District Hospital Mental Health Triage Queue Position and Acute Trauma Symptom Escalation in Nigerian Referral Facilities: A Target-Trial Emulation of Waiting-Time Thresholds

Mental health triage in Nigerian district referral facilities assigns trauma survivors to queue positions that determine how long they wait before clinical assessment, yet the waiting-time thresholds at which acute trauma symptoms escalate remain unquantified. 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 effect at 80% power under the declared variance structure, and that power falls below 0.80 at 32 clusters for the 3-percentage-point effect. The minimum detectable effect at 80% power declines as cluster count increases, but the decline is shallow beyond 24 clusters. The results imply that triage-threshold evaluations in Nigerian referral facilities are feasible only at effect sizes of 5 percentage points or larger unless cluster counts exceed 54, and that the intraclass correlation of 0.64 imposes a design constraint that no increase in within-cluster sample size can offset.