Why a PBPK Prediction Needs an Applicability Domain
A PBPK model can produce a numerical prediction for many inputs, including inputs unlike those used to develop or evaluate it. The ability to calculate an output does not establish that the model is supported for that use. Before interpreting a prediction, specify the conditions under which the model has a relevant evidentiary basis. This bounded region of use is its applicability domain.
For a PBPK prediction, the domain may depend on the compound, population, biological pathways represented, dose, route, and physiological conditions. These dimensions describe what is being predicted and under what circumstances. A model may be supported for an adult population at one dose and route, yet not for children, a different formulation, or a condition that changes a relevant physiological process. The introductory material on mapping evidence to PBPK model components provides a basis for connecting evidence to model features; here the focus is on using that evidence to define the model’s supported scope.
The domain is not necessarily a simple interval or a rectangular combination of independent ranges. Some dimensions are categorical, such as oral versus intravenous administration. Others are continuous, such as dose or age. Some combinations may be supported even when other combinations using individually familiar values are not. The domain should therefore describe supported combinations, not merely list plausible values for each input separately.
Representing the Supported Prediction Space
Let \(x\) denote the set of conditions for one proposed prediction. It may include a compound description, the population, a pathway or process relevant to the prediction, dose, route, and physiological state. Let \(D\) denote the documented applicability domain for that prediction. In the simplest classification, the scenario is within the domain when its conditions are represented in \(D\), and outside when they are not. A partly supported scenario has some conditions represented but also has a material dimension or combination that is not supported.
This notation is a bookkeeping device, not a claim that every PBPK model uses these as independent mathematical inputs. Identify dimensions that matter to the particular prediction. For example, a prediction of systemic exposure after oral dosing may depend on formulation and absorption-related pathways, whereas a prediction of intravenous exposure does not involve absorption from the gut in the same way. Record the level of detail needed to distinguish relevant cases: “adult” may be too broad if evidence covers only healthy adults within a specified age range.
A useful domain statement makes boundaries explicit. For each dimension, record which values, categories, or combinations are supported and what evidence supports that statement. Separate “not evaluated” from “evaluated and found unsuitable”: absence of supporting evidence does not prove the model fails, but it does mean support for that use has not been established.
- Compound: identify the compound or the adequately described class, including features that matter to the prediction.
- Population: describe the relevant demographic or clinical group and any restrictions, such as age range or health status.
- Pathways: state which disposition or response processes are represented and for which the prediction has supporting evidence.
- Dose and route: specify supported dose range, administration route, and relevant formulation or regimen features.
- Physiological conditions: specify conditions such as organ function or other states that may alter the processes relevant to the prediction.
Why Separate Ranges Can Overstate Support
Suppose evidence covers a set of observed or evaluated combinations. A tempting summary is to report the range of each input separately and treat every combination within those ranges as supported. That inference is valid only if the evidence supports the combinations being claimed. Separate marginal ranges do not establish joint coverage.
For example, evidence might include adults with normal organ function at low dose and adults with a specified impairment at high dose. Reporting “both doses and both physiological states were studied” does not establish support for low dose in the impaired group or high dose in the normal group. Those cross-combinations may require evidence or justification of their own.
The product on the right represents all combinations formed from the listed marginal sets. The supported domain \(D\) may be a strict subset of that product. This is the key reason to document joint conditions rather than infer a full Cartesian product from separate ranges.
Worked Example: Checking Compound, Population, and Route Coverage
Hypothetical model description. A PBPK model has been evaluated for Compound A and Compound B in healthy adults aged 18–65 years. The evaluation includes oral immediate-release dosing and intravenous dosing, but evidence for Compound B is available only for the oral route. A proposed prediction concerns Compound B given intravenously to a 40-year-old healthy adult.
Step 1: List the proposed conditions. Compound B; healthy adult aged 40 years; intravenous route; the dose and relevant pathways are to be specified in the final prediction record.
Step 2: Compare each condition with documented support. Compound B is represented. The age and health status fall within the described population. But the intravenous route is not supported for Compound B; it was evaluated for Compound A only.
Conclusion. The proposed prediction is partly within, but not fully within, the documented domain. It is not sufficient that the model has been evaluated for Compound B orally and for intravenous dosing of a different compound. The combination of this compound and this route lacks the stated support. This classification identifies a support gap; it does not by itself establish whether the numerical prediction is inaccurate.
A Practical Procedure for Defining and Applying the Domain
The procedure below assumes that the prediction and context of use are specified, the relevant model components and evidence can be identified, and the domain boundaries are recorded at a level that distinguishes material conditions. It also assumes that the same terms are used consistently when describing the evidence and the proposed prediction. If those assumptions are not met, a domain classification may look precise while concealing ambiguity.
State the compound, predicted quantity, population, route, dose or regimen, and physiological conditions. Include only dimensions relevant to the prediction, but do not omit a condition that could change a relevant process.
For each dimension, identify the compounds, populations, pathways, doses, routes, and conditions represented by the available evidence and model evaluation. Record combinations where joint coverage matters.
Describe supported values or categories, any restrictions, and conditions that have not been evaluated. Do not silently extend an observed range or assume that separate ranges imply support for every combination.
Compare the proposed conditions with the documented domain dimension by dimension and as a joint scenario. Report whether it is within, partly within, or outside the stated support, and name any gap.
The logic of the comparison is straightforward. If the domain consists of supported combinations, a scenario is fully within it only when its relevant conditions jointly belong to that set. Checking each coordinate against a separate range is not enough unless joint coverage has also been established. Conversely, a single unsupported, relevant condition is sufficient to prevent a claim of full coverage.
This implication concerns domain membership only. It does not assert that the prediction is accurate, that uncertainty is small, or that the prediction is suitable for a particular decision. Those are separate questions.
Worked Example: Dose Range and Route Boundaries
Hypothetical model description. A model’s documented domain covers Compound C, healthy adults, oral administration of an immediate-release formulation, and doses from 10 to 100 mg inclusive. Evidence supports this dose range for the stated route and formulation. Consider three proposed predictions: (a) 50 mg orally using the same formulation; (b) 150 mg orally using the same formulation; and (c) 50 mg intravenously.
(a) 50 mg orally. The dose satisfies \(10 \leq 50 \leq 100\) mg, and the compound, population, route, and formulation match the description. Subject to the remaining physiological conditions also matching, this scenario is within the stated domain.
(b) 150 mg orally. The proposed dose exceeds the upper boundary by \(150 - 100 = 50\) mg. Its dose is therefore outside the documented range, even though the compound, route, and formulation match. A model may calculate an output at 150 mg, but calculation alone does not extend the domain.
(c) 50 mg intravenously. The dose is numerically within the oral dose range, but the route differs. Since route is a separate domain dimension, the oral support does not establish support for intravenous dosing. This scenario is outside the stated domain for route, regardless of its dose value.
Conclusion. The three cases are not interchangeable merely because they use the same compound and a dose number that appears in the supported range. Dose range, route, and formulation must be interpreted together.
Documenting Intersections and Partial Support
A compact table can make a domain auditable, provided it distinguishes supported combinations from separate marginal descriptions. Use specific entries rather than general labels such as “typical dose” or “adult population.” A table might look like the following for a hypothetical model:
| Dimension | Documented support | Boundary or gap to record |
|---|---|---|
| Compound | Compound C | No claim for related compounds without separate support |
| Population | Healthy adults aged 18–65 years | Children and adults over 65 years not represented |
| Pathways | Processes represented and evaluated for the stated prediction | State any unevaluated pathway relevant to the intended use |
| Dose and route | 10–100 mg orally, immediate-release formulation | Other routes, formulations, and doses not covered by this entry |
| Physiological conditions | Conditions matching the evaluated healthy-adult scenario | Altered physiology requires a separate domain statement |
A table should not imply that every row is independently sufficient. Its entries describe a joined scenario: Compound C in the stated population, with the represented pathways, under the specified dose, route, formulation, and physiological conditions. If evidence covers only selected combinations, list them explicitly or qualify the table so readers cannot mistake marginal coverage for joint coverage.
Worked Example: Detecting a Joint-Coverage Gap
Hypothetical evidence summary. A model has supporting evaluations for (1) 20 mg in adults with normal renal function and (2) 80 mg in adults with mild renal impairment. Both conditions use the same compound and oral route. A proposed prediction is 20 mg in adults with mild renal impairment.
Step 1: Summarize the separate values. The evaluated doses are 20 and 80 mg; the evaluated physiological groups are normal renal function and mild renal impairment. A marginal summary would list both doses and both groups.
Step 2: Preserve the observed combinations. The actual supported pairs are \((20\text{ mg},\text{normal renal function})\) and \((80\text{ mg},\text{mild renal impairment})\). The proposed pair \((20\text{ mg},\text{mild renal impairment})\) is not one of them.
Step 3: Classify the proposal. The scenario uses a dose and physiological category that each appear in the marginal summary, but their joint combination is not documented as supported. It is therefore not fully within the stated joint domain. The evidence summary should report this as a coverage gap rather than silently treating the two marginal ranges as a complete grid.
Diagnostics, Comparisons, and Limitations
Useful diagnostics focus on whether the domain description is internally consistent and adequately specific. Check that units and range boundaries are clear, that population labels have operational meaning, and that the route and formulation are not conflated. Compare the proposed prediction against all relevant dimensions and explicitly inspect combinations. A domain that changes depending on whether the reader interprets “adult,” “dose range,” or “supported compound” broadly is not sufficiently documented.
A common mistake is to reason: “The model can run these inputs, and each input falls within a range seen somewhere, so the prediction is within scope.” The correction is that computational feasibility is not evidence of support, and separate marginal ranges do not establish support for every combination. The relevant question is whether the specific proposed scenario is represented by the documented domain.
The domain is also not a substitute for a model’s uncertainty analysis or for an assessment of evidence quality. A prediction can lie inside a broadly stated domain yet retain substantial uncertainty. Conversely, a scenario outside the documented domain may still be scientifically plausible, but its use is not supported by that domain statement. Avoid interpreting “within domain” as “proven correct” or “outside domain” as “proven wrong.”
Compared with a single broad statement such as “the model applies to adults,” a multidimensional domain is more informative because it identifies boundaries and combinations. Compared with an exhaustive list of every possible input value, a structured set of dimensions and supported combinations is more usable. The appropriate detail depends on the prediction: too little detail hides meaningful gaps, while irrelevant detail obscures the conditions that actually define scope.
Check Your Understanding
Answer each question, then compare with the solutions below.
- A model is supported for oral dosing of Compound D in adults aged 18–60 years. A proposed prediction is for the same compound and route in a 70-year-old adult. Is it fully within the stated domain? Why?
- Evidence covers doses of 10 mg in a normal physiological state and 40 mg in an altered state. Does that establish support for 10 mg in the altered state?
- A model returns an output for a dose above its documented range. What does that establish about applicability?
- State two reasons why domain membership should not be interpreted as proof that a prediction is accurate.
Solutions. 1. No. The proposed age is outside the stated 18–60-year population boundary, so full domain membership has not been established. 2. No. The evidence describes two combinations; separate dose and state values do not establish support for their untested cross-combination. 3. Only that the software can produce an output for those inputs. It does not show that the prediction is supported by the documented domain. 4. Domain membership records the scope represented by the stated evidence; it does not guarantee small uncertainty or correct predictions. Accuracy and uncertainty require separate assessment.