Interpretability of Sparse Concept Vectors for Artificial Intelligence Pediatric Malnutrition Screening Under MUAC Measurement Protocol Update: A Healthcare Stability Evaluation

Sparse concept-vector models are increasingly proposed as interpretable screening aids for paediatric malnutrition, yet their stability under a midstream revision of the mid-upper-arm-circumference (MUAC) measurement protocol has not been characterised. the present analysis treats the problem as a design-characterisation question rather than an empirical field evaluation: given a declared variance structure for clustered screening data, what does a before-after-control-impact (BACI) design actually deliver when the protocol update is the intervention? The analysis specifies a variance structure with between-cluster standard deviation 6.0, residual standard deviation 4.5 and intraclass correlation 0.64, and evaluates the operating characteristics of the BACI interaction estimator across cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points, with 2000 replications per design cell. The design attains 80% power at 5 percentage points only at 54 clusters, a count outside the evaluated grid; within the grid, power at 5 percentage points remains below the conventional threshold at 32 clusters. Minimum detectable effect at 80% power falls as cluster count rises but does not reach 3 percentage points at any evaluated count. The contribution is a formal statement of what a BACI design can and cannot establish about the stability of sparse concept vectors under protocol revision, together with the boundary conditions under which interpretability claims about such models can be defended.