Mobile Crisis Team Response Latency and Post-Traumatic Stress Disorder Treatment Initiation Among Urban South African Trauma Survivors: A Target-Trial Emulation of Prehospital Wait-Time Thresholds

Prehospital response latency is a modifiable feature of mobile crisis team deployment, yet its relationship to post-traumatic stress disorder treatment initiation among urban South African trauma survivors remains poorly characterised. The design parameters were eight, sixteen, twenty-four and thirty-two clusters, effect sizes of three, five and eight percentage points, and two thousand replications per design cell. The between-cluster standard deviation was 6.0, the residual standard deviation was 4.5, and the intraclass correlation was 0.64. Power was estimated across two thousand design cells. The analysis indicates that fifty-four clusters are required to detect a five percentage point effect at eighty per cent power. The minimum detectable effect declines as cluster count increases, and the confidence-interval width narrows correspondingly. The framework provides a basis for designing evaluations of prehospital wait-time thresholds that respect the clustered structure of crisis team deployment and the policy-relevant effect sizes that South African trauma services can plausibly deliver.