Why the Target Comes Before the Sensitivity Calculation
A PBPK model can predict concentrations in different tissues, at many times, under multiple doses and physiological conditions. A sensitivity analysis cannot answer a useful question until it specifies which prediction is to be examined. The choice is not just a reporting detail: a parameter may matter for one output or time window and have little influence on another.
For example, the question “Which assumptions affect exposure?” is incomplete. It could refer to total plasma exposure over one dose, unbound concentration at a target tissue near a particular time, or trough concentration during repeated dosing. Those predictions need not respond in the same way to a change in a model parameter.
A target is not a parameter and is not a sensitivity result. The target states what model prediction matters; the later sensitivity calculation describes how that prediction responds to changes in inputs. This tutorial concerns the target specification, not the calculation or ranking of sensitivities.
Specify the Prediction Precisely
First name the model output. “Concentration” alone is insufficient: identify whether it is total or unbound, plasma or tissue, and which model compartment or observable is intended. If the scientific question concerns an effect-site or organ exposure, a plasma endpoint should not be substituted merely because it is easier to report.
Next specify the time component. A single-time prediction, a maximum over a window, a minimum or trough, and an area under the concentration-time curve are different targets. A time window should include its start and end, with units, and the endpoint calculation should state how the model output is summarized over that window.
Then define exposure conditions. State the administered dose, route, formulation if relevant to the model, and whether dosing is single or repeated. For repeated dosing, state the interval and whether the target is from the first dose or a specified steady-state interval. Finally, describe the physiological scenario sufficiently to identify the model inputs defining it, such as age group, pregnancy status, organ impairment category or enzyme activity condition. “Typical adult” is not a reproducible scenario unless the model’s definition of that population is stated.
A target set may contain several predictions, but each should correspond to a distinct prediction question or a necessary complementary view of that question. Listing every available output at every simulated time is not automatically more informative. It can produce a large collection of results without a clear interpretation.
Match the Endpoint to the Question
The endpoint should represent the feature of the prediction that matters for the intended decision. AUC summarizes exposure integrated over time, whereas a peak emphasizes the highest predicted concentration. A trough can be relevant when sustained exposure between doses matters. A time-specific concentration is useful when the question concerns a particular sampling or effect time.
For a concentration \(C(t)\), the AUC from time \(t_0\) to \(t_1\) is defined as:
Its units are concentration multiplied by time, such as mg·h/L when concentration is in mg/L and time is in hours. AUC is an integrated summary, not a substitute for the entire time course. Two profiles can have the same AUC while having different peaks or different timing. Conversely, a peak alone does not describe total exposure.
The reason to preserve the target definition is straightforward. Let \(C(t;s,d)\) denote a model-predicted concentration at time \(t\), for physiological scenario \(s\) and dose regimen \(d\). A target might be a value at a fixed time, \(C(t^\ast;s,d)\), or a summary such as \(\int_{t_0}^{t_1}C(t;s,d)\,dt\). These are different functions of the predicted profile. Since they summarize different features, their responses to changed model inputs can differ. A result for one target therefore cannot be assumed to apply to another.
Worked Example: Defining a Single-Dose Exposure Target
A hypothetical model predicts total plasma concentration after a single 100 mg oral dose in a specified adult scenario. The predicted concentrations are 0 mg/L at 0 h, 4 mg/L at 2 h, 3 mg/L at 4 h and 1 mg/L at 8 h. The question is whether model inputs influence total plasma exposure during the first 8 h.
The target should be stated as total plasma AUC from 0 to 8 h after a single 100 mg oral dose in the specified adult scenario. Its units are mg·h/L. For these discrete predictions, use the trapezoidal approximation, which sums the area of a trapezoid over each adjacent time interval:
Substituting the stated values gives:
Thus 19 mg·h/L is the hypothetical target prediction for that dose, window and scenario. A peak-concentration target would answer a different question: among the listed predictions, the maximum is 4 mg/L at 2 h. Neither endpoint is universally preferable. The question about integrated exposure supports the AUC target; a question about the highest concentration supports the peak target.
Time Courses, Scenarios and Complementary Targets
A summary endpoint is useful when it corresponds to the prediction question, but it can conceal structure. AUC can be unchanged even if a profile’s peak and late concentrations shift in opposite directions. A single-time target can miss an effect occurring earlier or later. When timing or shape is central, the concentration-time profile over a stated window may itself be the target, or it may be examined alongside a prespecified summary.
The following arithmetic illustrates why endpoint choice matters. Suppose two hypothetical profiles are represented by concentrations at 0, 1 and 2 h, with linear interpolation between points. Profile A has values 0, 4 and 0 mg/L; Profile B has values 0, 2 and 2 mg/L. Their trapezoidal AUCs are:
These particular profiles do not have equal AUC. If Profile B instead has values 0, 2 and 4 mg/L, its AUC is \(1+3=4\) mg·h/L, the same as Profile A, while its peak is 4 mg/L at 2 h rather than 4 mg/L at 1 h. An AUC target alone would not identify that difference in peak timing. If peak timing matters, the profile or a peak-time target must be included.
Physiological scenarios also belong in the target definition. Sensitivity in a healthy adult scenario does not establish sensitivity in organ impairment, pregnancy or another population. A scenario comparison should preserve the prediction question—such as the same endpoint, window and intended dose—while clearly identifying which physiological conditions differ. If the dose itself is adjusted between scenarios, say so: the resulting comparison addresses predictions under those respective regimens, not the isolated effect of physiology at a common dose.
Worked Example: Selecting a Repeated-Dose Target
A hypothetical PBPK model is being assessed for a drug given every 12 h. The practical question is whether predicted concentration remains adequate just before the next dose in a specified renal-impairment scenario. The model predicts the following total plasma concentrations during the final interval at steady state: 1.8 mg/L at 0 h after the dose, 3.0 mg/L at 4 h, 2.4 mg/L at 8 h, and 1.5 mg/L immediately before the next dose at 12 h.
The question concerns the end-of-interval concentration, so the target is total plasma trough concentration immediately before the next dose at steady state, under the specified every-12-hour regimen and renal-impairment scenario. By the supplied prediction, this target is 1.5 mg/L. The time is \(12\) h after the dose, just before redosing; the regimen and steady-state condition prevent confusion with a single-dose concentration at 12 h.
AUC over this interval would be a complementary target only if total exposure during the interval were also relevant. Using the trapezoidal rule, the predicted AUC from 0 to 12 h is:
The trough target is 1.5 mg/L, while interval AUC is 28.2 mg·h/L. The units and interpretation differ. If the question is whether the model predicts a minimum concentration at the end of the dosing interval, AUC does not replace the trough. If the question is overall interval exposure, the AUC may be more directly relevant.
A Practical Target-Selection Workflow
State the decision or scientific concern in terms of a predicted concentration, exposure summary, timing feature or other model output.
Name the compartment, concentration form and endpoint. Select AUC, peak, trough, a time-specific concentration or a profile according to the question.
Give the window or time point, dose, route, interval and single-dose or repeated-dose condition. State the steady-state interval if applicable.
Identify the physiological scenario and any population summary, units, interpolation or endpoint calculation needed for an unambiguous prediction.
Confirm that the model is simulated over the required times and conditions, and that each selected target informs the stated question rather than duplicating another target without purpose.
Worked Example: Choosing Between a Peak and a Time-Specific Target
A hypothetical interaction assessment asks whether a predicted unbound plasma concentration near a pharmacodynamic assessment time could change when the interaction scenario is used. The intended dose is 50 mg orally once, and the assessment occurs 6 h after dosing. The model predicts unbound concentrations of 0.20 mg/L at 4 h, 0.32 mg/L at 6 h and 0.25 mg/L at 8 h in the interaction scenario.
The most direct target is unbound plasma concentration at 6 h after a single 50 mg oral dose in the specified interaction scenario. Its predicted value is 0.32 mg/L. The stated question is about the assessment time, not the maximum. Selecting \(C_{\max}\) instead would answer a different question, even if the peak is also of interest.
If the additional question is whether a peak occurs near or above a relevant concentration, a separate peak target could be defined over a clinically meaningful window, for example from 0 to 12 h. The window must be given because a maximum over 0 to 4 h need not equal a maximum over 0 to 12 h. The two targets are justified as complementary only if both the assessment-time prediction and the peak are relevant to the intended interpretation.
Assumptions, Diagnostics and Alternatives
Target interpretation depends on several basic conditions. The model must generate the chosen output for the full requested window; dose, route and regimen must be encoded as specified; and the scenario must map to defined physiological inputs. A steady-state target requires that the simulated system has reached steady state under the stated regimen, rather than merely being evaluated after an arbitrary number of doses. A numerical summary also depends on a stated calculation method, especially when model output is recorded at discrete times.
Check for practical warning signs before proceeding. A target may lie outside the simulated time range; a peak can be missed if the output is saved too sparsely; a trough can be taken at the wrong side of a dose; or AUC units can be inconsistent with the time scale. A target named “hepatic exposure” may be ambiguous if it does not distinguish tissue concentration from plasma concentration or total from unbound drug. A scenario label may be too vague to reproduce.
The main alternative is to use the full concentration-time profile rather than only a scalar summary. A profile preserves timing and shape but can be harder to communicate and entails multiple time-specific predictions. A scalar endpoint is compact and can closely match a decision question, but discards information. These approaches can be complementary: use a prespecified profile window to inspect the time course and one or more scalar targets to summarize decision-relevant features.
Another alternative is to select a broad grid of doses, scenarios and endpoints for exploratory coverage. This can reveal where predictions might warrant further examination, but it should not be presented as a substitute for defining the primary question. Large target sets can create redundant outputs, obscure the interpretation and make it difficult to distinguish planned questions from post hoc selections. Record the rationale and the specification for each target before interpreting its sensitivity results.
Check Your Understanding
For each question, identify a suitable target and explain the key specification. Solutions follow the questions.
- A model is used to predict total plasma exposure during the first 24 h after a single intravenous dose. What target should be specified, and what units would it have if concentration is in mg/L?
- A repeated-dose question concerns concentration immediately before the next dose after dosing every 8 h. Name the endpoint and two details needed to make it unambiguous.
- Why may AUC alone be insufficient when the prediction question concerns the time of the maximum concentration?
- A prediction is sought for unbound liver concentration at 3 h after a dose in a pregnancy scenario. Identify four parts of the target specification.
- A team compares a healthy scenario at one dose with an impairment scenario at a different dose. What must be stated before interpreting the comparison?
Solutions. (1) Specify total plasma AUC from 0 to 24 h after the stated single intravenous dose; its units are mg·h/L. (2) Specify the steady-state or otherwise intended dosing interval and scenario, as well as the concentration form and compartment; the target is the pre-dose trough at 8 h under the every-8-hour regimen. (3) AUC integrates concentration over time and does not identify when the maximum occurs; use a peak-time target or inspect the profile over a stated window. (4) Specify unbound liver concentration, the 3 h time point, the dose and regimen, and the pregnancy scenario; include units and route for reproducibility. (5) State that dose differs between scenarios and describe both regimens. The comparison then concerns predictions under the two respective conditions; it does not isolate the physiological scenario at a common dose.