Indigenous Healer Referral Networks and Psychosis Treatment Interval in Nigerian Yoruba Communities: A Snowball-Sampled Survival Estimation of Diviner-Psychiatrist Brokerage

The central problem is that conventional sampling frames miss the brokerage function of indigenous diviners, who operate as informal gatekeepers within closed referral chains. The design specifies a before-after-control-impact estimator with a variance structure of between-cluster SD = 6.0, residual SD = 4.5, and intraclass correlation = 0.64, and characterises its operating characteristics across 2000 replications per design cell. Power analysis indicates that 52 clusters are required to detect a 5 percentage-point effect at 80% power. The framework contributes a replicable protocol for studying informal referral brokerage in mental health systems where indigenous and biomedical sectors coexist, and it clarifies the conditions under which snowball sampling yields defensible survival estimates rather than biased convenience samples.