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Objective: Despite tremendous efforts to scale up key maternal and child health interventions in Zambia, progress has not been uniform across the country. This raises fundamental health system performance questions that require further investigation. Our study investigates technical and scale efficiency (SE) in the delivery of maternal and child health services in the country. Setting: The study focused on all 72 health districts of Zambia. Methods: We compiled a district-level database comprising health outcomes (measured by the probability of survival to 5 years of age), health outputs (measured by coverage of key health interventions) and a set of health system inputs, namely, financial resources and human resources for health, for the year 2010. We used data envelopment analysis to assess the performance of subnational units across Zambia with respect to technical and SE, controlling for environmental factors that are beyond the control of health system decision makers. Results: Nationally, average technical efficiency with respect to improving child survival was 61.5% (95% CI 58.2% to 64.8%), which suggests that there is a huge inefficiency in resource use in the country and the potential to expand services without injecting additional resources into the system. Districts that were more urbanised and had a higher proportion of educated women were more technically efficient. Improved cooking methods and donor funding had no significant effect on efficiency. Conclusions: With the pressing need to accelerate progress in population health, decision makers must seek efficient ways to deliver services to achieve universal health coverage. Understanding the factors that drive performance and seeking ways to enhance efficiency offer a practical pathway through which low-income countries could improve population health without necessarily seeking additional resources.
In the definition of efficiency, a distinction should be made between technical, allocative and scale efficiency (SE) measures.13–15 In this study, only technical and scale efficiencies were considered, mainly because the input prices needed for the estimation of cost functions were not available to us.12 14 To estimate the efficiency scores, we employed the Banker, Charnes and Cooper (BCC) formulation of the DEA model. The choice of the BCC approach is partially guided by the fact that all our variables were ratio based, and we endeavoured to take economies of scale into account in the analysis. In addition, similar to all other DEA models, the BCC model handles multiple inputs and outputs, an approach that is particularly suited to complex fields such as health systems,13 15 in which there is a multidimensional mix of input and output variables that have to be considered simultaneously.15–18 Further, we applied the approach developed by Charnes, Cooper and Rhodes to enable us to decompose the overall efficiency score into scale and pure technical efficiency (PTE). Given that each decision-making unit (DMU) may face locally unique conditions, the DEA approach assesses each unit separately, assigning a specific weighted combination of inputs and outputs that maximises its efficiency score.13 15 Algebraically, this is achieved by solving for each DMU (district) the following linear programming problem.15 where yo0, quantity of output ‘o’ for DMU0; uo, weight attached to output o, uo>0, o=1, …….., O; kio, quantity of input ‘i’ for DMU0; vi, weight attached to input i, vo>0, i=1, …….., I. The equation is solved for each DMU iteratively (for n=1, 2,…, N); therefore, the weights that maximise the efficiency of one DMU might differ from the weights that maximise the efficiency of another DMU.17 18 Theoretically, these weights can assume any non-negative value, whereas the resulting technical efficiency scores can vary only within a scale of 0–1, subject to the constraint that all the other DMUs also have efficiencies between 0 and 1. However, the ratio formulation expressed above leads to an infinite number of solutions, because if (u*, v*) is a solution, then (αu*, αv*) is another solution.15 17 19 20 To avoid this problem, one can impose an additional constraint by setting either the denominator or the numerator of the ratio to be equal to 1 (eg, v’xj=1), which translates the problem to one of either maximising weighted output subjected to weighted input being equal to 1 or of minimising weighted input subjected to weighted output being equal to 1.15 21 This would lead to the multiplier form of the equation as expressed as follows:15 19 20 subject to: v’xj=1, μ’yj−v’xj ≤0, j=1,2 …..J, μ, v ≥0. This maximisation problem can also be expressed as an equivalent minimisation problem.15 19 Technically, a DEA-based efficiency analysis can adopt either an input or output orientation. In an input orientation, the primary objective is to minimise the inputs, whereas in an output orientation, the goal is to attain the highest possible output with a given amounts of inputs. In our case, an output-oriented DEA model was deemed more appropriate based on the premise that district health teams have an essentially fixed set of inputs to work with at any given time.3 5 6 In other words, the district health system stewards would have more leverage in controlling outputs through innovative programming rather than by raising additional resources. As performance and institutional capacity are expected to vary across districts,4 a variable returns to scale (VRS) approach was also considered more relevant to the study setting. This approach allows for economies and diseconomies of scale rather than imposing the laws of direct proportionality in input–output relationships as espoused in a constant returns to scale model.16–22 A VRS model also offers the advantage of decomposing overall technical efficiency (OTE) into PTE and SE, which is essential in locating the source(s) of differences in performance across production units.16–18 The analyses were performed using R V.3.2.1, specifically the r-DEA package that has the capability to combine input, output and environmental variables into one stage of analysis. This package implements a double bootstrap estimation technique to obtain bias-corrected estimates of efficiency measures, adjusting for the unique set of environmental characteristics under which different DMUs are operating.11 23 To obtain robust estimates, we bootstrapped the model 1000 times and generated uncertainty around the estimates.23 24 The same approach was used to generate robust DEA efficiency scores corresponding to health intervention coverage, applying the same input and environmental variables. We used data from the Malaria Control Policy Assessment (MCPA) project in Zambia, which compiled one of the most comprehensive district-level data sets of U5MR, health intervention coverage and socioeconomic indices in the country based on standardised population health surveys.4 8 For both indicators, to capture the most recent period for the country, the data representing the year 2010 were used. In our DEA model, U5MR was used to measure district health system outcomes. To measure the outcome, output and inputs in the same direction in such a way that ‘more is better’, we converted the probability of dying before 5 years of age (which is conventionally known as the U5MR) into the probability of survival to age 5. This was accomplished by simply subtracting the reported U5MR per 1000 live births from 1000.11 25 Health intervention coverage was a composite metric that consisted of the proportion of the population in need of a health intervention who actually receive it.4 8 The composite metric consisted of DPT3 and measles immunisations, skilled birth attendance and malaria prevention. For malaria prevention, we included an indicator approximating malaria prevention efforts across districts, that is, a combination of insecticide-treated net ownership and indoor residual spraying coverage. The average of all five health interventions for each district was used to represent health intervention coverage.4 This innovative method of data reduction by combining a range of health interventions has the advantage of reducing the number of variables that are entered into the model. This in turn helps to maintain a reasonable balance between the number of DMUs and the input and output variables. This is required to avoid a scarcity of adjacent reference observations or ‘peers’, which if not addressed would lead to sections of the frontier being unreliably estimated and inappropriately positioned.15 16 18 For the inputs portion, we obtained a data set of annual operational funds from the governments of and donors to each of the 72 districts for the year 2010. These data are available through the Directorate of Health Policy and Planning of the MOH.8 Using population data from the Central Statistics Office of Zambia, we calculated the total population-adjusted funds disbursed to each district. We also obtained data from the MOH on the human resource complement for the year 2010, which covered the medical professionals (doctors and clinical officers) and nurses (including midwives) in each district and adjusted the data for the district population. In addition, we included the mean years of education among women aged 15–49 years, the proportion of district funds originating from donors, household access to electricity and the proportion of households with improved cooking methods as environmental variables that are external to district health units but nonetheless affect the performance and efficiency levels of the health system. These variables were chosen based on their importance in addressing the key global health targets related to maternal and child health in Africa.1–3 Donor funding is a major feature in African health systems and has been the subject of major debate in efforts to strengthen health systems. Similarly, the relationship between health and education, particularly among women, has been extensively documented.2–4 8 Both data sets were obtained from the MCPA database. Permission to conduct the study was obtained from the MOH, Zambia. Since our study used only de-identified secondary data, we were granted an exemption from the institutional review board, University of Zambia: IRB00001131 of IROG000074.
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