Community Health Worker Trauma Screening Uptake and Mental Health Treatment Initiation in Ethiopian Health Extension Posts: A Stepped-Wedge Analysis of Supervisory Audit Frequency

Supervisory audit frequency is widely assumed to strengthen community health worker performance, but the statistical conditions under which audit schedules can detect meaningful changes in trauma screening uptake and treatment initiation remain uncharacterised. 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.54 clusters are required to detect a 5 percentage point effect at 80% power under this variance structure, and that the minimum detectable effect at 80% power declines steeply between 8 and 24 clusters before flattening. The before-after-control-impact interaction is estimable at adequate power only when cluster counts exceed 24 for effects of 5 percentage points or larger. These results bound the inferential reach of supervisory audit trials in health extension settings and specify the design conditions under which stepped-wedge evaluations of audit frequency can distinguish real uptake gains from cluster-level noise.