Why Transport Requires More Than Passing a Prediction Forward
An integrated evidence chain may connect dose and formulation to exposure, exposure to response, and response to a trial outcome. A prediction from that chain is conditional on the scenario represented by its inputs and assumptions. If the proposed use changes the dose, formulation, population, or trial conditions, the relevant question is not simply whether the same model can produce a number. It is whether the links used to produce that number still represent the target scenario.
Transporting a prediction means using evidence from a source scenario to predict an outcome in a specified target scenario. A scenario includes the intervention or regimen, relevant patient characteristics, and conditions that can affect the modeled outcome. A change may be transportable if the affected inputs are represented correctly and the conditional relationships in the chain remain applicable. Otherwise, the prediction may be extrapolation beyond what the evidence supports.
This definition is deliberately conditional. It does not say that predictions are portable merely because the same model equations can be evaluated. For example, a pharmacokinetic model may calculate exposure at a higher dose, but that calculation is not justified if absorption becomes saturated outside the observed dose range. A response model may predict an outcome at that exposure, but only if its exposure-response relationship remains applicable in the target population and trial setting.
What Must Remain Applicable?
For each handoff in the chain, identify what changes and what is assumed to remain stable. A dose change primarily challenges the dose-exposure relationship. A formulation change may affect bioavailability, absorption rate, or both. A population change may alter clearance, sensitivity, or the distribution of effect modifiers. A trial-condition change may affect adherence, concomitant care, endpoint ascertainment, or the baseline outcome rate.
A useful formalization is to let \(Z\) denote relevant patient and trial characteristics, \(R\) the specified regimen, and \(Y\) the outcome. Let \(m_s(e,z,r)\) be the source model’s conditional prediction for the outcome given exposure \(e\), characteristics \(z\), and regimen context \(r\). A target prediction can be formed by averaging conditional predictions over the target distribution of inputs:
Here \(f_t\) is the joint distribution of the relevant inputs in the target scenario, including the exposure distribution induced by the target regimen. This calculation is justified only if the conditional relationship represented by \(m_s\) is applicable in the target and the inputs used in the integration are defined and measured compatibly. If the outcome model is conditional on exposure and patient characteristics but not on trial context, that omission is acceptable only when the omitted context does not alter the conditional outcome relationship.
Three checks are central. First, structural applicability: the mechanisms or conditional relationships used by each component must remain appropriate. Second, input support: the target values and combinations of inputs must be supported by data or by a defensible mechanistic basis. Third, scenario alignment: the modeled dose, formulation, population, endpoint, and trial conditions must match the intended target. These checks apply to the chain as a whole, not only to the final outcome model.
A Justification for Target Standardization
The standardization formula follows from averaging a conditional prediction over the target inputs. For a discrete set of target strata \(z\), the law of total expectation gives the target mean as the sum of each stratum’s conditional mean weighted by its target prevalence. The continuous version replaces the sum with an integral.
If the source conditional model is valid in the target, so that \(E_t(Y\mid e,z,r)=m_s(e,z,r)\) over the target support, substitution gives the transport formula above. If that equality fails—for example, because a trial-specific co-therapy changes the outcome relationship and is omitted—averaging the source conditional prediction over target inputs does not repair the misspecification. Likewise, if the target includes input combinations absent from the data and unsupported by scientific knowledge, the equality is an unverified extrapolation rather than an established transport result.
The joint distribution matters. If exposure and a patient characteristic are associated, separately averaging exposure and patient characteristics and then combining those averages can create combinations that are rare or absent in the target. Use the target joint distribution, or a conditional factorization that preserves the target dependence.
Worked Example: Changing Dose Under a Linear Pharmacokinetic Model
Suppose a hypothetical model predicts steady-state AUC over a dosing interval as \(AUC_{\tau}=FD/CL\), where \(F\) is bioavailability, \(D\) is dose per interval, and \(CL\) is clearance. In the source scenario, the hypothetical formulation has \(F=0.80\), the dose is \(100\) mg per interval, and \(CL=10\) L/h.
The source prediction is:
Consider a target scenario using the same formulation and population but a dose of \(150\) mg per interval. If bioavailability and clearance remain unchanged and the model’s dose-proportionality assumption holds over this range, then:
The predicted AUC increases by \(4.00\ \mathrm{mg\cdot h/L}\), or \(50.0\%\), matching the \(50.0\%\) dose increase. This transport is conditional on unchanged \(F\) and \(CL\), dose proportionality, and compatible dosing conditions. The arithmetic alone does not establish those assumptions. If the higher dose changes absorption or clearance, the simple scaling is not justified.
Transporting Across a Population and Formulation Change
When the target population differs from the source population, an overall source average is generally not the right prediction. If the conditional response relationship is stable given the relevant characteristics, the target average can be calculated using the target composition. A formulation change may also alter the exposure distribution that enters the response model; this change should be represented rather than ignored.
Worked Example: Standardizing a Response Prediction
Consider a hypothetical binary response model with predicted response probability \(p=0.10+0.02E+0.003(Z-50)\), where \(E\) is exposure in mg·h/L and \(Z\) is age in years. Assume the probabilities are valid over the stated values and that this conditional relationship applies to both scenarios. In the source scenario, exposure is \(10\) mg·h/L and the population is split equally between ages 40 and 60.
For age 40, the predicted probability is \(0.10+0.02(10)+0.003(40-50)=0.270\). For age 60, it is \(0.10+0.02(10)+0.003(60-50)=0.330\). The source average is therefore:
Now suppose a hypothetical target formulation produces exposure of \(8\) mg·h/L, and the target population is \(30\%\) age 40 and \(70\%\) age 60. The conditional predictions are \(0.10+0.02(8)+0.003(40-50)=0.230\) and \(0.10+0.02(8)+0.003(60-50)=0.290\). Standardizing to the target mix gives:
The target model prediction is a response probability of \(0.272\), or \(27.2\%\). This is not obtained by applying the source average of \(30.0\%\) unchanged. It reflects both the specified target exposure and the target age distribution. The result depends on the hypothetical response relationship remaining valid in the target and on the exposure and age inputs being represented correctly.
When Trial Conditions Change
A trial setting can change the prediction even when dose, formulation, and population appear similar. For example, background therapy, adherence support, rescue medication rules, follow-up duration, or endpoint measurement may differ. A changed condition can be handled by adding it as a relevant input and predicting over its target distribution only when the conditional outcome relationship is supported. If it changes the relationship itself, a simple reweighting is inadequate.
Worked Example: A Changed Background-Therapy Mix
Suppose a hypothetical trial model predicts an endpoint probability of \(0.260\) without a specified background therapy and \(0.410\) with it, for patients at the same exposure and with the same other modeled characteristics. In a source trial, \(10\%\) of participants receive that therapy; in a target trial, \(50\%\) do. Assume for illustration that the conditional probabilities apply in both trials and that the therapy is a defined scenario characteristic.
The source-trial average is \(0.90(0.260)+0.10(0.410)=0.275\), or \(27.5\%\). The target-trial average is \(0.50(0.260)+0.50(0.410)=0.335\), or \(33.5\%\). The target prediction differs because the target mix differs. This calculation is not justified if the therapy is recorded or administered differently in the target, or if other trial conditions modify the conditional probabilities and are not represented in the model.
Diagnostics, Alternatives, and Limitations
Transport assessment is not a single numerical test. It is a structured evaluation of whether each changed scenario feature is represented by a valid input or requires a new model component. Useful diagnostics include comparing source and target ranges for dose, exposure, covariates, and trial conditions; checking whether important combinations occur in both; and examining whether residual patterns or predictive discrepancies vary across the changed conditions. A target value outside the source range is a warning, not automatic proof of failure: mechanistic support may justify extrapolation, but the added assumptions should be made explicit and tested where possible.
A practical assessment proceeds in order:
State the dose or regimen, formulation, target population, endpoint, and trial conditions precisely.
Identify which component relationships and inputs could be affected by each difference.
Compare target inputs with component evidence and assess whether relevant conditional relationships remain credible.
Transport with explicit assumptions, add or revise a component, obtain local bridge data, or report that the prediction is not adequately supported.
Direct transport keeps the source component relationships and changes the target inputs. Recalibration adjusts a model’s predictions using external information, but does not by itself establish that every link is valid under a changed mechanism or population. Refitting with target data can improve local fit, though it may be infeasible with sparse data and may no longer preserve the source evidence structure. A bridge study directly measures the relevant target conditions and can test or estimate the uncertain link, at the cost of additional time and resources.
| Approach | Useful when | Main limitation |
|---|---|---|
| Transport with standardization | Conditional relationships are credible and target inputs can be represented | Does not resolve unsupported inputs or changed mechanisms |
| Recalibration | External target data indicate a systematic prediction shift | May correct average fit without correcting a misspecified component |
| Refitting or model revision | Target data are sufficient and a component relationship may differ | Can be unstable with limited target observations |
| Bridge data | A specific transport assumption needs direct evaluation | Requires a suitable study and may not cover all target conditions |
A common mistake is to carry a source prediction into a new scenario because the model accepts the new dose or covariate values. That confuses computational possibility with evidential support. The correction is to identify the assumptions that permit each handoff, check whether the target inputs are supported, and distinguish a modeled prediction from a validated target prediction. If a key condition is unsupported, report the prediction as extrapolative and state what additional data or model structure would address the gap.
Check Your Understanding
Answer each question, then compare with the solutions.
- A target dose is twice the source dose. Name two conditions needed before predicting twice the source AUC using proportional scaling.
- Why may the source population-average response probability fail to represent the target population?
- A target population includes a covariate combination absent from the source data. What does this imply for transport?
- A new trial changes endpoint ascertainment, but the integrated model contains no ascertainment component. Is reweighting patient characteristics enough?
Solutions. (1) The dose-exposure relationship must be proportional over the dose range, and bioavailability and clearance must remain applicable; dosing conditions must also be compatible. (2) The target may have a different distribution of effect-modifying characteristics, so the conditional predictions need to be averaged over the target distribution rather than using the source average. (3) The target involves a support gap. Transport is not established by the source data alone; mechanistic justification, added data, or a qualified extrapolation is needed. (4) No. If ascertainment changes how the endpoint is observed or defined, it can alter the outcome relationship or measurement process. It must be represented and justified, or the prediction should be treated as unsupported.