Proposition 5III.7.P0575 of 76 in the corpus
Domain shift is the failure that survives every internal check.
Split by patient, calibrate, choose the augmentation carefully — and the number can still collapse at another hospital, because every one of those checks drew from the distribution the model was fitted on.
Demonstration
Book I’s last proposition said a number is worth what the split makes it worth, and required the unit of the split to match the unit of the claim. This is the case where even a correct split is not enough.
Split by patient and you have answered does this work on a new patient at this hospital. Deployment asks does this work at another hospital, and the distributions differ in ways nobody enumerated: scanner manufacturer, acquisition protocol, reconstruction kernel, population, disease prevalence, what a technician does when an image looks poor.
Zech and colleagues measured it on pneumonia detection across three hospital systems. Internal performance was strong. External performance dropped substantially, and — the instructive part — the models had learned to detect which hospital a radiograph came from with high accuracy, from markers and positioning. Since prevalence differed between sites, exploiting hospital identity was a genuinely useful shortcut internally and pure noise externally.
That is the shape of the failure. Not the model being weak, but the model finding a signal that is real in the training distribution and absent outside it. A laterality marker, a scanner-specific texture, a chest drain that only appears in patients already known to be ill.
The defences are partial and worth knowing as partial. Multi-site training data helps most and is hardest to get. Augmentation that simulates acquisition variation — intensity, resolution, noise — helps. Test-time normalisation per volume helps for MRI. None of them substitutes for the measurement.
Corollary
An external validation cohort is not a nice addition to a medical imaging paper. It is the only measurement that answers the question the paper claims to answer, and its absence should be read as the result being unknown rather than as the result being good.