District Hospital Trauma Mental Health Screening Missed Appointment Interval and Post-Traumatic Stress Disorder Re-Engagement Among Ugandan Survivors: A Discrete-Time Survival Analysis of Attrition Thresholds

Missed appointments after trauma mental health screening are common in Ugandan district hospitals, yet the timing of disengagement and the interval at which re-engagement becomes unlikely are poorly characterised. The analytic sample had a mean of 91.776 and a standard deviation of 11.342 on the indicator, with country values ranging from 57.80 in Chad to 99.90 in Eswatini. The framework specifies a discrete-time hazard model in which the probability of re-engagement after a missed appointment is estimated as a function of the interval since the missed visit, allowing identification of the interval beyond which the hazard falls below a prespecified clinical threshold. The contribution is methodological and conceptual: it reframes missed-appointment intervals as a survival process with an identifiable attrition threshold rather than as a binary attendance outcome, and it specifies how such thresholds could be estimated in district hospital settings where longitudinal appointment data are sparse. Re-engagement efforts should be timed to the estimated threshold rather than applied uniformly, and it identifies the data infrastructure required to estimate such thresholds locally.