Eciency in Utilization of the Resources Allocated to Lower Level Health Facilities in Uganda: a Case Study of Health Centre IVs

Background: Everyone has a right to quality life with good health of the household and, thus, health sector nancing should be a top priority because when the population is healthy, it is very productive and wealthy. In Uganda, Health Centre IVs (HCIVs) created under Uganda National Minimum Health Care Package provide curative, prevention and promotion services. The eciency of these HCIVs is as critical as people’s health and this paper measures eciency in utilization of resources allocated to them. Methods: The study used Hospital and HCIV Census data for 2014 and health sector data for FY2015/16 reported by MOH in the Annual Health Sector Performance Report. STATA software was used to perform Data Envelopment Analysis for a preferred model was out-put oriented that optimizes variable returns to scale. In this way, eciency scores for every HCIV were calculated. Also, a Tobit regression model was run to estimate the factors contributing to the adjusted ineciency scores for HCIVs. Results: Overall, 7 HCIVs (23.3%) were operating under constant returns to scale, implying that they were ecient (both pure technical and scale eciency) while the 19 (63.3%) were operating under increasing returns to scale, implying that their health service outputs would increase by a greater proportion compared to any proportionate increase in health services if more inputs were added in the facility. Four HCIVs (13.3%) were operating at decreasing returns to scale meaning an additional input to the HCIVs would produce a less proportional change of outputs. The study identied catchment population, average length of stay, bed occupancy rate, and outpatient department visits as a proportion of inpatient days as the main factors of eciency among HCIVs. Conclusions: This study has shown how Data Envelope Analysis methods can be applied at the HCIV level of the health system to gain an insight into variation in eciency across health centers using routinely available data. And, with the majority of HCIVs operating at increasing returns to scale, it showed that there is a need to increase inputs like staff, medicines and beds to achieve the desired optimal scale in case of constant returns to scale.


Introduction Background
Health service delivery is a major priority both at the international and national levels. At the international level, Goal 3 of the Sustainable Development Goals (SDGs) [1] aims to ensure health and well-being for all at all ages by improving general health for mothers and children while reducing prevalence of noncommunicable diseases, improving health coverage for all and ensuring that medicines and vaccines are accessed at affordable rates in good quality.
The Ugandan government has indicated the priority of population health in several documents and one of the objectives of the National Development Plan [2] is to contribute to the production of a healthy human capital through the provision of equitable, safe and sustainable health services. The National Health Policy [3] states the health system objective is to ensure universal access to quality Uganda National Minimum Health Care Package (UNMHCP) consisting of Promotive, Preventive, Curative and rehabilitative and palliative services to all prioritized diseases and conditions with emphasis to the vulnerable population. This is also echoed in the Health Sector Development Plan (HSDP 2014/15 -2019/20) [4] whose goal is to accelerate movement towards Universal Health Coverage (UHC) with essential health and related services needed for the promotion of health and productive life.
To achieve these goals, mentioned above, means that hospitals, clinics, medicines, and doctors' services should be accessible, available, acceptable, and of good quality for everyone, on an equitable basis, where and when needed. Hospitals and Health centers at the lower levels of service delivery, therefore, become a vital part of any health care system and account for a large proportion of the government's budget in most African countries [5].
In low and middle-income countries, health facilities at lower levels, mainly in rural and semi-urban areas, continue to be the main providers of healthcare to the communities and in Uganda, they accounted for 14% of the government's health care budget [6]. The ability to measure and compare their performance within the context of e cient utilization of resources is an important step in beginning to address some of the health care challenges that exist in this region.

Healthcare Services in Uganda
In Uganda, the healthcare delivery system is made up of public facilities (government) owned as well as privately owned. The districts and health sub-districts are major players in delivering health services at their respective levels as the decentralization process equipped them to perform. The health services are structured with National Referral Hospitals (NRHs) at the top, followed by Regional Referral Hospitals (RRHs), General Hospitals, and Health Centres (HC IVs, HC IIIs, and HC IIs).
Health Centre level IV, run by a Senior Medical o cer, which in addition to all the services provided at HC III, is intended to provide blood transfusion services and emergency surgical services, and comprehensive emergency obstetric care including caesarean sections. The key feature of the UNMHCP was that each Health Sub District, which has approximately 100,000 people, would have a hospital or HC IV. According to the Health Sub-district (HSD) concept, an HC IV is the rst referral facility in HSD without a hospital (Government or PNFP). The total number of HC IVs is 206 of these 182 (88%) are government, 17 (8.2%) NGOs, and 7 (3.4%) privately owned (MOH, 2014) [15].
While some health facilities operate as designed and expected, others do not meet the expectations for different reasons that might be nancial, technical, or otherwise. This is even more visible in low and middle-income countries, who, have high-cost inputs, the inappropriate scale of service delivery, and inadequate staff remuneration [7] that combine to bring down the general health facility performance.
The functionality of the HC IV, in Uganda, is determined by outputs from selected components of minimum service standards i.e. maternity (deliveries), inpatient, blood transfusions, theatre (Caesarean Section, major and minor surgeries), HIV/AIDS Counselling and Testing, Prevention of Mother to Child Transmission, Anti-Retroviral Therapy, and long term contraception and outpatient services.
HC IV performance has been assessed using the Standard Unit of Output. The assessment covered 196 Health Centre IVs that reported through the district health information system. In total, for FY 2015/16, HC IVs attended to 4,274,028 outpatients; conducted 170,670 deliveries; and admitted 526,206 patients. The average outpatient attended to was 21,988, mean deliveries 748, and mean admission 2,347 as obtained from MOH [8]. Using this criterion, 45% (88/196) of the HC IVs were "functional" meaning able to do a cesarean section. For blood transfusion, 36% (70/196) were able to provide this service. Those able to provide both caesarean section and blood transfusion were 29% (57/196) which, overall, show low functionality of HC IVs.
The Uganda National Health Policy [9] while emphasizing that the sector will aim at mobilizing resources that are su cient for government programs in an equitable, e cient and transparent manner, also asserts that e ciency is not well addressed whether in mobilization process allocation to different facilities or in utilization to achieve intended outcomes. This desire to improve e ciency is being emphasized both in the short-term and long-term development plans of government as evidenced in the Health sector development plan [10]. For this to be achieved, therefore, information on the current level of e ciency in the delivery of the various health services and the drivers of ine ciency will be required and currently, there has been no study done on e ciency at the HC IV level.
In Uganda [11; 12], other developing countries [13], and developed countries [14], there have been studies that applied Data Envelopment Analysis (DEA) to measure e ciency in health facilities as well as in economic development. They however used data from hospitals big and small while they ignored health centers as independent facilities that deliver substantial healthcare services to the people, especially in Uganda. This study, therefore, will rst add a knowledge brick to the e ciency literature and bring forward evidence for Uganda's health sector so that policymakers can utilize the ndings for a well-developed policy.

Summary
This is an analytical study whose main focus is to assess the e ciency levels in the utilization of resources at the lower-level health facilities with data on HC IVs obtained from surveys by MOH [15]. We applied the Data Envelopment Analysis approach (output-oriented model with Variable Returns to Scale) in STATA was employed to calculate the e ciency scores for HC IVs in the sample. To estimate the factors that make impact on adjusted ine ciency scores of health centre IVs, a Tobit regression model was deemed t and run.
To assess Health Facility (HF) performance at the aggregate level and to inform policy decisions, there has been increasing use of the DEA method in the computation of e ciency scores. The DEA was used to test the e ciency of 30 HC IVs which were of different sizes and whose functionality was within the public domain both for-pro t and not-for-pro t. The scope of the analysis was to assess the technical e ciency and scale e ciency. The HF operations were represented employing an input-output model whereby each HF uses quantities of inputs to generate outputs in the form of services.

Conceptual Framework
Health centers speci cally the HC IVs use multiple health system inputs (e.g. health workers, medicines and supplies, electricity, water, infrastructure) to produce multiple health service outputs (e.g. inpatient care, outpatient care, surgery, blood transfusion) through a production process. These inputs which are summarized as labor and capital, combine via medical and surgical care to produce outputs. While the ultimate goal of healthcare is the marginal change in the health status of the people, this is di cult to measure in most data sets and the intermediate outputs or the episodes of care like the number of cesarean section operations and outpatient visits usually become the primary study outputs. Coelli T. et. al., (2005) [16] asserts that this production process, in health facilities, does not occur in a vacuum which means that it can be in uenced by several environmental factors both internal and external to the health center and this may manipulate how e ciently the production process occurs. Kumbhakar and Lovell (2000) [17] add that these factors are theorized either to affect the production process itself or to in uence directly the e ciency of the process. Figure 1 depicts the relationship between health system inputs, the production process, and the outputs which then forms the framework for our study.
The issue of measuring e ciency especially in the health sector is cumbersome because the service provision process is intricate enough regarding the true measurement of health improvement of an individual. The procedure of technical e ciency is often applied to answer this question and takes inputto-output formations to determine the outcome.
When dealing with the issue of output-oriented technical e ciency, the concentration of an analyst is on how to scale-up the amount of outputs while keeping the amount of inputs used xed. On the other hand, input-oriented technical e ciency focuses on reducing input quantities used without changing the number of outputs produced.
Frontier techniques and the rations which measure utilization level of hospitals can be employed to measure the performance of health centres basing on the production theory of microeconomics. Commonly used ratios include bed occupancy rate, turnover ratio, turnover interval, and an average length of stay. Frontier methods of e ciency measures include linear programming techniques (e.g. data envelopment analysis) and econometric techniques (e.g. production and cost functions). E ciency has been generally de ned as the allocation of scarce resources that maximizes the achievement of aims [18] while e ciency analysis of a production or service unit refers to the comparison between the outputs and inputs used in the process of producing a product or service [19]. According to Zainal and Ismail [20], e ciency relates to how best a rm utilizes the inputs to produce the desired products or services (outputs), which is indicative of the success of the rm and this is supported by Farell [21] who sees e ciency as success in producing as large as possible output from a given set of inputs and thus, in general, e ciency measures how best the value for money is being obtained from resources available.
The conceptual discussion of measuring e ciency is attributed to Koopmans [22] while an empirical measure of e ciency was pioneered by Farell [21], who classi ed e ciency into the two components of technical e ciency (TE) and allocative e ciencies (AE), both of which constitute the components of economic e ciency [17]. The idea is that a production unit is technically e cient if it is no longer possible to produce more output using more of the available inputs [22] which means an optimal position between inputs and outputs.
The aim of technical e ciency measurement, therefore, is to avoid wastage of resources by using more inputs when the technological and other support mechanisms have reached their limit of output produced. By implication, there can be an output augmenting orientation or an input conserving orientation dimension to the analysis of technical e ciency as observed by Kumar and Gulati [33]. Technically ine cient producers could use the same inputs to produce more of at least one output or could produce the same outputs with less of at least one input. Technical E ciency reveals the ability of rms to employ the 'best practice' in an industry, such that no more than a given level of output can be produced using the minimum level of input. On the other hand, allocative e ciency refers to the optimal combination of inputs and outputs at a given price.
The ability to combine inputs and/or outputs in optimal proportions in light of prevailing prices is the focus of allocative e ciency in a business entity and these are satisfactory for the rst-order conditions that a production facility is assigned. As implied by Chen and Zhu (2011), allocation of resources is considered e cient when the output from the last unit of resources is the same for different Decision-Making Units (DMUs) [34] or health centres in the case of this study. In the health context, e ciency is concerned with the relation between resource inputs (labour, capital, material, or equipment) and health outcomes (e.g. numbers of patients treated, lives saved). The existence of ine ciency is indicated by the possible reallocation of resources in a manner that increases health outcomes produced. The technical e ciency of a hospital or health facility refers to the physical relation between health resources (capital, labour, and materials) and health outcomes.
However, ndings have shown that most health HCIVs are not functioning as expected in terms of the major services they are meant to provide including caesarean sections and blood transfusion services (MOH, 2015) [10; 15]. This, therefore, calls for an examination of the challenges affecting the functionality of the HC IVs to provide a Minimum Health Care package. The question, therefore, is whether it is e ciency in resource utilization that is affecting the functionality of the lower-level facilities (HC IVs) or if there could be other factors that could be leading to the non-functionality of HC IVs. Data Envelopment Analysis (DEA) Data Envelope Analysis methodology, originally proposed in (Charnes et al., 1978) [23], was used to assess the relative e ciency of several entities using a common set of commensurate inputs to generate a common set of commensurate outputs. The original motivation for Data Envelope Analysis was to compare the productive e ciency of similar organizations, referred to as Decision Making Units. The problem of assessing e ciency is formulated as a task of fractional programming, but the application procedure for Data Envelope Analysis consists of solving linear programming (LP) tasks for each of the units under evaluation.
The e ciency of a Decision-Making Unit (DMU) is measured relative to all other Decision-Making Units with the simple restriction that all Decision-Making Units lay on or below the extreme frontier. Differing from other methods like regression equations that require any assumptions on their functional forms, Data Envelope Analysis is non-parametric in nature.
DEA was also used to calculate the e ciency scores for each of the health centers in the sample. The e ciency scores for each DMU (health centre) was tested through an out-put-oriented model that focussed of returns to scale that were variable using STATA software and was in the same sense used by Mujasi et al (2016) [12]. The VRS model estimated the pure technical e ciency and scale e ciency for each of the sample health centers. From the VRS model, analysis was made to establish whether an HC IV's production frontier indicated increasing returns to scale, constant returns to scale, or decreasing returns to scale.
Since not all health centres are functioning optimally, there was a need to look at variable returns to scale of each DMU so that the model chosen matches the reality of HCIVs in the country. Also, given the existence of unmet needs and low quality of care in developing countries like Uganda, there was a need to analyse the e ciency amounts that can be potentially saved and thus be used to escalate healthcare provision positively at health centre level as Mujasi et al (2016) [12] did for hospitals in Uganda.
On the ip side, however, it has been found that researchers have been reluctant to use Data Envelope Analysis as an analysis tool since it lacks a crucial error term (Valdmanis, 1992) [24]. However, a functional form was not the main goal or concern of this study but rather making the right mix between inputs and outputs for a health facility because DEA utilizes linear programming techniques to solve the service provision mix.
Data Envelope Analysis methodology, originally proposed in (Charnes et al., 1978) [23], was used to assess the relative e ciency of many entities using a common set of commensurate inputs to generate a common set of commensurate outputs. The original motivation for Data Envelope Analysis was to compare the productive e ciency of similar organizations, referred to as Decision Making Units. The problem of assessing e ciency is formulated as a task of fractional programming, but the application procedure for Data Envelope Analysis consists of solving linear programming (LP) tasks for each of the units under evaluation.
Assuming that there are j health centers, each with n inputs and m outputs, the relative e ciency score of a given health center (θ) is obtained by solving the following output-orientated DEA (Charnes et al., 1978) [23] linear programming model; Subject to the constraints that: Where: θ 0 = The e ciency score of hospital O x nj = The amount of health system input n utilized by the j th hospital Y mj = The amount of health system output m produced by the j th hospital U m = The weight is given to health system output m V n = The weight is given to health system input n Source: Mujasi et. al. (2016) As stated in Mujasi et al (2016) DEA faces one major shortcoming of producing e ciency scores that are susceptible to outlier-effect from DMUS [12] meaning that if there are few health centres which perform extremely well in the dataset, this will in uence the e ciency scores of the rest of facilities. In either case, the results for the remaining Decision-Making Units become shifted towards lower e ciency levels, the e ciency frequency distribution becomes highly asymmetric, and the overall e ciency scale becomes nonlinear.
Thus, in this study, jack-knife analysis was used to test for the robustness of the Data Envelope Analysis technical e ciency measures and assess if extreme outliers were affecting the frontier and e ciency scores. While trying to avert the consequences of outlier-effect, we decided to drop each health centre that was highly e cient, taking one after the other, and re-estimating the e ciency scores until there was stability in the model.

Econometric Analysis (Tobit Regression Model)
In the second stage of analysis, the DEA e ciency scores computed in the previous section were regressed against some institutional factors that affect or in uence health facility management and some factors that within the environment of the same facility so as to measure their effect on how well e cient is the facility.
Thus, using the VRS technical e ciency scores as a dependent variable and given that the scores have upper-censor-limit (100%), a Tobit regression model was used to estimate the adjusted e ciency scores for each health center, and this obtained estimates of the linear Tobit model, where the dependent variable is either zero or positive. Maximum likelihood method was applied, in this study, following the assumption that all normal disturbances of the model are homoscedastic. The following Tobit regression Model was used: Tobit(Y i ) = α 0 + α 1 x j1 + α 2 x j2 + α 3 x j3 + K + ε j …... (3.2) Where: Y j = The variable return to scale e ciency score for the j th hospital x j = The explanatory variables ε j = The disturbance (error) term assumed to be normally distributed with mean µ and standard deviation δ α = The Tobit coe cients indicate how a one-unit change in an independent variable alters the latent dependent variable. Sometimes, the values of the Tobit coe cients cannot be interpreted but their signs are very helpful for interpreting the results of the study.
Following Asbu [43], the Variable Returns to Scale DEA technical e ciency scores were transformed into ine ciency scores, left-censored at zero using the formula: The initially estimated general model contained all the identi ed explanatory variables and was: Ineff = α + β 1 BOR + β 2 OPDIPD + β 3 ALOS + β 4 OWN + β 5 POPNCAT + β 6 SIZE + ε i ... 3.4 Where β is the vector of unknown parameters or coe cients; and ε i is the stochastic/random error term. I estimate the Tobit regression using STATA_13 for Windows®.
Secondly, we tested the hypothesis that βn is not signi cantly different from zero in either direction. Thus, the null (Ho) and alternative hypotheses (Ha) are: Ho: βn = 0 while Ha: βn≠0 The t-distribution tests were preferred to measure the signi cance of each and every individual null hypotheses.
However, the objective was to estimate a parsimonious Tobit model that would help explain the observed ine ciencies. Such a model would be signi cant based on the Chi-Square. Thus, through an iterative process, several models were run containing various combinations of the explanatory variables.
The nally accepted model based on the Chi-Square was: Ineff = α + β 1 BOR + β 2 OPDIPD + β 3 ALOS + β 4 OWN + β 5 POPNCAT + β 6 SIZE + ε i Based on past two-stage health facilities e ciency studies, I would expect a negative relationship between the Ineff and OPDIPD, and thus, β 2 is assumed to be a negative sign. Tobit coe cients indicate how a one-unit change in an independent variable xi alters the latent dependent variable Ine ciency.

Data and Variable Choice
This study used different sources of data of which some are primary (use of questionnaires) while other sources are secondary. The secondary sources consisted of Uganda hospital and HC IV Census data for 2014 [15] and the health sector data for FY2015/16 Financial year (July 1, 2015, to June 30, 2016) as reported by the MOH in the annual health sector performance report (AHSPR) [25] to explore the technical e ciency of health center IVs during that period.
In this study, the focus was put on HC IV Inputs and outputs. Data was assembled for 2 different inputs (HC IV staff, hospital beds) and 6 outputs (inpatient days, C-Sections, Blood Transfusions, deliveries, OPD visits, and immunizations). Based on the completeness of available data, the nal selection was limited to 2 inputs and 3 outputs. The inputs included the total number of health center staff a proxy to labor and hospital beds a proxy to Capital. The outputs included outpatient visits, C-Sections performed, and inpatient days. It was assumed that this input-output mix elucidates most of the HCIV activities. The Caesarean sections were, for example, added to the mix because it is one of the major factors government considers while determining the functionality of HC IVs.
The choice of the variables (input, output, and explanatory) shown in Table 1 [27], and Tlotlego et. al. (2010) [28] that undertook e ciency of hospitals in Africa also employed similar inputs and outputs except for C-Section which was added speci cally for Uganda's case. Secondly, the availability of relevant data in the ministry of health's annual health sector performance report for FY 2015/16 [25] and the availability of data that is routinely compiled by hospitals to demonstrate ways in which the Uganda Ministry of Health can get additional informational value from such data without investing a lot of resources. indicates that some of the factors that impact health facility e ciency include, catchment population, distance, location (urban/rural), ownership (pro t/not-for-pro t), teaching status, payment source (out-ofpocket/health insurance), occupancy rate, the average length of stay, outpatient visits as a proportion of inpatient days, and quality, and these were chosen as the explanatory variables for the health centre IV's e ciency. In this study, we selected the explanatory variables based on the availability of data as they are also described in Table 4.
We used labor to de ne staff/workers and the measurement was based on the total number of health workers at the facility, capital was de ned as beds basing on the total number of beds in the health facility in a year as measurement. We, also, used funding and the measurement was total PHC funds allocated to the HF in a year.
Output variables were inpatient days which were de ned as total inpatient days in a year, outpatient visits which were de ned as total outpatient visits made in a year, C-Section de ned as total C-Sections done in a year, and blood transfusions de ned as total blood transfusions done in a year.
Explanatory variables were bed occupancy rate measured as a proportion of beds which were occupied over a speci c period, proportion of outpatients to inpatients was measured as total OPD visits divided by the total number of inpatient days in a year, and catchment area was measured as the total population in the catchment area, average length of stay is measured by dividing the total number of inpatients days by the total admissions in the year and size of the hospital is measured by a bed capacity of the facility.
The data collected on inputs, outputs, and explanatory variables were entered into a computer using Excel software from where STATA 13 was used to import and analyse this same data for all stages.
The research used largely the secondary data from Ministry of Health which was approved by the research committee since it did not contradict the ethics and regulations of the institution. The questionnaires which were open-ended were sent to selected health centre managers to give their opinions on the e ciency of the HC IVs and they were required to consent before lling the forms. The questionnaires did not have names or personal information that would link the respondent to opinion or information shared and that was to protect their privacy with guidance from SPEED INITIATIVE Program under Makerere University School of Public Health.
In summary, with supervision from Makerere University School of Public Health, we con rm that, in this study, all methods were performed in accordance with the relevant guidelines and regulations. The study went through all o cial protocols and was given a waiver by IRB which in this case was Makerere University School of Public Health and it was deemed unnecessary according to national regulations.

Findings
Descriptive statistics of study variables  Determination of e ciency using DEA Table 3 shows the HC IV DEA scores where 7 HC-IVs (23.3%) Mukono, Dokolo, Wakiso, Rubaale, Bbale, Kakindo, and Kataraka were operating under constant returns to scale, implying that they were e cient (both pure technical and scale e ciency) concerning available sample. 19 of HC-IVs (63.3%) were operating under increasing returns to scale, implying that a unit increase in the inputs of these HC IVs would result in a bigger proportionate increase in their health service outputs. These health centers would need to increase their size of inputs like labor and capital to achieve the optimal provision of healthcare services.
Four (04) of HC IVs (13.3%) Bugangari, Luwero, Bugono, Anyeke were operating under decreasing returns to scale implying that a proportionate unit increase in inputs would have a detrimental effect on the health services outputs.  Table 3 and Figure 2, Health facilities like Bugangari, Luwero, Bugono, Anyek do not need to be added more resources because according to the study they are already receiving enough resources.
The cause of their ine ciency could be either lack of staff motivation, poor administration, absenteeism, non-functionality of equipment, or other factors that could be leading to ine ciencies.
Those on increasing returns to scale need more resources to improve their e ciency so that they can perform at their optimal levels. Resources needed could be equipment, human resource, improvement in administration, and other factors that can improve e ciency in the health facility.
Those working at constant returns to scale like Kakindo, Bbale, Mukono, Wakiso, Dokoro, Rubaale, and Kataraka need to be expanded to the hospital level because they have reached their maximum capacity of the operation. Additional of more resources may not add any value in the actual sense. They are performing at their optimal levels given the sample available.

Econometric Analysis of the determinants of ine ciency -Tobit Model
From Table 4, the higher the health center IV's OPD is, the lower the predicted ine ciency score consistent with our a priori expectation and statistically signi cant at a 5 percent level of signi cance (p>|t| = 0.033).
OPD with a coe cient of -0.0000338 means that a unit increase in OPD visits leads to a reduction in ine ciency by 0.00338% The Bed Occupancy Rate (BOR) has a negative sign indicating that the higher the bed occupancy rate the higher the e ciency score. In other words, a 1% increase in Bed Occupancy Rate (BOR) increases the e ciency score by 2.12% while holding all other factors in the model constant. The score coe cient is statistically signi cant at a 5% level (p < 0.05).
The size of HC IV, according to this study analysis, is not a signi cant factor in explaining health center ine ciency. The results indicate that the predicted ine ciency score for big HC IVs is 0.252 points lower than the reference category of small HC IVs (those with less than 30 beds) when all other factors are held constant.
The coe cient for ALOS (0.0906) has a positive sign and statistically not signi cant at the 5 percent level (p>|t| = 0.427). This means that a unit increase in the average length of stay of patients at the HC IV leads to a decrease in e ciency of 9%, holding all other variables constant. The higher a health center's ALOS, the lower the predicted ine ciency score With regards to catchment population (POPNCAT, results point out that the predicted ine ciency score for HC IVs with less than 60,000 people in their o cial catchment area is 0.3982 points lower than for the counterparts (those with at least 60,000 people in their catchment area) when all other factors are held constant. This shows that HC IVs with lower catchment areas have lower ine ciencies compared to their counterparts with higher population areas. However, it should be noted that in this study ndings indicate that the catchment population of HC IV is not statistically signi cant.
The coe cient for nancing has a positive sign and is not statistically signi cant at a 5 percent level (p>|t| = 0.891). This means that a unit increase in the nancial resources at health center IV does not affect its e ciency.  [32] who also show that a high BOR is associated with increased e ciency. However, this nding on BOR needs to be contextualized as ndings from other countries (the United Kingdom and Australia) have instituted a target occupancy rate as there was evidence that rates exceeding 85% in acute care hospitals are associated with problems in handling both emergency and elective admissions were not ideal for infection control and ensuring quality of care.
Policy Implications basing on ndings Based on the ndings presented above, we draw the following implications for policymakers involved in developing strategies for ensuring that all health facilities are made more e cient: We note that most facilities are under-resourced and hence providing additional resources would be critical to improving their e ciency. The focus on increasing resources should be to those that directly affect the production process such as human resources, infrastructure, and medical supplies.
For instance, most of these facilities are operating below their set norms.
For the facilities identi ed to be operating under decreasing returns to scale, policymakers need to ensure that any additional investments are followed by addressing within-facility factors that may impact the productivity of the facility and it is best done for each facility as an independent case.
There is a need to institutionalize monitoring of e ciency measurement within the routine performance assessment of the Ministry of Health as part of the broader framework of performance management Limitations of the study 1. This study assesses technical e ciency but does not attempt to address allocative e ciency. This is an area that future studies could consider.
2. The study also does not address issues of long-term productivity and only provides a snapshot of e ciency but there could be changes over time in uenced by various factors.
In an expanded e ciency study, more analysis would be made to get the input reductions and/or output increases that would have been required to make the individual pure technically ine cient HC IVs e cient. Future studies could also look at the optimal inputs required to obtain the desired inputs and hence inform the revision of sta ng and funding norms where need be.

Conclusion
The ndings provided empirical evidence of the technical e ciency of the sampled HC IVs. The study also identi ed some of the factors that in uence the attainment of e ciency among HC IVs. As policymakers focus on increasing access to health services, there is a need to address e ciency in providing these services. In addition to pushing strategies for ensuring e ciency to maximize the use of the scarce resources, there is a need to further interrogate within facility factors that may impact service delivery. This will be critical in addressing unmet needs especially for maternal health services which these HC IVs are supposed to provide.
The inappropriate size of an HC IV (too large or too small) may sometimes be a cause of technical ine ciency and many take this as scale ine ciency where it can be best described as either increasing returns-to-scale or decreasing returns-to-scale. Decreasing returns to scale (also known as diseconomies of scale) implies that a health center is too large for the volume of activities that it conducts. Unit costs increase as outputs increases. In contrast, a health center with increasing returns to scale (economies of scale) is too small for its scale of operation. Unit costs decrease as outputs increase. A Health Centre that is scale-e cient is said to operate under constant returns to scale.

VRS Variable Returns to Scale
Declarations Ethics approval and consent to participate The research used largely the secondary data from Ministry of Health which was approved by the research committee since it did not contradict the ethics and regulations of the institution.
The questionnaires which were open-ended were sent to selected health centre managers to give their opinions on the e ciency of the HC IVs and they were required to consent before lling the forms. The questionnaires did not have names or personal information that would link the respondent to opinion or information shared and that was to protect their privacy with guidance from SPEED INITIATIVE Program under Makerere University School of Public Health.
In summary, with supervision from Makerere University School of Public Health, we con rm that, in this study, all methods were performed in accordance with the relevant guidelines and regulations. The study went through all o cial protocols and was given a waiver by IRB which in this case was Makerere University School of Public Health and it was deemed unnecessary according to national regulations.

Consent for publication
All tables, graphs and charts in this paper are original and were done by Authors. This means that the "Consent for Publication" from another source is NOT APPLICABLE

Availability of data and material
The data set generated to use in this study was obtained from a government database and when needed, it can be availed through right channels. The dataset used can be obtained from Mr. Ahimbisibwe Expeditus on email expeditus2010@gmail.com .

Competing interests
The Authors declare that they have no competing interests Funding The Authors prepared this manuscript by themselves and were not paid to do this.