Summary
This is an analytical study whose main focus is to assess the efficiency 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 efficiency scores for HC IVs in the sample. To estimate the factors that make impact on adjusted inefficiency scores of health centre IVs, a Tobit regression model was deemed fit 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 efficiency scores. The DEA was used to test the efficiency of 30 HC IVs which were of different sizes and whose functionality was within the public domain both for-profit and not-for-profit. The scope of the analysis was to assess the technical efficiency and scale efficiency. 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 specifically 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 difficult 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 influenced by several environmental factors both internal and external to the health center and this may manipulate how efficiently the production process occurs. Kumbhakar and Lovell (2000) [17] add that these factors are theorized either to affect the production process itself or to influence directly the efficiency 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 efficiency 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 efficiency is often applied to answer this question and takes input-to-output formations to determine the outcome.
When dealing with the issue of output-oriented technical efficiency, the concentration of an analyst is on how to scale-up the amount of outputs while keeping the amount of inputs used fixed. On the other hand, input-oriented technical efficiency 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 efficiency measures include linear programming techniques (e.g. data envelopment analysis) and econometric techniques (e.g. production and cost functions).
Efficiency has been generally defined as the allocation of scarce resources that maximizes the achievement of aims [18] while efficiency 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], efficiency relates to how best a firm utilizes the inputs to produce the desired products or services (outputs), which is indicative of the success of the firm and this is supported by Farell [21] who sees efficiency as success in producing as large as possible output from a given set of inputs and thus, in general, efficiency measures how best the value for money is being obtained from resources available.
The conceptual discussion of measuring efficiency is attributed to Koopmans [22] while an empirical measure of efficiency was pioneered by Farell [21], who classified efficiency into the two components of technical efficiency (TE) and allocative efficiencies (AE), both of which constitute the components of economic efficiency [17]. The idea is that a production unit is technically efficient 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 efficiency 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 efficiency as observed by Kumar and Gulati [33]. Technically inefficient 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 Efficiency reveals the ability of firms 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 efficiency 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 efficiency in a business entity and these are satisfactory for the first-order conditions that a production facility is assigned. As implied by Chen and Zhu (2011), allocation of resources is considered efficient 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, efficiency 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 inefficiency is indicated by the possible reallocation of resources in a manner that increases health outcomes produced. The technical efficiency of a hospital or health facility refers to the physical relation between health resources (capital, labour, and materials) and health outcomes.
However, findings 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 efficiency 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 efficiency 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 efficiency of similar organizations, referred to as Decision Making Units. The problem of assessing efficiency 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 efficiency 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 efficiency scores for each of the health centers in the sample. The efficiency 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 efficiency and scale efficiency 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 efficiency 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 flip 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 efficiency 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 efficiency of similar organizations, referred to as Decision Making Units. The problem of assessing efficiency 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 efficiency score of a given health center (θ) is obtained by solving the following output-orientated DEA (Charnes et al., 1978) [23] linear programming model;
…... (3.1)
Subject to the constraints that:
v1x1j + v2x2j + K + vmxmj
Where:
θ0 = The efficiency score of hospital O
xnj = The amount of health system input n utilized by the jth hospital
Ymj = The amount of health system output m produced by the jth hospital
Um = The weight is given to health system output m
Vn = 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 efficiency 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 influence the efficiency scores of the rest of facilities. In either case, the results for the remaining Decision-Making Units become shifted towards lower efficiency levels, the efficiency frequency distribution becomes highly asymmetric, and the overall efficiency scale becomes nonlinear.
Thus, in this study, jack-knife analysis was used to test for the robustness of the Data Envelope Analysis technical efficiency measures and assess if extreme outliers were affecting the frontier and efficiency scores. While trying to avert the consequences of outlier-effect, we decided to drop each health centre that was highly efficient, taking one after the other, and re-estimating the efficiency scores until there was stability in the model.
Econometric Analysis (Tobit Regression Model)
In the second stage of analysis, the DEA efficiency scores computed in the previous section were regressed against some institutional factors that affect or influence health facility management and some factors that within the environment of the same facility so as to measure their effect on how well efficient is the facility.
Thus, using the VRS technical efficiency 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 efficiency 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(Yi) = α0 + α1xj1 + α2xj2 + α3xj3 + K + εj …... (3.2)
Where:
Yj = The variable return to scale efficiency score for the jth hospital
xj = The explanatory variables
εj = The disturbance (error) term assumed to be normally distributed with mean µ and standard deviation δ
α = The Tobit coefficients indicate how a one-unit change in an independent variable alters the latent dependent variable. Sometimes, the values of the Tobit coefficients 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 efficiency scores were transformed into inefficiency scores, left-censored at zero using the formula:
…... (3.3)
The initially estimated general model contained all the identified explanatory variables and was:
Ineff = α + β1BOR + β2OPDIPD + β3ALOS + β4OWN + β5POPNCAT + β6SIZE + εi ...3.4
Where β is the vector of unknown parameters or coefficients; and εi is the stochastic/random error term. I estimate the Tobit regression using STATA_13 for Windows®.
By estimating the empirical model, I will test two hypotheses; first, to test the overall significance of the model, where the joint null hypothesis was as follows:
H0 : β1 = β2 = β3 = β4 = β5 = β6 = 0
And the alternative hypothesis was as follows:
HA : β1 = β2 = β3 = β4 = β5 = β6 ≠ 0 The joint null hypothesis was tested using the likelihood ratio test (LL).
Secondly, we tested the hypothesis that βn is not significantly 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 significance of each and every individual null hypotheses.
However, the objective was to estimate a parsimonious Tobit model that would help explain the observed inefficiencies. Such a model would be significant based on the Chi-Square. Thus, through an iterative process, several models were run containing various combinations of the explanatory variables.
The finally accepted model based on the Chi-Square was:
Ineff = α + β1BOR + β2OPDIPD + β3ALOS + β4OWN + β5POPNCAT + β6SIZE + εi
Based on past two-stage health facilities efficiency studies, I would expect a negative relationship between the Ineff and OPDIPD, and thus, β2 is assumed to be a negative sign. Tobit coefficients indicate how a one-unit change in an independent variable xi alters the latent dependent variable Inefficiency.
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 efficiency 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 final 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 in-patient 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 was guided by three considerations. First of all, past studies including Zere et. al. (2006) [26], Kirigia et. al. (2008) [27], and Tlotlego et. al. (2010) [28] that undertook efficiency of hospitals in Africa also employed similar inputs and outputs except for C-Section which was added specifically 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.
Table 1
Description of the study variables for HCIVs (n=30)
VARIABLE
|
DEFINITION
|
MEASUREMENT
|
DATA SOURCES
|
Input Variables
|
|
⊗ Questionnaires
⊗ Hospital and HC IV Census report 2014
⊗ Annual Health Sector Performance Report
⊗ HRH REPORTS
⊗ FY2015/16
|
Labour
|
Staff/workers
|
Total no. of health workers at the facility year year
|
Capital
|
Beds
|
Total no. of beds in an HF in a year
|
Funds
|
Funding
|
Non-Wage + PHC in a given year
|
Output Variables
|
|
IPD
|
Inpatient days
|
Total inpatient days in a year
|
OPD
|
Outpatient visits
|
Total outpatient visits made in a year
|
C-Sect
|
C-Sections
|
Total C-sections done in a year
|
Blood
|
Blood transfusions
|
Total blood transfusions done in a year
|
Explanatory Variables
|
|
BOR
|
Bed Occupancy Rate
|
The proportion of beds that were occupied over a specific period
|
OPDIPD
|
The proportion of outpatients to inpatients
|
Total OPD visits divided by total inpatient days in a year
|
ALOS
|
Average Length of Stay
|
Dividing the total number of inpatient days by the total admissions in a year
|
POPNCAT
|
Catchment Population
|
Total population in the catchment area
|
SIZE
|
Size of the hospital
|
Proxy: Bed capacity of the facility where 1=30 beds and above while 0=otherwise
|
The literature including Vladmanis (1992) [24], Rosko et. al. (1995) [29], and Zere et. al. (2006) [26] indicates that some of the factors that impact health facility efficiency include, catchment population, distance, location (urban/rural), ownership (profit/not-for-profit), teaching status, payment source (out-of-pocket/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 efficiency. 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 define staff/workers and the measurement was based on the total number of health workers at the facility, capital was defined 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 defined as total inpatient days in a year, outpatient visits which were defined as total outpatient visits made in a year, C-Section defined as total C-Sections done in a year, and blood transfusions defined 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 specific 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 efficiency of the HC IVs and they were required to consent before filling 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 confirm that, in this study, all methods were performed in accordance with the relevant guidelines and regulations. The study went through all official 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.