District Health Management Team Autonomy and Public Health Emergency Detection Latency in Rwandan Health Systems: A Stepped-Wedge Implementation Evaluation

District health management teams in Rwanda operate with varying degrees of fiscal and administrative autonomy, yet the relationship between autonomy and the speed of public health emergency detection remains poorly characterised. The design was a before-after-control-impact (BACI) structure with a stepped-wedge rollout, and its operating characteristics were evaluated through a replication-based power analysis under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.640). Power was estimated across 2000 design cells spanning cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The analysis indicates that 54 clusters would be required to detect a 5-percentage-point reduction in detection latency at 80% power, a requirement that exceeds the eight districts available for the stepped-wedge rollout. The BACI estimator's operating characteristics, rather than the substantive autonomy hypothesis, impose the binding constraint on what the Rwandan evaluation can credibly establish, and it proposes a design-reconciliation framework that treats the power ceiling as a substantive finding about the limits of district-level causal inference in small health systems.