District Hospital Trauma Mental Health Follow-Up Transport Voucher Redemption Timing and Post-Traumatic Stress Symptom Persistence in Tanzanian Referral Clinics: A Target-Trial Emulation of Voucher Expiry Windows

Transport vouchers are widely used to support follow-up attendance after traumatic injury in Tanzanian referral clinics, yet the timing of voucher redemption relative to the expiry window is rarely treated as a modifiable determinant of post-traumatic stress symptom persistence. No observational data are used or claimed: the analysis is a design and power evaluation conducted 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 effect sizes of 3, 5 and 8 percentage points. The analysis identifies 50 clusters as the number required to detect a 5 percentage point effect at 80% power, and reports the minimum detectable effect at 80% power as a function of cluster count. The framework clarifies how voucher expiry windows can be operationalised as a target trial, specifies the estimand and identification conditions, and shows that the before-after-control-impact design is adequately powered only at cluster counts well above those typical of district-level quality improvement evaluations. The contribution is a design specification for a causal question that current voucher programmes pose but do not answer.