District Hospital Trauma Survivor Mental Health Screening Interval Compression and Post-Traumatic Stress Disorder Detection Yield in Kenyan Referral Clinics: A Target-Trial Emulation of Surveillance Cadence

Post-traumatic stress disorder among district hospital trauma survivors in Kenya is frequently missed when mental health screening is scheduled at wide intervals after discharge. No observational data are used or claimed. The analysis is a replication-based evaluation of the before-after-control-impact estimator under a declared variance structure: between-cluster standard deviation 6.0, residual standard deviation 4.5, and intraclass correlation 0.64. Power was estimated across 2000 design cells defined by cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The design would require 54 clusters to detect a 5 percentage point improvement at 80% power. Interval compression is a plausible surveillance lever, that its evaluation is feasible only with cluster counts well above those typical of district-level pilots, and that the intraclass correlation of 0.64 is the binding constraint on precision. The contribution is a design-theoretic account of what a credible test of screening cadence would require, not a report of one that was executed.