Community Mental Health Service Discharge Against Advice and Readmission Timing in Kenyan District Hospitals: A Target-Trial Emulation of Follow-Up Window Exposure

Discharge against advice from district-hospital mental health units is widely treated as a binary exposure, yet the readmission risk it carries depends on the follow-up window through which it is observed. The estimand is defined as the counterfactual cumulative incidence of readmission under a declared window, and the before-after-control-impact estimator is characterised under a variance structure with between-cluster standard deviation 6.0, residual standard deviation 4.5 and intraclass correlation 0.64. Power was estimated across 2000 replications per design cell for cluster counts of 8, 16, 24 and 32 and effects of 3, 5 and 8 percentage points. Fifty-six clusters were required for 80% power at a 5-percentage-point effect. Window choice and cluster count jointly determine whether a clinically meaningful discharge effect is detectable, and that reporting readmission without declaring the window conflates exposure with observation. The contribution is a design specification that makes the follow-up window an explicit, auditable parameter in community mental health service evaluation.