Methodological Evaluation of District Hospitals Systems in Kenya: Quasi-Experimental Design for Measuring Adoption Rates

District hospitals in Kenya play a critical role in providing medical services to underserved areas, yet their efficiency and effectiveness are often uncertain. A mixed-methods approach was employed, including surveys and interviews with healthcare workers. Data were analysed to assess protocol adoptions in different districts. Across 10 randomly selected districts, the adoption rate of new antiretroviral therapy protocols varied from 45% to 72%, indicating a moderate level of implementation variability. The quasi-experimental design successfully highlighted differences in protocol adoptions across hospitals, providing insights for improvement strategies. District hospital managers should prioritise training and support programmes to enhance the adoption rates of new healthcare protocols. Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.