District Hospital Trauma Mental Health Screening Alcohol Withdrawal Co-Detection Timing and Post-Traumatic Stress Disorder Assessment Completion in Namibian Referral Clinics: A Target-Trial Emulation of Withdrawal Window Exposure

Alcohol withdrawal frequently complicates the acute presentation of injured patients to district hospitals in Namibia, yet the timing of withdrawal co-detection relative to trauma mental health screening may determine whether post-traumatic stress disorder assessment is completed before discharge or lost to follow-up. No observational data were analysed; the study characterises the operating characteristics of the BACI estimator 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 indicates that 54 clusters are required to detect a 5 percentage point improvement in PTSD assessment completion at 80% power, a requirement that exceeds the cluster counts examined and that carries direct implications for the feasibility of clinic-level randomisation in Namibian referral settings. The withdrawal window is a modifiable structural determinant of assessment completion, and that target-trial emulation offers a defensible inferential route when cluster-randomised designs are underpowered at realistic site numbers.