Introduction
Measuring the performance of hospitals’ clinical laboratories as an important and costly unit is essential for their managers1 as they can demonstrate its strengths and weaknesses, identify areas that need improvement, and increase productivity in the hospital.2
A laboratory is a place where various operations such as empirical tests, various measurements, and the analysis and identification of materials and impurities are performed.3 In this regard, medical diagnostic laboratories play an important role in diagnosing and providing high-quality care to patients.4 Now that communities have recognized the value of health, it is not possible to maintain community health, prevent the spread of infectious diseases, and combat genetic diseases without the use of medical diagnostic laboratories.5
The laboratory is a highly sensitive and important work environment as it employs specialized labors in various fields as well as various costly equipment, and its performance and efficiency require a great deal of attention. 6 In this regard, economic efficiency demonstrates the ability of the laboratory to obtain maximum benefit according to price and input levels. 7 Economic efficiency is associated with a combination of technical efficiency and allocative efficiency. 8Technical efficiency indicates the ability of the laboratory to maximize the product (service delivery) with respect to specific production factors or to minimize production factors regarding the particular product. 9 Allocation efficiency is also the allocation of limited resources to different inputs in order to maximize output.10
A laboratory has economic efficiency only if it is efficient both in the technical and allocational sense. That is, economic efficiency can be achieved if the best use is made of resources in the laboratory unit without wasting the resources.11 This requires a combination of institutions with the lowest cost; algebraically, economic efficiency is obtained by multiplying the quantities of technical and allocative efficiencies.
Different methods are used to evaluate the performance of service and manufacturing units. These methods are generally divided into nonparametric and parametric categories.12 One of the most common parametric methods is stochastic frontier analysis (SFA) in which statistical disturbances are considered, and it is necessary to take into account assumptions about the frontier form of the function. This method is an econometric technique that shows deviation from the best performance frontier and demonstrates the effect of the noise term on efficiency (such as device failure, measurement error, and strikes) which is beyond the control of production units. This feature divides the deviation of the frontier into two components of inefficiency and random error. 13 In this method, the production function is estimated as the maximum product that can be produced from a set of production factors, and provides a better definition of inefficiency based on economic theory. The SFA seems to be an appropriate method if the rate of product factors and production is a random mechanism.14,15
The 2017 study by Alinejad et al. entitled “The economic efficiency of clinical laboratories in public hospitals: A case study in Iran”1, the 2015 study by Taheri entitled “The efficiency of clinical laboratories affiliated with Shiraz University of Medical Sciences: an application of data envelopment analysis”16, and the 2017 study by Lamovsek entitled “Defining the optimal size of medical laboratories at the primary level of healthcare with data envelopment analysis: defining the efficiency of medical laboratories”4 have investigated the performance and types of efficiency of laboratories through data envelopment analysis and SFA.
Since studying the performance of hospitals’ clinical laboratories and identifying their strengths and weaknesses are of great importance in the optimal allocation of facilities, the present study aimed to evaluate the efficiency of resource use in clinical laboratories of hospitals affiliated with Urmia University of Medical Sciences (UUMS) in 2017 via the SFA method. The results can help hospital managers and chiefs to improve the economic performance of laboratory units by avoiding the waste of scarce resources and thus reducing unit costs.
Methods
In this descriptive-analytical study, the technical and economic efficiency of 22 diagnostic laboratories of the hospitals affiliated with the UUMS was estimated using the SFA method by the variable returns to scale (VRS) and input-oriented assumptions via Frontier 4.1 software in 2017.
The general form of the Cobb-Douglas production function to calculate the technical efficiency of the laboratory units in this study is as follows 17:
\begin{equation} \text{Ln\ }Y_{\text{it}}=\ \beta_{0}+\sum{\beta_{j}X_{\text{jit}}}+(V_{\text{it}}-U_{\text{it}})\nonumber \\ \end{equation}\begin{equation} \text{Ln}\left(Y_{\text{it}}\right)=\beta_{0}{+\beta}_{1}\text{Ln}\left(P_{\text{it}}\right)+\beta_{2}\text{Ln}\left(E_{\text{it}}\right)\ +\beta_{3}\text{Ln}\left(T_{\text{it}}\right){+\beta}_{4}\text{Ln}\left(I_{\text{it}}\right)+\beta_{5}\text{Ln}\left(S_{\text{it}}\right)+(V_{\text{it}}-U_{\text{it}})\nonumber \\ \end{equation}
where Ln: logarithm at the base of natural number, Yit: production of unit i at time t, Xjit: rate of using factor j by unit i at time t, Vit: random disturbance component, and Uit: model inefficiency. Inputs include the number of specialists (P), experts (E), technicians (T), tools and equipment (I), and materials and solutions (S), and the output contains the number of patients admitted to the laboratory unit (Y).
The general form of the Cobb-Douglas cost function for estimating the economic efficiency of the laboratory units by the SFA method is as follows 17:
\begin{equation} \text{Ln\ }\left(C_{\text{it}}/W_{\text{Pit}}\right)=\ \beta_{0}+\beta_{1}\text{Ln}\left(Y_{\text{it}}\right)+\beta_{2}\text{Ln}\left(\frac{W_{\text{Eit}}}{W_{\text{Pit}}}\right){+\beta}_{3}\text{Ln}\left(\frac{W_{\text{Tit}}}{W_{\text{Pit}}}\right)+\beta_{4}\text{Ln}\left(\frac{W_{\text{Iit}}}{W_{\text{Pit}}}\right)\ +\beta_{5}\text{Ln}\left(\frac{W_{\text{Sit}}}{W_{\text{Pit}}}\right)+(V_{\text{it}}-U_{\text{it}})\nonumber \\ \end{equation}
where Ln: logarithm at the base of natural number, Cit: total cost, Yit: number of patients admitted, WPit: specialist wages, WEit: expert wages, WTit: technician wages, WIit: the price of tools and equipment, WSit: the price of materials and solutions, Vit: random disturbance component, and Uit: model inefficiency. To calculate the total cost, the costs of properties (including medical and non-medical), construction, consumable, equipment and salaries of all employees in the laboratory unit, which are a valid representation of the total cost of that unit, were used. Moreover, part of the costs of the laboratory unit is the overhead costs that are split or shared between different parts of the hospital.
The price of the equipment is actually its annual depreciation expense, and the straight line method was used to calculate the depreciation of equipment.
Also, in the SFA method, the numbers obtained for economic efficiency were divided into the highest economic efficiency figure until the most efficient laboratory unit acquired number 1 and the residual units fell <1; this allowed for the easy comparison of the technical and economic efficiency of efficient and inefficient units. In this case, the most efficient laboratory unit equaled one in technical and economical terms, and the rest were sub-one.18