Efficiency measurement method

DEA was first used to measure efficiency by Charnes et al. (Reference Charnes, Cooper and Rhodes1978), building on Farrell’s (Reference Farrell1957) productive efficiency ideas. The basic model of DEA is fractional programming (FP), which is difficult to compute. Later, the FP model was modified into linear programming (LP), making it easy to calculate efficiency values. DEA LP models can be divided according to production technology criteria into two types: constant returns to scale, known as CCR, and variable returns to scale (VRS), commonly called BCC (Banker et al., Reference Banker, Charnes and Cooper1984). Each type can be further divided based on the orientation of measurement into two categories: input-oriented and output-oriented.

DEA is a method for measuring the technical efficiency (TE) of an organization with no specified form of production function and is considered a nonparametric technique. DEA uses the theories of LP as the basis for determining efficiency index values. The DEA method is appropriate if a decision-making unit (DMU), THPH in this case, has multiple inputs and outputs and if the inputs’ and outputs’ market prices are unavailable or difficult to estimate. Therefore, DEA is suitable for measuring the operational efficiency of government agencies or non-profit organizations (Charnes et al., Reference Charnes, Cooper and Rhodes1978; Gouveia et al., Reference Gouveia, Dias, Antunes, Mota, Duarte and Tenreiro2016).

In brief, DEA works by using the inputs and outputs of all DMUs to construct an efficiency frontier of DMUs in the form of a linear combination. A DMU located on the frontier is considered 100% efficient since it produces the maximum outputs using a given level of inputs, while a DMU outside the frontier is deemed inefficient or has fewer than 100% efficiency scores. The efficiency index (ranging from 0 to 1.00) is directly proportional to the DMU’s distance from the efficiency frontier. For any given set of weights, a DMU that produces one-half the outputs that a 100% efficient DMU produces using the same level of inputs is considered to have an efficiency index of 0.5.

Based on the above details, the efficiency index obtained through DEA is regarded as a relative efficiency measure. This is because the efficiency index of an inefficient DMU is determined by comparing its inputs and outputs with those of a specific set of efficient DMUs on the efficiency frontier, which is called a reference set.

In this study, a VRS output-oriented model was used to measure the operational efficiency of THPHs. The model can be written as follows.

$${\rm{Max\;}}{{\rm{Z}}_{\rm{k}}}={{\rm{\theta }}_{\rm{k}}} + {\rm{\varepsilon }}\left( {{\rm{\;\;}}\mathop \sum \limits_{\matrix{ {r =1} }}^{\matrix{ s}} {\rm{S}}_{{\rm{rk}}}^ + {\rm{ + \;}}\mathop \sum \limits_{\matrix{{i\; = 1}}}^{\matrix{ m}} {\rm{S}}_{{\rm{ik}}}^ - } \right)$$

Subject to ${{\rm{X}}_{{\rm{ik}}}} - {\rm{S}}_{{\rm{ik}}}^ - - \mathop \sum \limits_{\matrix{ {j\; = 1}} }^{\matrix{ n } } {\rm{\;}}{{\rm{\lambda }}_{\rm{j}}}{{\rm{X}}_{{\rm{ij}}}} = {\rm{}}0$ ; i = 1,2,3,…,m; j = 1,2,3,…,k,…,n

$\mathop \sum \limits_{\matrix{{j= 1}} }^{\matrix{ n} } {{\rm{\lambda }}_{\rm{j}}}{{\rm{Y}}_{{\rm{rj}}}} - {\rm{}}{{\rm{\theta }}_{\rm{k}}}{{\rm{Y}}_{{\rm{rk}}}} - {\rm{S}}_{{\rm{rk}}}^ + {\rm{}} = {\rm{}}0$ ; r = 1,2,3,…,s

$$\mathop \sum \limits_{\matrix{{j= 1}} }^{\matrix{ n}} {{\rm{\lambda }}_{\rm{j}}}{\rm{}} = {\rm{}}1$$

${{\rm{\lambda }}_{\rm{j}}}{\rm{,\;S}}_{{\rm{rk}}}^ + {\rm{,\;S}}_{{\rm{ik}}}^ - {\rm{\;}} \ge {\rm{\;0\;\;\;;\;\;}}{{\rm{\theta }}_{\rm{k}}}$ (unrestricted)

${\rm{\varepsilon }}$ is an infinitesimally small number,

where

θ_k = The output augmentation index of the k^th DMU

Y_rj = The value of r^th output for the j^th DMU

X_ij = The value of i^th input for the j^th DMU

${\rm{S}}_{{\rm{rk}}}^ + $ =The slack variable of the r^th output for the k^th DMU

${\rm{S}}_{{\rm{ik}}}^ - $ = The slack variable of the i^th input for the k^th DMU

The significant data obtained from the application of the chosen DEA model comprised the following: 1) the efficiency index of each THPH (TE), with ${\rm{T}}{{\rm{E}}_{{\rm{k\;\;\;}}}} = 1/{{\rm{\theta }}_{\rm{k}}}\;$ ; 2) the slack variable values of the outputs ( ${\rm{S}}_{\rm{r}}^ + $ ); and 3) the slack variable values of the inputs ( ${\rm{S}}_{\rm{i}}^ - $ ). These data could be used to determine input and output targets in order to improve the efficiency of inefficient THPHs, as detailed below.

$${\rm{X}}_{{\rm{ik}}}^{/{\rm{\;}}}{\rm{\; = \;}}{{\rm{X}}_{{\rm{ik}}}} - {{\rm{S}}^ - }_{{\rm{ik}}}^{\rm{*}}$$

$${\rm{Y}}_{{\rm{rk}}}^{/}{\rm{=(\theta }}{{\rm{*}}_{\rm{k}}}{\rm{\;)\;Y}}_{{\rm{rk}}}^{\rm{\;}}{\rm{\; + \;}}{{\rm{S}}^ + }_{{\rm{rk}}}^{\rm{*}}$$

where

${\rm{X}}_{{\rm{ik}}}^{/{\rm{\;}}}$ = The input target value

${\rm{Y}}_{{\rm{rk}}}^{/{\rm{\;}}}$ = The output target value

Data and variables

EEC consists of three provinces, as indicated, all of which are considered homogeneous in terms of social, economic, and demographic characteristics. Therefore, we defined each province as a cluster and then employed a cluster random sampling approach to select one province, Chachoengsao, as the sample area. Initially, the efficiency of all 117 THPHs in this province was intended to be examined. Data collection was carried out between September 18 and November 15, 2023. Questionnaires were sent online to each THPH to gather THPHs’ inputs and outputs for fiscal year 2022. Follow-up measures were taken in the case of incomplete or delayed data submission. Finally, 104 THPHs provided complete data and served as the sample in this study. A sample size of 104 THPHs highly met the DEA criterion of n ≥ 3(number of input variables + number of output variables) proposed by Banker et al. (Reference Banker, Charnes, Cooper, Swarts and Thomas1989). The present study had five input variables and seven output variables, so the appropriate sample size should be n ≥ 36.

Selecting variables for use in efficiency evaluation is a critical step. The DEA model’s variables must be able to clearly reflect the operational characteristics of production units, both in terms of inputs and outputs, in order to obtain DEA results that can be used to effectively improve operational efficiency according to organizational contexts (Bowlin, Reference Bowlin1998). The researchers selected the variables in this study based on two criteria: 1) they had to be commonly and widely used in PHC performance studies around the world; and 2) they had to be relevant to THPHs’ operational contexts, especially output variables that cover the four main missions. The selection process included two steps: 1) the researchers reviewed relevant literature and research to develop a tentative set of input and output variables and 2) seven experts were asked to examine the content validity using the index of item objective congruence (IOC). Based on the results, five input variables and seven output variables with an IOC value of 0.7 or higher were included in the model. The description of each input variable is provided below.

1. 1) Personnel (I1): Personnel are a significant input variable commonly used in efficiency studies of public health agencies (Pelone et al., Reference Pelone, Kringos, Romaniello, Archibugi, Salsiri and Ricciardi2015; Stefko et al., Reference Stefko, Gavurova and Kocisova2018; Zakowska and Godycki-Cwirko, Reference Zakowska and Godycki-Cwirko2020). There are two types of personnel involved in THPHs’ healthcare service operations: first, THPH employees, and second, village health volunteers (VHVs). Since VHVs are working based on their willingness to help in the tasks of THPHs and THPHs have no direct administrative control over their performances, we decided to employ VHVs as a different input variable (I5).In this study, personnel refers to the total actual number of full-time public health personnel working in THPHs during fiscal year 2022, comprising public health technical officers, registered nurses, Thai traditional medicine doctors, public health officers, and dental assistants. Some THPHs might not have enough personnel for all of the aforementioned positions, depending on their size and the Ministry of Public Health’s manpower framework.

2. 2) Overtime costs (I2): Overall, most THPHs have problems with insufficient numbers of personnel, so they assign personnel to take turns working overtime (OT). In this study, OT costs refer to the total cost for the year 2022 based on reimbursement documents.

3. 3) Pharmaceuticals and medical supplies (I3): THPHs provide public health services to outpatients only. Most of their medical treatment is based on medication and giving accurate health advice, including prenatal care, postpartum care, vaccination services, health screening, mental healthcare, disabled and elderly care, and providing basic medical procedures for non-serious accidents by nurses and public health officers. The measure for I3 is the total expenses incurred during the year 2022 for drugs and medical supplies involving the above-mentioned services as well as medicines for non-communicable diseases (NCDs).

4. 4) Other costs (I4): This input variable covers utility and fuel costs, maintenance costs, and costs for contractual tasks such as cleaning and waste collection.

5. 5) VHVs (I5): VHVs have been established in Thailand since 1977 to play an important role as change agents concerning the health behaviour of local people. Their responsibilities to support and facilitate the work of public health officers, including THPHs, contribute to the efficiency and effectiveness of public healthcare missions. Those that want to be VHVs must have their names listed in the house registration, have lived in the village for at least 6 months and be voluntarily willing to help in public health operations. A group of 10–15 households can vote for one VHV. Once selected, VHVs will receive training according to the curriculum of the Ministry of Public Health and are responsible for taking care of the households in the village (Thianjuruwatthana et al., Reference Thianjuruwatthana, Nawsuwan and Vachiraprapun2021). In this study, we use the total number of VHVs in each THPH catchment area as the measure of the VHV variable.

The details of the seven output variables are summarized below.

1. 1) Visits and consultations (O1): This output variable is concerned with the number of hospital visits that directly receive medical and public health services in terms of health promotion, disease prevention, disease diagnosis, medical treatment, health rehabilitation, and health consultations. Since THPHs do not have full-time doctors, nurses and public health officers are responsible for providing medical services and useful advice to patients. Doctors from community hospitals or district hospitals in the same PHC network come to see patients at the THPHs from time to time, usually once a month.

2. 2) Health screening (O2): Health screening is an effective approach to health promotion and disease prevention in the THPH healthcare system. It helps to minimize disease incidence, reduce deaths from various diseases, and make people have a better quality of life (Phiphitaporn and Buaphat, Reference Phiphitaporn and Buaphat2021). Early disease detection helps patients receive appropriate care in time and can lessen disease severity. The present study uses as the measure of this variable the total number of times that each THPH similarly provides health screening services to general people and high-risk groups to detect common diseases, including diabetes, high blood pressure, cervical cancer, mental disorders, and elderly health status.

3. 3) Quality antenatal care (O3): It is the mission of THPHs to provide health promotion and disease prevention services to pregnant women and infants in order to ensure safe pregnancy and childbirth and to prevent complications or dangers that may occur. Several studies have found that investing in human capital during the first trimester of pregnancy yields a greater economic return than investing at later periods (Doyle et al., Reference Doyle, Harmon, Heckman and Tremblay2009). In this study, quality antenatal care refers to services offered to normal pregnant women, including health screening and risk assessment. THPHs should provide health knowledge to pregnant women based on determined standards, provide them with physical examinations, laboratory tests, and essential vitamins, and arrange five doctor or nurse visits for them beginning when the gestational age is ≥ 12 weeks. Pregnant women should also receive continuous care from public health agencies until after giving birth. The measure of this variable is the total number of pregnant women receiving quality antenatal care during the year 2022.

4. 4) Postpartum care (O4): This variable refers to the number of postpartum women receiving three health visits by medical and public health personnel and/or VHVs in accordance with the required criteria; the first visit being within seven days of birth, the second within eight to fifteen days, and the third within sixteen to forty-two days.

5. 5) Vaccinations (O5): The mission of THPHs to enhance local people’s immunity through vaccinations is crucial because it can contribute to disease prevention and basic health promotion and minimize patient care expenses. In this study, vaccinations are measured according to the number of times that they are administered to people of all age groups, according to Ministry of Public Health policy.

6. 6) Community healthcare projects (O6): Most of the THPHs’ community healthcare projects obtain most of financial support from the Community Health Security Fund, which receives partial funding from the National Health Security Fund to encourage local public health units, THPHs, and other related local agencies, groups, and clubs to submit budget requests for new healthcare projects necessary for the target groups in their communities, including pregnant women, postpartum women, toddlers, preschoolers, students, adolescents, working-age people, the elderly, chronically ill people, disabled people, and NCD patients. Most of the projects of the THPHs receiving a budget from this fund are initiated to support the THPHs’ main missions. (National Health Security Office, 2018).This output measure is the total number of projects, both ongoing and completed, during fiscal year 2022.

7. 7) Referrals (O7): In this study, referral refers to the number of times that patients were referred from THPHs to higher-level hospitals or public health agencies. As THPHs are PHC hospitals, there may be limitations in terms of resources or specialized personnel for treating complex illnesses. As a result, THPHs have a mission to coordinate with other public health agencies to refer patients in the community to receive appropriate medical services.