District Hospital Trauma Mental Health Screening Missed Appointment Rescheduling Intervals and Post-Traumatic Stress Disorder Assessment Completion in Kenyan Clinics: A Target-Trial Emulation of Scheduling Gap Exposure

Missed appointments after trauma mental health screening are common in Kenyan district hospitals, and the interval before a rescheduled appointment may influence whether post-traumatic stress disorder assessment is ever completed. No observational data were analysed; instead, the operating characteristics of the design were characterised under a declared variance structure with between-cluster standard deviation of 6.0, residual standard deviation of 4.5, and intraclass correlation of 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 identified that 52 clusters would be required to detect a 5-percentage-point effect at 80% power. The results quantify the trade-off between cluster numbers and detectable effects, and they show that the BACI estimator can recover scheduling-gap effects when the design is adequately powered.