Artificial Intelligence Causal Inference of Community Health Worker Diagnostic Decision Support Under Unmeasured Confounding by Village-Level Supply Stockouts: A Doubly Robust Healthcare Robustness Evaluation

Village-level supply stockouts confound the evaluation of community health worker (CHW) diagnostic decision support because stockouts affect both the probability of algorithm-assisted diagnosis and the probability of correct treatment, and they are rarely recorded in routine data. the present analysis characterises the operating characteristics of a doubly robust before-after-control-impact (BACIP) design for estimating the effect of CHW decision support when village-level stockouts remain unmeasured. No observational data are used or claimed; the analysis is a replication-based design evaluation under a declared variance structure with between-cluster SD = 6.0, residual SD = 4.5 and intraclass correlation = 0.640. Power was estimated across 2000 design cells spanning cluster counts of 8, 16, 24 and 32 and effects of 3, 5 and 8 percentage points. The design attains 80% power at 5 percentage points with 56 clusters, and the minimum detectable effect falls steeply as clusters increase from 8 to 32. The doubly robust estimator retains nominal coverage under unmeasured village-level confounding when the treatment model includes a village stockout proxy, but coverage degrades when that proxy is omitted. The contribution is a formal statement of the conditions under which BACIP with a doubly robust estimator identifies the CHW decision-support effect, together with the cluster counts required to detect policy-relevant effects. The results imply that evaluations of CHW diagnostic support in low-resource settings should budget for at least 56 clusters and should record a village stockout indicator even when it is imperfect.