Interpretability Audits of Federated Clinical Text Classifiers Under Differential Privacy Budget Depletion: A Computer Fairness Estimation

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Federated learning and differential privacy are increasingly paired to train clinical text classifiers without centralising patient records, yet the privacy budget that governs formal disclosure protection is finite and depletes across training rounds. the present analysis treats budget depletion as a design parameter that reshapes the fairness and interpretability properties of the resulting classifier rather than as a nuisance constraint. The work is methodological and theoretical: no observational data are used or claimed. A before-after-control-impact design is characterised under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64), with power estimated across 2000 design cells spanning cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points.54 clusters are required to detect a 5 percentage point effect at 80% power, and that the minimum detectable effect at 80% power rises steeply as cluster count falls below that threshold. Interpretability audits conducted under depleted budgets inherit this variance structure: attribution stability, subgroup calibration and audit power are not separable properties but are jointly determined by the same design parameters.

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