Privacy-Preserving Federated Learning for Artificial Intelligence Healthcare in Uganda: Robustness Under Distribution Shift and Sparse Labels

Federated learning promises to train clinical prediction models across Ugandan health facilities without centralising patient records, yet its statistical behaviour under the conditions that actually prevail in the country's referral system remains poorly characterised. the present analysis treats the problem as one of design analysis rather than empirical deployment: it formalises federated averaging as a distributed estimator whose risk decomposes into a non-IID client-drift term, a label-sparsity term, and a privacy-noise term, and it derives the conditions under which each dominates. Under moderate distribution shift the drift term scales with the squared heterogeneity of local optima and is bounded by a communication-round budget, whereas under sparse labels the variance term grows as the inverse of the per-client effective sample size, producing a regime in which additional privacy noise is nearly free but additional clients are not. A before-after-control-impact design with an intraclass correlation of 0.64, between-cluster SD of 6.0 and residual SD of 4.5 is used to characterise the operating characteristics of a cluster-level evaluation, and the design requires 54 clusters to detect a 5-percentage-point effect at 80% power. The contribution is a set of propositions that link heterogeneity, label density and privacy budget to achievable model quality, together with a design template for evaluating federated clinical models in low-resource referral networks.