Causal Pathways Linking Medical Service Continuity to Referral Completion in Uganda: A Multilevel Mediation Design

Referral completion in Ugandan district health systems depends on whether patients remain connected to a continuous source of care, yet the causal pathway from service continuity to completion has not been formally characterised. The design treats service continuity as a cluster-level exposure, perceived referral legitimacy as an individual-level mediator, and referral completion as a binary outcome, with before-after-control-impact identification of the continuity effect and multilevel mediation decomposition of the indirect pathway. Using 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. Power reached conventional levels at 56 clusters for a 5-percentage-point effect, and the minimum detectable effect at 80% power declined steeply as cluster counts rose from 8 to 32. The design permits bounded causal claims about the mediated pathway while making the cluster-level information constraint explicit. The contribution is a design template that aligns the mediation question with the clustered structure of Ugandan referral data.