Surrogate Substitution Preserves PHI Detectability: A Multi-Detector Equivalence Study

Structure-preserving de-identification replaces each detected identifier with a realistic same-type surrogate ("Anna S." -> "Maria S.") rather than a tag such as [NAME]. If downstream PHI detectors no longer recognise surrogates, hiding-in-plain-sight protection and second-pass safety nets weaken. We ask: on the spans a de-identifier actually replaced, do detectors find the surrogate as often as the original value? We call this detectability preservation and treat it as a proxy, not a full measure of utility. Our paired protocol (i) scores detectability only on replaced spans, separately from coverage; (ii) runs an identical heterogeneous detector panel on original and transformed text; and (iii) bounds the paired change with document-level cluster-bootstrap equivalence testing and posterior probabilities instead of significance tests. For one commercial transform on 7 clinical and general-PII benchmarks in 7 languages (1,750 documents, 5,333 replaced spans, 11 detectors), masked-span recall moves from 75.8% to 74.6% (90% CI of the change [-1.62, -0.82] points; posterior probability > 0.99 of lying within +/-2 points). The change reaches 2-3 points on dense Spanish and Dutch text, and replaced spans are easier to detect than unreplaced ones (+16.6 points), so the result describes the replaced population only. Coverage is a separate, weaker axis (48% of gold PHI on MEDDOCAN). On financial, legal and enterprise text (750 documents, 10 detectors) the pooled result replicates (72.4% -> 72.8%), but rule-based and fine-tuned detectors lose 2-4 points on finance, and the transform edits substantial non-PII text. Redaction and Faker baselines give reference points. We release per-span predictions and analysis code.