Mortality Effects of Essential Medicines Stock-Out Duration in Kenyan Public Facilities: Target-Trial Emulation of Health-System Exposure

Essential medicines stock-outs are routinely recorded in Kenyan public facilities, yet their mortality consequences remain poorly identified because stock-out duration is an endogenous health-system exposure shaped by facility, district and patient factors. The design treats stock-out duration as a time-varying exposure assigned at the facility level, with clusters defined by facility catchment and outcomes aggregated over calendar periods. 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. The analysis indicates that 54 clusters are required to detect a 5 percentage point mortality difference at 80% power under this variance structure. The framework clarifies the conditions under which BACI estimates of stock-out mortality effects are credible and identifies the design parameters that most strongly constrain inference in Kenyan public-sector settings.