Community Mental Health Service mHealth Relapse-Alert Asymmetry and Outreach Visit Yield in Tanzanian Catchments: A Target-Trial Emulation of Alert-Triggered Contact Exposure

Community mental health services in low-resource catchments increasingly rely on mobile-health relapse alerts to trigger outreach contact, yet the design of such alert systems is rarely evaluated before deployment. The analysis characterises power, minimum detectable effect size and interval coverage across a declared variance structure with between-cluster standard deviation of 6.0, residual standard deviation of 4.5 and intraclass correlation of 0.64, over 2000 replications per design cell and cluster counts of 8, 16, 24 and 32. The results indicate that 54 clusters are required to detect a 5 percentage-point effect at 80% power, and that power falls steeply below this threshold. Alert asymmetry, the systematic difference between alert generation and outreach capacity, is the principal threat to the interpretability of alert-triggered contact effects, and that BACI designs must be sized against the alert-conditional contact rate rather than the nominal catchment population. The contribution is a design framework that specifies the cluster counts, effect sizes and variance assumptions under which target-trial emulation of alert-triggered contact can yield credible estimates.