Medical Sociology of Emergency Obstetric Referral Insurance Verification and Transfer Delay in Ghanaian District Hospitals: A Difference-in-Differences Estimation of Preauthorization Exposure

The unresolved problem is that insurance verification at the district level is a cluster-level administrative exposure, yet the design most commonly proposed for evaluating it — a simple pre-post comparison within exposed facilities — confounds the exposure with secular trends in referral practice and with facility-level heterogeneity in obstetric case-mix. Using a replication-based evaluation with 2000 replications per design cell, the analysis characterised power and minimum detectable effect across cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points, under a declared variance structure with between-cluster SD of 6.0, residual SD of 4.5 and intraclass correlation of 0.64. The results indicate that the BACI interaction achieves 80% power at 56 clusters for a 5-percentage-point effect, and that the minimum detectable effect at 80% power declines steeply as cluster count rises from 8 to 32. The intraclass correlation of 0.64 is the dominant constraint on precision: it implies that facility-level clustering absorbs most of the variance in transfer delay, so designs that randomise or compare at the facility level must budget for cluster counts well above those typical of district-level obstetric audits. The BACI estimator is defensible for this exposure only when the cluster count is treated as a design parameter rather than an afterthought, and it specifies the boundary conditions under which preauthorization effects of policy-relevant magnitude become detectable.