District Hospital Trauma Mental Health Screening Same-Day Discharge Comorbidity Density and Post-Traumatic Stress Disorder Detection in Zambian Referral Clinics: A Multilevel Analysis of Competing Clinical Demand

Same-day discharge after trauma stabilisation compresses the observation window in which post-traumatic stress disorder (PTSD) can be detected, yet the detection loss is usually attributed to screening instruments rather than to the density of competing clinical demands that determines whether a screen is completed at all. The model specifies three levels: the patient encounter, the clinic-day, and the referral facility, with comorbidity density operating at the clinic-day level as a constraint on clinician attention. The analysis derives the conditions under which same-day discharge produces differential detection loss across facilities, proposes a decomposition of observed detection into true prevalence, screen completion, and screen sensitivity, and identifies the design parameters that a cluster-randomised evaluation of discharge timing would need to estimate. The contribution is a formal statement of why PTSD detection loss under same-day discharge is a function of competing demand rather than of instrument performance alone, and a specification of the multilevel estimand that would make this distinction empirically testable in Zambian referral settings.