Federated Learning for Multi-Site Malaria Microscopy Under Variable Giemsa Staining Protocols: A Privacy-Utility Evaluation of Artificial Intelligence Diagnostic Parity

Multi-site malaria microscopy with artificial intelligence (AI) faces a structural tension: diagnostic parity across sites requires models trained on staining variation, yet patient privacy and data-sovereignty rules prevent the central pooling of slide images. Federated learning (FL) is proposed as a resolution, but its utility under realistic staining heterogeneity has not been characterised in a way that separates privacy protection from diagnostic cost. the present analysis develops a formal framework for evaluating FL under variable Giemsa staining protocols, treating stain variation as a domain shift that decomposes into a site-specific colour-appearance component and a shared morphological component. We derive a federated averaging bound that isolates the contribution of stain-induced feature divergence to diagnostic parity loss, and we specify a privacy-utility frontier that makes the trade-off between differential-privacy noise and diagnostic agreement explicit. The framework is operationalised as a design-evaluation protocol with declared variance components (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64) and a replication-based power analysis across 2000 design cells. The analysis characterises the operating characteristics of a before-after-control-impact evaluation of FL diagnostic parity, identifying the cluster counts at which a five-percentage-point parity effect is detectable at 80% power. The contribution is a specification of the conditions under which FL can be expected to deliver diagnostic parity without central data pooling, and a statement of the boundary conditions under which stain heterogeneity overwhelms the privacy benefit.