Why Model Interfaces Need to Be Made Explicit
A chain of models is only as interpretable as the handoffs between its components. A physiologically based pharmacokinetic (PBPK) model may report concentration-time profiles under specified physiological and dosing conditions. A population pharmacokinetic (population PK) model may estimate population parameters and predict exposure for individuals. An exposure-response model may relate a defined exposure measure to an outcome. A simulation then uses that relationship to evaluate a proposed scenario. Connecting these outputs is not just drawing arrows: the team must say exactly what each component receives, what it returns, and what has to be true for the handoff to make sense.
An interface map is a structured record of those connections. It identifies each component’s role, inputs, outputs, assumptions, and the quantities passed to the next component. The map is not itself a pharmacological model, nor does it establish that the models are valid. Its purpose is to make the proposed chain inspectable: a reviewer can see where a quantity came from, how it is intended to be used, and which conditions limit its interpretation.
What an Interface Map Records
A useful map makes the relationship between models concrete enough to check before results are combined. For each component, record its decision role, inputs, outputs, assumptions, and applicable conditions. For each handoff, name the source and destination, specify the quantity and its units or data structure, and state whether it is an observation, prediction, estimate, or scenario definition. Also record any transformation applied at the boundary and who is responsible for it.
The distinction between a model output and a handoff is important. A PBPK model could produce many outputs, but only some may be intended for the next component. The map should identify those selected outputs rather than imply that every reported result flows downstream. It should also identify information that travels with a quantity: for example, dose, route, sampling times, physiological scenario, and model version. Without this context, a number can be copied accurately while being interpreted incorrectly.
| Map field | Question it answers |
|---|---|
| Component and role | What does this model contribute to the development decision? |
| Inputs | Which data, parameters, and scenario definitions does it use? |
| Outputs | What predictions, estimates, or derived quantities does it produce? |
| Assumptions and scope | Under what conditions are those outputs intended to apply? |
| Handoff contract | What exactly crosses the boundary, with what units and metadata, and for what use? |
| Checks and provenance | How can the handoff be verified and traced to its source? |
A compact map can use one row per component and a separate row per connection. A diagram is helpful for showing order and direction; a table is often better for documenting details. Either format should make it possible to follow a handoff back to its source and forward to its intended use.
Conditions for a Meaningful Handoff
A handoff is interpretable only when the source and destination agree on what the quantity represents. Before using it, check the quantity’s definition, units, time basis, and role. Check that its scenario metadata are retained and that the receiving component is designed to use information of that kind. If the source output is conditional on assumptions that do not hold in the receiving analysis, the map should flag that limitation rather than leave it implicit.
Each model also has its own assumptions. The interface map does not replace documenting them; it highlights the assumptions that matter at the boundary. For example, a PBPK prediction may depend on specified physiology and enzyme activity, while an exposure-response model may assume a particular exposure metric and outcome definition. A chain requires more than acceptable components considered separately: the output of each component must be a defensible input to the next for the intended use.
One simple way to express the logic is to let \(M_i\) denote component \(i\), \(Y_i\) its output, and \(H_i\) the handoff specification connecting it to component \(i+1\). The receiving input \(X_{i+1}\) is formed according to that specification:
Here, \(\theta_i\) represents the component’s parameters, and \(Z_i\) represents metadata or other information needed to interpret the output. This notation is a bookkeeping device, not an assumption that every handoff is a numerical transformation. The handoff might instead be a profile, a parameter set, a prediction function, or a defined dataset. The key requirement is that the map specifies what \(H_i\) does and what information it preserves.
The map supports a basic check of composability: can the receiving component interpret the handoff exactly as intended, under the conditions stated? If not, the chain has an interface problem even if each component appears plausible on its own. This check is distinct from proving that a model is correct; interface documentation makes assumptions visible but cannot validate them by itself.
Worked Example: Mapping a PBPK Prediction to a Population PK Review
Consider a hypothetical PBPK model for a 100 mg oral dose. Under one stated physiological scenario, it predicts an AUC of 12.0 mg·h/L and a maximum concentration \(C_{\max}\) of 1.20 mg/L. Under a second scenario, with a specified reduction in metabolic activity, it predicts an AUC of 15.0 mg·h/L. The intended population PK use is to review whether the fitted clinical PK model’s predictions across the relevant covariate range are broadly consistent with these mechanistic predictions. The PBPK outputs are not being used as observations.
Source output. The handoff consists of the two scenario-specific predictions: AUC values of 12.0 and 15.0 mg·h/L, plus the corresponding predicted concentration-time profiles. The map records the dose, oral route, scenario definitions, model version, and the time interval used to calculate AUC.
Derived comparison. The predicted AUC difference is \(15.0 - 12.0 = 3.00\) mg·h/L. Relative to the first scenario, this is \(3.00/12.0 = 0.250\), or a 25.0% higher predicted AUC. This calculation describes the difference between these two PBPK predictions; it is not an estimate of a clinical effect.
Destination and assumption. The population PK review receives the predictions as a mechanistic comparison, not as clinical data or as a parameter constraint. The comparison is interpretable only if the clinical model predictions being reviewed refer to compatible dosing and scenario conditions. The map records that condition explicitly and flags any difference for resolution before comparison.
Tracing the Full Workflow
For the workflow considered here, the interface map follows four connected components. The PBPK component supplies mechanistic predictions under defined scenarios. The population PK component uses clinical PK data to estimate population-level PK behavior and produce exposure predictions for the intended analysis. The exposure-response component relates its designated exposure measure to an outcome. The simulation component uses the exposure-response relationship and a specified scenario to predict outcomes relevant to a decision.
At each boundary, record the handoff quantity and its intended use. The PBPK-to-population-PK connection may carry mechanistic predictions for contextual review. The population-PK-to-exposure-response connection may carry individual exposure values paired with the corresponding outcome records. The exposure-response-to-simulation connection may carry the fitted response function and the information required to evaluate it for simulated exposures. The exact choice of quantity depends on the decision question; a map should not silently substitute a convenient output for the quantity that the receiving model requires.
The assumptions also travel conceptually, even when they are not numerical inputs. If a prediction is conditional on a specific scenario, retain that condition with the prediction. If a receiving component uses an exposure summary, state its definition and interval. If a simulation evaluates a particular regimen or population, name that scenario. These records make it possible to see when a downstream conclusion depends on an upstream condition.
Worked Example: Checking a Population PK Exposure Handoff
Suppose a hypothetical population PK model predicts concentrations for one individual at 0, 6, 12, and 24 hours after a dose: 0, 2.0, 1.0, and 0.20 mg/L, respectively. The exposure-response analysis has specified AUC from 0 to 24 hours as its exposure input. The interface map must therefore identify both the predicted concentration profile and the AUC calculation used to produce the handoff.
Calculation. Using the trapezoidal rule for the intervals between these times,
The three contributions are \(6.00\), \(9.00\), and \(7.20\) mg·h/L. Thus, \(\mathrm{AUC}_{0-24} = 22.2\) mg·h/L. The units follow from concentration in mg/L multiplied by time in hours.
Interface check. The handoff record names the individual, dose, 0–24-hour interval, concentration profile, calculated AUC, and units. It also states that this is a model-predicted exposure paired with the corresponding outcome record, not a directly measured concentration. Because the receiving analysis specified the same exposure quantity and interval, this example passes the definition check. If the receiving analysis instead required a different exposure summary, the map would flag the mismatch rather than silently relabel this AUC.
From Exposure-Response to Simulation
An exposure-response handoff should identify the response function and its intended input and output, not merely pass a table of fitted coefficients. For example, a logistic model may describe the probability of a binary response at a given exposure. The simulation component must receive the model’s coefficient values, the exposure scale used to define them, and the outcome definition. It must also know how to obtain the exposure values at which the function will be evaluated.
A simple calculation illustrates why the coefficient scale belongs in the interface contract. Suppose a hypothetical model is
The value \(x\) is dimensionless because AUC is divided by \(10\) mg·h/L. The map should preserve that definition; passing AUC in mg·h/L while treating it as \(x\) would change the model input.
Worked Example: Evaluating an Exposure-Response Handoff
For the hypothetical logistic model above, suppose the simulation supplies an AUC of 30.0 mg·h/L for a simulated individual. First calculate the model’s input:
The linear predictor is \(-2 + 0.5(3.00) = -0.500\). Converting from log odds to probability gives
Under this model, the predicted probability of response at this exposure is 0.378, or about 37.8%. This is a model-based probability conditional on the specified exposure and model, not a guarantee about an individual’s outcome. The handoff check confirms that the simulation used the dimensionless input defined by the exposure-response model and retained the stated response definition.
Diagnostics, Alternatives, and Limitations
Several practical checks help reveal interface failures before they become difficult to trace. Verify that every handoff quantity has a named source, a named destination, a definition, units where applicable, and the metadata needed to interpret it. Check that the receiving component is configured to use the quantity in the role stated in the map. Compare a small number of handoffs manually with the values passed by the software, and confirm that the same scenario labels and model versions appear in the analysis record.
Warning signs include a downstream input with no clear source; a quantity whose definition changes between components; scenario labels that are missing or inconsistent; a predicted value treated as if it were an observation; or a downstream result that cannot be reproduced from the documented inputs. A suspicious final result does not by itself identify the problem. Trace the value backward across interfaces: determine whether it was produced as documented, transformed as specified, and interpreted as intended at each receiving component.
A common pitfall is to assume that an arrow between two boxes is a sufficient interface definition. The wrong reasoning is, “Both models use exposure, so the PBPK or population PK exposure can be passed directly into the next model.” The correction is to name the exact exposure quantity, its units, its time interval, its scenario, and its role at the destination. Similar labels do not guarantee identical meanings.
A table-based interface register is often easiest to audit, while a diagram is often easiest to scan for overall flow. They are complementary representations, not competing statistical methods. A diagram alone can hide assumptions and transformations; a detailed table alone can obscure the structure of the chain. A combined map can provide both the overview and the boundary-level record.
An interface map has limits. It does not demonstrate that a component is adequately supported, that its assumptions hold in a new setting, or that predictions are accurate. Nor does a complete map remove uncertainty from the model outputs. Its contribution is narrower and practical: it exposes what is being passed and under which conditions, so model evaluation and decision-making can focus on an explicitly defined chain rather than an ambiguous sequence of outputs.
State what decision-relevant information it contributes, without treating its outputs as interchangeable with those of another component.
Record the quantity, definition, units or data structure, scenario metadata, and intended use in the receiving component.
Confirm that the receiving component can interpret the handoff as stated and that relevant source assumptions remain applicable.
Record model versions, transformations, and checks so a downstream result can be followed back to its inputs.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions below.
- A PBPK model reports a predicted \(C_{\max}\) of 1.5 mg/L, but the map records only “exposure” as the handoff. Name two details that should be added.
- A population PK model predicts an AUC of 18 mg·h/L. The exposure-response model defines \(x=\mathrm{AUC}/10\ \mathrm{mg\cdot h/L}\). What value of \(x\) should be passed?
- A simulation result changes substantially after a software update. What interface records should be checked first?
- Why is a prediction from one model not automatically an observation for the next model?
Solutions. (1) Record the precise quantity as \(C_{\max}\), its units, and the scenario and dose conditions; also state its intended role at the destination. (2) \(x=18/10=1.80\), a dimensionless input. The AUC should not be passed as though it were already \(x\). (3) Check the model versions, handoff definitions, transformations, scenario metadata, and the values actually passed across each boundary; reproduce a small handoff manually if needed. (4) A prediction is generated by a model under its assumptions, while an observation is recorded data. Their roles and uncertainty differ, so the map must state how a prediction is used rather than silently reclassifying it as data.