District Hospital Trauma Mental Health Screening Same-Day Discharge Policy and Post-Traumatic Stress Disorder Detection Loss in Nigerian Clinics: A Difference-in-Differences Analysis of Observation Window Compression

Same-day discharge policies for trauma patients in Nigerian district hospitals compress the observation window during which post-traumatic stress disorder (PTSD) can be detected, yet the magnitude of detection loss attributable to this compression remains unquantified. The framework treats the observation window as a measurable exposure and specifies a two-period, two-group design comparing district hospitals that adopted same-day discharge with those that retained extended observation. Identification rests on the parallel-trends assumption, which is assessed through pre-policy event-study estimates and placebo outcomes. The proposed estimator decomposes detection loss into a temporal displacement component and a severity-selection component, permitting inference about whether compression disproportionately removes mild or severe presentations from the detected caseload. A secondary analysis links detection loss to subsequent treatment initiation and symptom trajectory. The framework is developed for the Nigerian district hospital context, where trauma registries are incomplete and PTSD screening is not universally embedded in discharge workflows. The contribution is methodological: it specifies how observation-window compression can be evaluated as a policy exposure rather than treated as an unmeasured confounder, and it derives the conditions under which difference-in-differences estimates of detection loss are credible. The paper does not report empirical estimates; it provides the design, assumptions, and inferential boundaries for a study that Nigerian trauma services can execute with existing administrative data.