Community Mental Health Service Community-Based Rehabilitation Enrollment Timing and Functional Recovery in Zambian Districts: A Target-Trial Emulation of Rehabilitation Exposure

The timing of community-based rehabilitation (CBR) enrollment after a mental health service contact is a modifiable determinant of functional recovery, yet the observational designs used to study it are vulnerable to confounding by indication and to the clustering of outcomes within districts. the present analysis characterises the operating characteristics of a before-after-control-impact (BACI) estimator for CBR enrollment timing under a declared variance structure, using a replication-based design evaluation rather than observational data. The design assumed a between-cluster standard deviation of 6.0, a residual standard deviation of 4.5, and an intraclass correlation of 0.640. Power was estimated across 2000 replications per design cell for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The analysis identified 52 clusters as the number required to detect a 5 percentage point effect at 80% power. The results indicate that the BACI estimator is sensitive to cluster count at small effect sizes and that the minimum detectable effect declines steeply between 8 and 24 clusters before flattening. Target-trial framing of CBR enrollment timing is feasible in Zambian district settings only when the cluster count is planned against the intraclass correlation, and it specifies the boundary conditions under which the estimator retains nominal coverage.