Interpretability of Concept Activation Vectors for Artificial Intelligence Echocardiography Ejection Fraction Estimation Under Probe Replacement: A Healthcare Robustness Evaluation

Concept activation vectors (CAVs) are increasingly used to justify left ventricular ejection fraction (LVEF) estimates produced by artificial intelligence (AI) echocardiography systems, yet their stability under routine probe replacement has not been characterised. the present analysis treats CAV-based interpretability as a measurement instrument whose operating characteristics can be evaluated before clinical deployment. The problem is framed as a before-after-control-impact (BACI) design in which probe replacement is the intervention, and the quantity of interest is the power to detect a clinically meaningful shift in CAV alignment. Using a declared variance structure with between-cluster standard deviation 6.0, residual standard deviation 4.5 and intraclass correlation 0.64, power was estimated across 2000 replications per design cell for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The analysis indicates that 52 clusters are required to detect a 5 percentage point CAV shift at 80% power, a requirement that exceeds the cluster counts typically available in single-centre echocardiography laboratories. Minimum detectable effect curves and receiver operating characteristic behaviour show that underpowered designs conflate probe-induced CAV drift with genuine concept instability. The contribution is a design-theoretic account of when CAV evidence can bear clinical weight, and a specification of the cluster counts and effect sizes at which it cannot.