Urban development-induced relocation of informal pharmacy clusters and antibiotic-dispensing referral chains in Nairobi: a difference-in-differences estimation of cluster-exposure thresholds

Because no observational data are available, the study characterises the operating characteristics of a before-after-control-impact design under a declared variance structure with an intraclass correlation of 0.64, a between-cluster standard deviation of 6.0 and a residual standard deviation of 4.5. 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.52 clusters are required to detect a 5-percentage-point effect at 80 per cent power, and that the minimum detectable effect at 80 per cent power declines steeply as cluster count rises. Cluster-exposure thresholds in relocation research are not merely empirical quantities but design artefacts shaped by the intraclass correlation of dispensing behaviour within clusters. The contribution is a methodological framework for sizing difference-in-differences studies of informal pharmaceutical relocation, together with a set of boundary conditions that qualify causal claims about referral-chain disruption.