Privacy-Preserving Federated Learning for Multi-Site Tuberculosis Drug Resistance Prediction Under Heterogeneous Laboratory Information Systems: An Asynchronous Aggregation Evaluation of Artificial Intelligence Treatment Initiation Equity

Multi-site tuberculosis drug resistance prediction with federated learning faces a structural tension: asynchronous aggregation accommodates heterogeneous laboratory information systems but may systematically disadvantage sites whose data arrive late or infrequently, producing treatment-initiation recommendations that are less accurate for the patients those sites serve. We define a federated optimisation problem with staleness-dependent aggregation weights, derive a convergence bound that separates the contribution of data heterogeneity from that of staleness, and propose an equity-auditing procedure that compares per-site treatment-initiation error under synchronous and asynchronous aggregation. The framework is evaluated through a replication-based design study: no observational data are used or claimed. Operating characteristics are characterised under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64) across 2000 replications per design cell, with cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The analysis identifies the conditions under which asynchronous aggregation preserves treatment-initiation equity and the conditions under which it does not, and it specifies the audit statistics that a deployment should report. The contribution is a design-evaluation framework, not an empirical finding about any particular tuberculosis programme.