{ "background": "District hospitals in Kenya face persistent challenges in resource allocation and service delivery, yet robust methodologies for quantifying systemic efficiency are lacking. Existing analyses often fail to account for the hierarchical structure of health system data, leading to potentially biased estimates of performance drivers.", "purpose and objectives": "This protocol details a methodological evaluation to measure efficiency gains within Kenyan district hospital systems. The primary objective is to develop and apply a multilevel regression model that accounts for patient-, facility-, and county-level variations to identify key determinants of technical efficiency.", "methodology": "A retrospective panel dataset will be constructed from national health management information systems and financial records. Technical efficiency scores will be calculated using data envelopment analysis. These scores will serve as the dependent variable in a three-level linear mixed model: $\\text{Efficiency}{ijk} = \\beta0 + \\beta X{ijk} + u{k} + v{jk} + e{ijk}$, where $i$, $j$, and $k$ index patients, facilities, and counties, respectively. Inference will be based on 95% confidence intervals derived from robust standard errors.", "findings": "As a research protocol, this paper does not present empirical results. The anticipated analytical output will quantify the proportion of efficiency variance attributable to each hierarchical level and estimate the direction and magnitude of key predictors, such as nurse-to-patient ratios.", "conclusion": "The proposed methodology is designed to provide a more nuanced, system-level understanding of efficiency, moving beyond facility-centric assessments. It is expected to validate the necessity of multilevel modelling in health systems research.", "recommendations": "Future research should apply this analytical framework longitudinally and to other health system tiers. Policymakers should consider hierarchical data structures when designing hospital performance metrics.", "key words": "health systems research, efficiency analysis, multilevel modelling, data envelopment analysis, hospital management", "contribution statement": "This protocol introduces a novel integration of data envelopment analysis with a three-level linear mixed model