Trauma Ward Mental Health Chaplaincy Referral Timing and Post-Traumatic Stress Disorder Treatment Initiation Among Ghanaian Inpatients: A Target-Trial Emulation of Spiritual Care Integration Windows

The timing of mental health chaplaincy referral within trauma wards may condition whether inpatients with post-traumatic stress disorder initiate evidence-based treatment, yet the causal estimand for such referral windows has not been formally specified. The design assumes eight, sixteen, twenty-four or thirty-two clusters, effect sizes of three, five or eight percentage points, and a between-cluster standard deviation of 6.0 with a residual standard deviation of 4.5, yielding an intraclass correlation of 0.64. Across 2000 replications per design cell, power curves, minimum detectable effect curves, and coefficient plots were generated to map the conditions under which the estimator recovers the referral-timing effect. The analysis indicates that fifty-two clusters are required to detect a five-percentage-point effect at eighty per cent power under the declared variance structure. The framework provides a template for causal inference on chaplaincy integration windows without requiring observational data, and it clarifies the design conditions under which trauma ward spiritual care timing can be credibly evaluated in Ghanaian and comparable settings.