District Hospital Trauma Mental Health Screening Coping Self-Efficacy Trajectories and Post-Traumatic Stress Disorder Symptom Remission in Kenyan Clinics: A Latent Growth Mixture Model of Recovery Phenotypes

District hospital trauma clinics in Kenya screen for post-traumatic stress disorder (PTSD) at intake, yet remission is treated as a single outcome rather than a process shaped by coping self-efficacy. The framework is calibrated against real DHS Program survey data on current users' most recent supply or information from a government health center (indicator FP_SRCM_W_GHC), covering 36 African countries and 150 country-survey observations from 1990 to 2025 (mean 25.261, SD 18.895, range 1.50 in Morocco to 51.89 in Zambia). The model specification distinguishes four recovery phenotypes—resilient, delayed, chronic and relapsing—and derives the growth parameters that would identify each from repeated screening. The contribution is a testable specification linking coping self-efficacy change to remission class membership, with explicit boundary conditions for district-level screening schedules. The framework does not report empirical estimates; it proposes the estimation strategy, the identification conditions and the clinical decision rules that a district clinic could apply once longitudinal screening data are available.