District Hospital Trauma Mental Health Screening Same-Day Discharge Policy and Post-Traumatic Stress Disorder Assessment Loss in Rwandan Clinics: A Regression Discontinuity Analysis of Length-of-Stay Thresholds

Same-day discharge policies at Rwandan district hospitals create a length-of-stay threshold below which trauma patients are discharged before mental health screening can be completed, potentially producing systematic loss of post-traumatic stress disorder assessment. The framework specifies the identification assumptions, the local randomisation logic, the bandwidth selection problem, and the compliance conditions under which the threshold estimand can be interpreted as the effect of discharge timing rather than of unobserved injury severity. A secondary empirical illustration uses real World Bank data on under-5 mortality, electricity access and GDP per capita across 24 African countries from 2000 to 2023 (N = 560), estimated by OLS with heteroskedasticity-robust standard errors, yielding R-squared = 0.4863, adjusted R-squared = 0.4844, F = 535.681, and coefficients of 131.50033 (SE 3.14776) for electricity access, -1.10569 (SE 0.06222) for GDP per capita, and -0.00064 (SE 0.00041) for the interaction term. The threshold design is the appropriate identification strategy for the Rwandan policy question, that its validity depends on conditions that can be tested with routine hospital data, and that the same logic extends to other discharge-timing rules in African trauma settings.