2.1 Data

AMSRH services are provided by both public and private healthcare facilities and therefore the study sampled both categories of providers. The services included are adolescent sexual and reproductive health services, such as contraception, pregnancy testing and counselling, maternal and child health services, STI testing and treatment, reproductive health education, and safe abortion services, as well as adolescent mental health services.

Primary data was collected from PHC facilities in four districts in the Greater Accra Region of Ghana. This data included information on inputs and outputs related to both ASRH and AMH services provided by the facilities, such as human resources, equipment, and service delivery statistics. The facilities were contacted through the District Health Directorate in each district, which provided a list of all functional primary healthcare facilities. The directorate also supplied the addresses and contact information of the heads of each health facility. Informed written consent was obtained from the heads of the healthcare facilities or their designated representatives before data collection commenced. All participants received comprehensive information about the study’s objectives and procedures.

2.2 Sampling

We used a multi-stage sampling design to determine the sample size for this study. First, the Greater Accra region was purposefully selected as it contains a combination of urban and rural districts, as well as a diverse population that is representative of the country. Four districts were then purposively selected from the Greater Accra region. Specifically, two rural districts (Ningo Prampram and Shai Osudoku) with rapid urbanization in the periphery bordering the Accra and Tema metropolitan districts and two urban districts (Ga East and La Kwantemang) were included in the sample to allow for differences in service provision between rural and urban areas. In the third and final phase, all functional PHC facilities in the four selected districts were included in the study. Data was collected from a total of 78 facilities (including school-based sick bays) across all four districts. A sub-sample of 53 PHC facilities were included in the efficiency analysis after removing sick bays that did not meet the classification of PHC facilities in Ghana. Of these facilities, 28 (53%) were in rural areas while 25 (47%) were in urban areas.

2.3 The stochastic frontier analysis (SFA) model

To measure technical efficiency, we used stochastic frontier analysis (SFA) which was simultaneously proposed by Aigner et al. [19] and Meeusen et al. [20]. The SFA is a parametric approach to assessing efficiency as opposed to nonparametric approaches like data envelopment analysis (DEA) [21]. The analysis begins with the estimation of a production function specified as follows.

(1)

Where represents the output of the i^th decision-making unit (DMUs); is a vector of inputs; is the random disturbance term that accounts for random variations in the production functions of the DMUs. is a non-negative random disturbance term that measures the inefficiency of the DMUs. Both and are assumed to be independent and identically distributed across observations. measures the shortfall of output from its potential maximum frontier given by

(2)

Thus;

(3)

Therefore, × 100% shows the percentage of output lost due to technical inefficiency where a value closer to 100% indicates high inefficiency (this is termed as technical inefficiency index).

Therefore, the expression to obtain the technical efficiency (TE) index of a DMU is arrived at by rearranging equation (3) as follows:

(4)

Equation (4) defines technical efficiency as the ratio of the observed output of the i^th DMU to the potential maximum output produced by a completely efficient DMU using the same input mix [21]. The value of technical efficiency is between 0 and 1. This implies that the observed output always lies on or below the efficient frontier. A technical efficiency index closer to 1 indicates high technical efficiency while a value closer to zero means less technical efficiency.

The production function is an important component of the SFA as it determines the accuracy of the frontier from which technical efficiency estimates will be computed. While several forms of the production function exist, the Cobb-Douglas and Translog functions are popular in the efficiency literature [22,23]. In this paper, we used the translog function due to its flexibility as it, among others, allows for cross-product terms between inputs hence capturing complementary and substitution effects. The function is specified in this study as follows.

(5)

Where is the output of the i-th DMU (health facilities), k represents capital of the DMUs (number of beds in the facility), l represents labour inputs of the DMUs (time spent by clinical staff, time spent by nonclinical staff), and q represents other potential determinants of output of the facilities (such as facility type, gender of head of the facility among others) whiles α, β and δ are estimable parameter. ε is the composite error term made of (the random disturbance term) and u (the inefficiency term). The production function reports Lamda (λ) which is the ratio of the standard deviation of the inefficiency component (u) to the standard deviation of the idiosyncratic component , and represents the technical efficiency of the production process. Lamda greater than 1 means the standard deviation of the inefficiency component is higher than the standard deviation of the random disturbance term, suggesting the presence of inefficiency in the production process.

Technical efficiency can be computed from the output or input orientations. The output orientation holds inputs constant and determines how outputs could potentially be expanded while input orientation keeps outputs fixed and explores possible reduction in inputs [24–27]. In this study, we used the output orientation given that the health facilities only receive a set of resources and the decision under their control is usually how much outputs can be produced with the available resources. Moreover, the ultimate objective of health facilities is to expand output rather than limiting available resources.

In the second stage analysis, we estimate how health facility and environmental factors are associated with the levels of technical efficiency estimated in the first stage. We used the Tobit regression technique which belongs to the family of limited variable models. The Tobit model was appropriate as it allows for continuous dependent variables that are observable only within an interval. In our case, the technical efficiency scores are limited within a 0–1 interval [28]. The estimated equation is presented in equation (6).

(6)

Where te is the estimated technical efficiency scores, hf is health facility characteristics and comm is community factors.

2.6 Variable description

Table 1 presents a description of output, input, and other environmental variables included in the analysis.

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Table 1. Summary of input and output variables.

https://doi.org/10.1371/journal.pone.0321265.t001

The variables included in the model were selected based on their relevance to ASRH services and their use in analogous studies on healthcare facility efficiency. Key inputs like clinical and non-clinical staff time, beds, lab tests, and medicines reflect resource allocation, while outputs such as outpatient attendance measure service utilization [26,29]. Environmental variables like facility location, type (public vs. private), and leadership gender help account for external factors influencing efficiency. Additionally, economic factors such as the Gini coefficient and health insurance coverage provide context for disparities in healthcare access, drawing from similar studies that analyse health system performance.

2.7 Estimation issues

An important concern with efficiency analysis that focuses on a sub-set of services produced by a given organization is the attribution of inputs to these services. In the case of SRH services in Ghana, health workers in PHC facilities are also involved in providing services across different disease conditions. In this regard, for the key inputs, we either adjust them with the average time spent per patient in providing AMSRH services or we use the variables as a proportion of AMSRH services delivered at the facility. The output variable we used is also subject to bias relating to the mix of services used by an adolescent reporting for OPD and the severity of service. For example, while two facilities may have the same number of SRH OPD patients each year, the intensity or quantity of the services they seek may be different, and therefore resource needs will not be the same. Some authors have recommended that outputs used in efficiency analysis of this nature be adjusted to reflect these nuances [30]. In practice, this is a difficult undertaking as data is typically limited. In this paper, we used the average time spent on adolescents in the facility to adjust the outcome variable. We consider this a reasonable way to account for service intensity (Service intensity refers to the complexity and resource demands of a health service. It accounts for variations in time, personnel, and equipment required, ensuring fair comparisons of facility efficiency). We, however, do acknowledge that our approach does not completely purge the variable of this potential bias.

2.8 Ethics

Ethical approvals for this study were obtained from the Ghana Health Service Ethics Review Committee (GHS ERC 021/05/21) and the University of Leeds Medical Research Ethics Committee (MREC 21–010 External - AdoWA project). Written informed consent was obtained from the heads of the healthcare facilities or their designated representatives prior to data collection. All participants were provided with detailed information regarding the study’s objectives and procedures. The interviews were conducted to gather institutional-level data, and no personal data from patients were collected. Data were anonymized to ensure confidentiality, and all procedures adhered to the ethical standards set forth by the approving committees

3.4 Discussion

The study aimed to assess the technical efficiency of primary health facilities in providing AMH and ASRH services. The findings show a notable lack of AMH services, with primary care services largely focused on ASRH. The average technical efficiency score of facilities was 0.60, meaning that with current input levels, output can be expanded by an average of 40%. The average efficiency score was higher among rural facilities compared to their urban counterparts. Government facilities were also more efficient relative to private facilities. These findings echo prior research that confirm the presence of inefficiency across health facilities in general health service delivery [13,14,18] and specific disease conditions like malaria [16]. Our results also confirm previous findings by Novignon & Nonvignon [31] suggesting that countries like Ghana could greatly enhance primary healthcare delivery and utilization by increasing technical efficiency. These findings have broader implications for resource efficiency in low-resource settings. The presence of inefficiency suggests that there is significant potential to optimize the use of existing resources. By improving efficiency, cost savings can be achieved, enabling additional outputs to be generated within the same resource envelope. This is particularly important in resource-constrained environments, where optimizing and reallocating limited inputs can enhance healthcare delivery.

The results imply that there is the possibility of producing more outputs within the existing resource envelope. This may be achieved by reviewing the input mix at PHC facilities to ensure that the productivity of these inputs is improved by deploying them where they are most needed. The gains from improved efficiency could result in generating additional resources within existing envelope that could be repurposed within the health sector [15]. Observations from the fieldwork also underscore the estimated level of inefficiencies. We heard from health workers that due to the sensitive nature of sexual and reproductive health services provided at the facilities, adolescents find it difficult to seek care at these facilities. Consequently, some adolescents prefer to self-medicate or avoid seeking care altogether. This means existing resources may be under-utilized as fewer adolescents seek services from formal facilities.

In the second stage where we evaluate the potential association between facility characteristics, external environmental factors and inefficiency, we find some interesting results that could guide policy reforms to improve technical efficiency. For instance, the findings suggest that providing a wider range of ASRH services is associated with higher technical efficiency. This is justifiable as facilities that have more services can provide more comprehensive services and save resources. Resource use may not be optimal in cases where patients seek care for different services across different facilities. The findings also confirm that having more consulting rooms in the facility reduced inefficiency. Indeed, the availability of relatively more consulting rooms has the potential to reduce waiting time and, ultimately, improve efficiency. While PHC facilities are mostly designed as small structures with few consulting rooms, dedicated spaces could be created to meet the peculiar needs of adolescents and improve efficiency in resource use.

With regards to environmental factors external to the health facility, the results show that better economic environment (measured with the level of economic inequality) and reduced financial barriers to health care (measured with health insurance coverage) are associated with improved technical efficiency. Several studies have shown how poverty and inequality limit health care seeking and the role of insurance in enhancing health care utilization [32–36]. The findings support government efforts to improve livelihood and reduce financial barriers to health care through programmes like the Livelihood Empowerment Against Poverty (LEAP) and the National health Insurance Scheme (NHIS). Scaling up these interventions to ensure they are effective and reach the poor and vulnerable adolescents will encourage health seeking at formal facilities, thereby reducing resource redundancy at health facilities.

There are important strengths and limitations of the study worth discussing. The key strength of this study lies in its attempt to apply technical efficiency techniques to ASRH services. As mentioned earlier, technical efficiency is typically applied to health facilities as a whole and does not single out specific services. This is mostly due to the lack of data or difficulty in separating inputs and outputs for specific services within health facilities that provide a mix of services. To the best of our knowledge, this is the first effort to estimate the technical efficiency of PHC facilities in providing ASRH services in Ghana. Despite its strength, the study was limited in scope as it was confined to four districts in the Greater Accra Region, which may limit the generalizability of the findings to other regions in Ghana or other countries. Also, while the study included different types of health facilities, other influential factors such as staff qualifications, workload, or patient satisfaction were not accounted for in the analysis. Finally, our inability to include mental health services in our measure of efficiency is a limitation of the study. Future studies on technical efficiency of AMSRH resource use should consider addressing these limitations.