence to a Domain?
A PBPK model may be evaluated against data from one dose, one population, or one drug, while its intended use covers a much wider range of conditions. A validation result is informative only in relation to the conditions actually observed and the predictions the model is meant to make. Mapping those conditions makes the scope of the evidence explicit: it shows where a prediction is directly represented in validation data, where it lies between observed conditions, and where it is outside the observed evidence.
The earlier material on selecting validation studies for a prediction question establishes why study relevance matters. The next step is to compare the selected studies’ actual conditions with the full intended prediction domain. This is not a pass-or-fail judgment about the model. It is a structured account of which parts of its intended use have evidence and which do not.
Represent Conditions as Combinations
A useful domain description includes the dimensions that could affect the prediction. Depending on the intended use, these can include dose, dosing schedule, route or formulation, physiological characteristics such as age or renal function, drug properties such as solubility or metabolic pathway, and the outcome being predicted. Include only dimensions relevant to the prediction question, but do not omit a dimension merely because the validation studies held it constant.
For clarity, imagine a prediction domain described by dose and physiology. Each condition is then a pair: a dose together with a physiological state. If drug properties or formulation also vary, each condition requires those values as well. The intended domain can be written as a set \(D\) of such combinations, and the validation observations as a set \(V\). Exact direct coverage concerns conditions in both sets, \(D\cap V\). It is not the same as a range of values that happens to contain observations.
This set-based view prevents a common error: combining separately observed ranges as if every combination within them had been tested. A dose may have been observed in healthy adults and a physiological subgroup may have been observed at a different dose. Those marginal facts do not mean the dose-subgroup combination was observed.
Worked Example: Observed Doses Versus the Dose Span
Suppose a hypothetical PBPK model is intended to predict exposure for oral doses from 10 to 150 mg, under otherwise comparable conditions. An independent validation data set contains observations at exactly 25, 50, and 100 mg. What dose conditions are directly observed, and how should doses between or outside them be described?
The intended dose set is \(I=[10,150]\) mg. The directly observed dose set is \(V=\{25,50,100\}\) mg. Therefore, the exact direct overlap is:
The span from the smallest to the largest observed dose is \([25,100]\) mg. That interval summarizes the extent of the observed dose range, but it is not the set of doses actually administered. For example, 75 mg is within the span but is not an observed validation dose. A prediction at 75 mg is between observed dose levels, so it is an interpolation with respect to dose, conditional on the other relevant conditions being comparable. Doses from 10 mg up to but not including 25 mg, and doses above 100 mg through 150 mg, are outside the observed span and are extrapolations with respect to dose.
This classification does not itself establish that interpolation or extrapolation will be accurate. It records the relationship between the prediction and the observed doses. If formulation, schedule, or physiology differs, dose position alone is not enough to characterize the evidence.
Coverage Must Be Checked Jointly
Suppose a hypothetical intended domain includes two doses, 50 and 100 mg, and two physiological groups, healthy adults and adults with moderate renal impairment. The intended combinations are all four pairs. Imagine validation observations at 50 mg in healthy adults and 100 mg in adults with moderate renal impairment. Both intended doses occur in the validation data, and both physiological groups occur there, but two combinations are missing.
Thus, \(D\cap V\) contains only two of the four intended combinations. Separate summaries would say that the dose range and both physiological groups are represented; the joint map shows that the dose-by-physiology combinations are not fully covered. In practice, dimensions can be continuous, categorical, or both, so a map may need ranges, strata, and specific combinations rather than a simple list.
Worked Mapping Across Physiology and Drug Properties
Worked Example: Locating an Untested Physiological Group
A hypothetical model is intended to predict exposure in adults with normal renal function, mild renal impairment, and moderate renal impairment. For this example, the intended groups are defined as eGFR at least 90, 60–89, and 30–59 mL/min/1.73 m², respectively. A validation study contains participants with eGFR from 72 to 104 mL/min/1.73 m², all receiving the same dose and formulation.
The observed range overlaps the normal-function and mild-impairment categories: values from 90 to 104 fall in the defined normal group, and values from 72 to 89 fall in the mild group. No validation participant has eGFR below 60, so moderate impairment is not represented. The study therefore provides direct observations in portions of two physiological groups, but none in the intended moderate-impairment group.
Even within the represented groups, the range does not mean that every possible value or clinically relevant combination was observed. The mapping should retain the actual participant values, the dose and formulation, and any other important characteristics. It would be inaccurate to describe the entire intended renal-function domain as validated merely because two of its three named groups are represented.
Worked Example: Mapping Drug Properties
Consider a hypothetical model intended for a new compound with fraction unbound in plasma of 0.05 and a dominant hepatic metabolic pathway. Validation data are available for two other compounds: Compound A has fraction unbound 0.04 and the same dominant pathway; Compound B has fraction unbound 0.08 but a different dominant pathway. Assume, for this example, that the other study conditions are comparable.
The new compound’s fraction unbound lies between the two observed values, 0.04 and 0.08. With respect to this property alone, 0.05 is within the observed span. However, the observed compounds do not jointly provide a close match on both properties: A is similar on pathway and fraction unbound, while B is similar only in the broad sense of lying in the fraction-unbound span and differs in pathway. The available data therefore do not directly observe the new compound, and the one-dimensional property range cannot establish that the combined drug-property profile is covered.
This map identifies what is and is not represented; it does not quantify the model’s expected error for the new compound. Mechanistic similarity, including properties not listed in this simplified example, must be judged in relation to the model structure and the prediction question.
A Practical Mapping Procedure
Before interpreting validation results, specify the intended domain at a useful level of detail and link each validation observation to its actual conditions. The following sequence makes the comparison auditable without turning a broad applicability statement into an unsupported claim.
State the outcome, time period or endpoint, and intended use. Identify relevant condition dimensions such as dose, population, formulation, and drug properties.
Use the observed values or categories from the validation studies, including units and study context. Do not replace discrete observations with an interval without labelling it as a span.
Check whether the validation observations match the intended combinations across dimensions. Mark exact observations, between-observation conditions, and conditions outside the observed range or categories.
Describe which regions are represented and which are untested. Keep the claim tied to the model version, endpoint, and conditions actually evaluated.
Interpretation, Alternatives, and Failure Modes
An observed range, a multidimensional envelope, and a list of directly observed conditions answer different questions. A range is concise for a continuous variable, such as dose, but suppresses gaps between observed values. A multidimensional envelope summarizes the extent of several variables but may contain combinations never tested. A condition-by-condition map is more informative about joint coverage, though it may be longer and less convenient to summarize. These are complementary descriptions, not interchangeable measures of validation strength.
| Description | What it tells you | Main limitation |
|---|---|---|
| Observed values and combinations | Which specific conditions are represented in data | Can be lengthy when many studies or observations are involved |
| Range or category summary | The extent of observed values for selected dimensions | Can conceal gaps and missing combinations |
| Intended-domain envelope | How broad the planned use is relative to the evidence | May imply coverage of conditions that were never observed |
A mapping can be misleading if study conditions are recorded too coarsely, units are inconsistent, or physiological categories are defined differently across studies. It can also overstate support if the validation endpoint differs from the intended prediction, or if observations are pooled across formulations or populations without preserving those distinctions. Check that condition definitions are comparable before interpreting apparent overlap.
Another limitation is that mapping is descriptive. A condition lying within an observed range is not automatically supported if the model’s response changes nonlinearly, if another relevant dimension differs, or if the observations are sparse. Conversely, an unobserved condition may be addressed by mechanistic reasoning, but that reasoning is not the same as direct validation evidence. The map clarifies the basis for a claim; it does not prove model adequacy in every region it labels as represented.
Common Mistake
A related mistake is to combine marginal coverage: “The studies include the intended doses and the intended patient groups, so the full domain is covered.” Coverage must be checked for the combinations that define the intended use. A dose observed only in healthy volunteers does not directly cover that dose in a disease subgroup.
Check Your Understanding
Answer each question using the distinction between exact observations, spans, and combinations.
- A validation set contains dose observations at 10, 30, and 60 mg. Is 45 mg directly observed? Is it within the observed dose span?
- The intended domain includes 25 mg in both healthy and impaired adults. Validation includes 25 mg only in healthy adults, and 50 mg only in impaired adults. Is the intended 25 mg impaired condition directly covered?
- A validation study includes eGFR values from 65 to 95 mL/min/1.73 m². If moderate impairment is defined as eGFR 30–59, is that group represented?
- Why can a new compound’s property value lying between values observed for other compounds fail to establish coverage of its full drug-property profile?
Solutions. (1) No. The directly observed set is \(\{10,30,60\}\) mg; 45 mg is within the span \([10,60]\) mg and is between observed dose levels. (2) No. The exact intended condition \((25\ \mathrm{mg},\mathrm{impaired})\) is absent, even though 25 mg and impaired participants occur separately in the data. (3) No. All observed values are at least 65, so none is in the defined 30–59 range. (4) Because other relevant properties, such as pathway or solubility, may differ, and the combination of properties for the new compound may not be represented by any validation compound.