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A trigger calibrated on one protocol may not keep the same sensitivity and specificity after temperature, thickness, sensor or visit rules change. The useful question is not whether calibration exists, but which conditional error rates can travel to the target experiment.
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Chapter contents
Choose the route closest to the decision, or read from Chapter 1. The chapters remain open; these grouped routes are a navigable index.
Route 1 · Define the evidence
Route 2 · Work the ledgers
Route 3 · Transfer the method
Route 4 · Check limits and evidence
Route 5 · Ask and continue
CHAPTER 1 OF 12 · DEFINE THE EVIDENCE
1. Pooled calibration can hide differential error
A clouding alarm may detect a latent transition well at high contrast and poorly in thin films or low temperatures. If error rates depend on covariates, one pooled sensitivity is a mixture over the validation cohort rather than a universal sensor property.
Differential error is not automatically malicious or unusable. It means the observation model changes with a condition related to the state, outcome or sampling process. Analysis must retain those conditions instead of averaging them away.
CHAPTER 2 OF 12 · DEFINE THE EVIDENCE
2. Transport is a conditional question
Calibration transport asks whether the conditional relation among the true state, observed trigger and relevant covariates is shared between validation and target protocols. Even when stratum-specific sensitivity transfers, the pooled value changes if the covariate mix changes.
Measure the covariates that drive threshold performance: temperature, thickness, ageing time, sensor gain, operator, batch and signal-to-noise ratio. A transport model cannot adjust for a hidden firmware change or an unrecorded trigger override.
CHAPTER 3 OF 12 · WORK THE LEDGERS
3. A stratified validation ledger
Suppose the reference assay identifies 100 true transition windows. Trigger sensitivity differs by thermal condition.
| Condition | True transitions | Trigger positives | Sensitivity |
|---|---|---|---|
| High contrast | 80 | 72 | 90% |
| Low contrast | 20 | 12 | 60% |
| Pooled validation | 100 | 84 | 84% |
| Target mix | 30% high / 70% low | Not yet observed | Requires reweighting |
If the target protocol contains mostly low-contrast windows, importing 84% sensitivity overstates detection.
CHAPTER 4 OF 12 · WORK THE LEDGERS
4. Worked transported sensitivity
Assume the stratum-specific sensitivities of 90% and 60% transport. In a target protocol with 30% high-contrast and 70% low-contrast windows, standardisation gives 0.30×0.90 + 0.70×0.60 = 0.69, or 69% sensitivity.
| Quantity | Validation mix | Target mix |
|---|---|---|
| High-contrast share | 80% | 30% |
| Low-contrast share | 20% | 70% |
| Weighted sensitivity | 84% | 69% |
| Difference | — | −15 percentage points |
If stratum-specific performance also changes, reweighting is insufficient. A bridge sample measured under both protocols is then more credible.
CHAPTER 5 OF 12 · WORK THE LEDGERS
5. Specificity needs the same treatment
Sensitivity is estimated among true target states; specificity is estimated among true non-target states. Their relevant covariate distributions can differ. Reweight each conditional error parameter using the covariates appropriate to its reference population.
Predictive values add the prevalence of the latent state. They can change even when sensitivity and specificity transport perfectly. Report which direction of conditioning is used because P(trigger|state) and P(state|trigger) require different transport assumptions.
CHAPTER 6 OF 12 · TRANSFER THE METHOD
6. Design bridge validation
A bridge study samples positives, negatives and difficult conditions from the target protocol, then applies the reference assay. Over-sampling rare strata is efficient if analysis restores the intended target weights.
Include quiet windows so false negatives are observable. Validation only after alarms can estimate false-positive composition but cannot recover sensitivity. If the assay is destructive, use matched replicates or a design that recognises the intervention.
CHAPTER 7 OF 12 · TRANSFER THE METHOD
7. Changed-context transfer: optical cure monitoring
Transfer the method to an optical trigger for resin cure. Lamp intensity and specimen thickness change contrast, so carry condition-specific error rates into the production protocol rather than one pooled laboratory value.
The transfer check asks whether the reference assay measures the same cure state, whether target covariates overlap the validation range and whether the trigger changes the inspection schedule. Extrapolation beyond overlap should remain a sensitivity scenario.
CHAPTER 8 OF 12 · TRANSFER THE METHOD
8. Connect the observation branch
The trigger-misclassification guide separates state, signal and visit. The informative-inspection guide handles visits created by the trigger.
Use probabilistic mechanism attribution when the final exit label is also uncertain.
CHAPTER 9 OF 12 · CHECK LIMITS AND EVIDENCE
9. Limits and identifiability
Sparse validation strata trade bias for variance: a flexible covariate-specific model can become unstable where few reference states are observed. Pooling may be necessary, but the pooling rule and residual heterogeneity should be visible.
Transport assumptions cannot be verified entirely from the main dataset because the true state is missing there. Negative controls, bridge samples and repeated calibration reveal failures, but unmeasured differential error remains a sensitivity problem.
CHAPTER 10 OF 12 · CHECK LIMITS AND EVIDENCE
10. Practical evidence checklist
Archive protocol versions, raw trigger signals, reference assays, covariates, sampling probabilities, missed validations and the direction of every conditional error parameter. Plot sensitivity and specificity by condition before pooling.
Compare pooled, stratified, standardised and bridge-sample results. Report overlap, extreme weights, sparse cells and conclusions under plausible departures from conditional transport. Keep uncertainty in error parameters inside the final mechanism map.
CHAPTER 11 OF 12 · ASK AND CONTINUE
11. Frequently asked questions
Can I transport a receiver-operating curve?
Only after checking that the conditional score distributions and relevant covariate mix are sufficiently comparable. A common threshold can perform differently across protocols.
Is covariate adjustment always better?
It reduces bias when the covariate explains error and is measured well, but sparse strata can greatly increase variability.
Does a fresh positive-control sample suffice?
Not by itself. Positives inform sensitivity; specificity requires true non-target states, and both need target-relevant conditions.
CHAPTER 12 OF 12 · ASK AND CONTINUE
12. Sources and next reading
Edwards and colleagues study covariate-differential outcome misclassification. Ross and colleagues examine transporting measurement-error parameters from external validation data. Edwards and colleagues develop flexible adjustment with external validation. The polymer ledgers above are original teaching examples.
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