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