Technical and scale efficiency in the delivery of child health services in Zambia: Results from data envelopment analysis

BMJ Open, Volume 7, No. 1, Year 2017

Interpretação

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.

AI Digest

Study Justification:

– Despite efforts to scale up maternal and child health interventions in Zambia, progress has been uneven across the country.
– This study aims to investigate the technical and scale efficiency in the delivery of maternal and child health services in Zambia.
– Understanding the factors that drive performance and seeking ways to enhance efficiency can help improve population health without requiring additional resources.

Study Highlights:

– The study focused on all 72 health districts of Zambia.
– A district-level database was compiled, including health outcomes, health outputs, and health system inputs for the year 2010.
– Data envelopment analysis was used to assess the performance of subnational units in terms of technical and scale efficiency.
– Nationally, the average technical efficiency for improving child survival was 61.5%, indicating significant inefficiency in resource use.
– Districts with higher urbanization and educated women were more technically efficient.
– Improved cooking methods and donor funding did not have a significant effect on efficiency.

Study Recommendations:

– Decision makers should seek efficient ways to deliver services to achieve universal health coverage.
– Efforts should be made to understand the factors that drive performance and enhance efficiency.
– Low-income countries can improve population health without requiring additional resources by focusing on efficiency.

Key Role Players:

– Ministry of Health, Zambia
– District health teams
– Health system decision makers
– Donors

Cost Items for Planning Recommendations:

– Financial resources for health interventions
– Human resources for health
– Education and training programs for health professionals
– Infrastructure development for health facilities
– Monitoring and evaluation systems for performance assessment

Força da prova

The strength of evidence for this abstract is 8 out of 10.
The evidence in the abstract is strong because it presents the results of a study that investigated technical and scale efficiency in the delivery of maternal and child health services in Zambia. The study used data envelopment analysis to assess the performance of subnational units across Zambia and found that there is a huge inefficiency in resource use in the country. The abstract also highlights the need for decision makers to seek efficient ways to deliver services to achieve universal health coverage. To improve the evidence, the abstract could provide more details about the methodology used in the study and the specific findings related to technical and scale efficiency.

Resumo

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.

Materiais

N/A

Inovações

Based on the provided information, here are some potential innovations that could improve access to maternal health:

1. Telemedicine: Implementing telemedicine services can provide remote access to healthcare professionals, allowing pregnant women in remote areas to receive prenatal care and consultations without having to travel long distances.

2. Mobile health (mHealth) applications: Developing mobile applications that provide information and resources related to maternal health can empower women with knowledge and support throughout their pregnancy journey.

3. Community health workers: Training and deploying community health workers who can provide basic maternal health services, education, and support in underserved areas can help bridge the gap in access to healthcare.

4. Transportation solutions: Improving transportation infrastructure and implementing transportation services specifically for pregnant women can ensure that they can reach healthcare facilities in a timely manner, especially during emergencies.

5. Public-private partnerships: Collaborating with private healthcare providers to expand access to maternal health services can help increase the availability of quality care in areas where public healthcare facilities are limited.

6. Financial incentives: Introducing financial incentives, such as cash transfers or subsidies, for pregnant women seeking antenatal care and delivering in healthcare facilities can encourage utilization of maternal health services.

7. Maternal waiting homes: Establishing maternal waiting homes near healthcare facilities can provide a safe and comfortable place for pregnant women to stay during the final weeks of pregnancy, ensuring they are close to medical care when labor begins.

8. Task-shifting: Training and empowering non-medical healthcare workers, such as nurses and midwives, to perform certain tasks traditionally done by doctors can help alleviate the shortage of skilled healthcare professionals and improve access to maternal health services.

9. Health information systems: Implementing robust health information systems that capture and analyze data related to maternal health can help identify gaps in service delivery and inform evidence-based decision-making for targeted interventions.

10. Quality improvement initiatives: Implementing quality improvement initiatives in healthcare facilities, such as training healthcare providers on best practices for maternal care and ensuring the availability of essential supplies and equipment, can enhance the quality of care provided to pregnant women.

It is important to note that the specific context and needs of the target population should be considered when implementing these innovations to ensure their effectiveness and sustainability.

AI Innovations Description

Based on the provided description, the study aims to investigate technical and scale efficiency in the delivery of maternal and child health services in Zambia. The findings suggest that there is a significant inefficiency in resource use in the country, indicating the potential to expand services without injecting additional resources into the system. The study also identifies factors that drive performance, such as urbanization and the proportion of educated women in districts.

Based on these findings, the following recommendation can be developed into an innovation to improve access to maternal health:

1. Improve resource allocation: The study highlights the need for more efficient resource allocation in the delivery of maternal and child health services. This can be achieved by identifying districts with low technical efficiency and reallocating resources to those areas. By targeting resources where they are most needed, access to maternal health services can be improved.

2. Strengthen urban health facilities: The study shows that districts with higher urbanization rates tend to have higher technical efficiency. Therefore, investing in and strengthening urban health facilities can help improve access to maternal health services. This can include upgrading infrastructure, increasing staffing levels, and providing necessary equipment and supplies.

3. Enhance education and awareness: The study indicates that districts with a higher proportion of educated women tend to be more technically efficient. Promoting education and awareness among women, particularly in rural areas, can help improve access to maternal health services. This can be done through community-based education programs, outreach initiatives, and partnerships with local organizations.

4. Foster collaboration and innovation: To achieve universal health coverage and improve population health, decision-makers should seek efficient ways to deliver services. This can be done by fostering collaboration between different stakeholders, including government agencies, healthcare providers, and community organizations. Additionally, promoting innovation in service delivery, such as telemedicine and mobile health solutions, can help overcome geographical barriers and improve access to maternal health services in remote areas.

By implementing these recommendations, it is possible to develop innovative approaches that improve access to maternal health services in Zambia and potentially in other low-income countries facing similar challenges.

AI Innovations Methodology

Based on the provided description, here are some potential recommendations for improving access to maternal health:

1. Strengthening health system performance: The study highlights the need to investigate and address fundamental health system performance issues. This could involve improving the efficiency of resource utilization, enhancing coordination and collaboration among different health districts, and implementing effective management and governance structures.

2. Addressing regional disparities: The study found that progress in maternal and child health interventions was not uniform across the country. To improve access, targeted interventions should be implemented in regions with lower performance indicators. This could involve increasing investment in infrastructure, healthcare facilities, and skilled healthcare providers in underserved areas.

3. Enhancing education and awareness: The study identified a higher proportion of educated women as a factor associated with greater technical efficiency. Promoting education and awareness about maternal health, family planning, and the importance of antenatal and postnatal care can contribute to improved access and utilization of maternal health services.

4. Strengthening financial resources: The study highlighted the inefficiency in resource use in the country’s health system. To improve access to maternal health, it is important to ensure adequate and sustainable funding for maternal health services. This could involve increasing government investment, exploring innovative financing mechanisms, and leveraging donor funding effectively.

To simulate the impact of these recommendations on improving access to maternal health, a methodology could be developed using data envelopment analysis (DEA) or a similar approach. Here is a brief description of a possible methodology:

1. Data collection: Collect data on health outcomes (e.g., maternal mortality rates, infant mortality rates), health outputs (e.g., coverage of antenatal care, skilled birth attendance), and health system inputs (e.g., financial resources, human resources for health) for different health districts or regions.

2. Data envelopment analysis: Use DEA to assess the performance of each health district or region in terms of technical and scale efficiency. DEA is a mathematical modeling technique that compares the relative efficiency of different decision-making units (in this case, health districts) by measuring their ability to convert inputs into outputs.

3. Environmental factors: Control for environmental factors that are beyond the control of health system decision-makers, such as urbanization, education levels, and donor funding. This can be done by including these factors as additional variables in the DEA model.

4. Efficiency scores: Calculate efficiency scores for each health district or region, indicating their level of efficiency in delivering maternal health services. This can help identify districts or regions that are performing well and those that need improvement.

5. Simulating impact: Simulate the impact of the identified recommendations on improving access to maternal health by adjusting the input variables in the DEA model. For example, increase the financial resources allocated to underserved areas or improve education levels in regions with lower efficiency scores. Measure the resulting changes in efficiency scores and health outcomes to assess the potential impact of the recommendations.

6. Sensitivity analysis: Conduct sensitivity analysis to test the robustness of the results and assess the potential variability in the impact of the recommendations under different scenarios or assumptions.

By following this methodology, policymakers and health system decision-makers can gain insights into the potential impact of different recommendations on improving access to maternal health and make informed decisions on resource allocation and policy interventions.

Autor

Dima Health

Statistics:

Citations: 9

Identifiers:

DOI: 10.1136/bmjopen-2016-012321

Research Areas:

Community Interventions, Disparities, Health System and Policy, Infectious Diseases, Maternal Access, Maternal and Child Health, Quality of Care, Social Determinants, Workforce

Study Countries:

Zambia

Study Design:

Cross Sectional Study, randomised-control-trial

Participants Gender:

Female

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