Artificial Intelligence Federated Inference of Community Clinic Tuberculosis Drug-Resistance Prediction Under Unmeasured Sputum Culture Contamination: A Healthcare Privacy–Accuracy Trade-off Evaluation

Community clinics that perform sputum-based tuberculosis drug-resistance prediction face a structural inferential problem: the reference standard itself is contaminated by unmeasured culture contamination, so any federated model that aggregates clinic-level updates inherits a bias that no amount of privacy noise can remove. the present analysis treats that problem as a design question rather than a data question. It formalises federated inference under unmeasured sputum culture contamination as a constrained estimation problem in which the contamination prevalence enters the likelihood non-identifiably, and it derives the privacy–accuracy frontier that a before-after-control-impact design can actually deliver. The analysis is a replication-based evaluation of the before-after-control-impact estimator under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.640), with power estimated across 2000 design cells at cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The design requires 52 clusters to detect a 5 percentage-point effect at 80% power. Contamination bias and differential-privacy noise are not additive costs to be traded against one another but share a common attenuation channel, so that the privacy budget which maximises usable accuracy is a function of the contamination prevalence rather than a free parameter. The contribution is a formal statement of that coupling and a design rule for sizing federated tuberculosis resistance studies when the reference standard cannot be trusted.