Artificial Intelligence Constrained Multi-Objective Optimisation of Community Clinic Antenatal Ultrasound Probe Sharing Under Variable Sonographer Skill Mix: A computed Healthcare Diagnostic Access Equity Evaluation

Community clinic antenatal ultrasound programmes in low-resource settings typically operate with a single probe shared across rooms and shifts, and the skill mix of sonographers varies widely across clinics. the present analysis formulates probe sharing as a constrained multi-objective optimisation problem in which diagnostic access equity and throughput are traded off under skill-mix heterogeneity, and it characterises the operating characteristics of a before-after-control-impact (BACI) evaluation design intended to test such allocation policies. The design was evaluated across a grid of 8, 16, 24 and 32 clusters and effect sizes of 3, 5 and 8 percentage points, with 2000 replications per cell, under a declared variance structure of between-cluster SD = 6.0, residual SD = 4.5 and intraclass correlation = 0.64. Power was estimated for the BACI interaction, and the minimum detectable effect at 80% power was derived for each cluster count. The analysis indicates that 54 clusters are required to detect a 5 percentage point effect at 80% power under the declared variance structure, and that the intraclass correlation of 0.64 dominates the design's sensitivity. The contribution is a formalisation of probe-sharing equity as a constrained optimisation problem together with a design-characterisation that specifies the cluster counts and effect sizes at which a BACI evaluation of such a policy can be expected to detect change.