\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage{natbib}




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[T2A]{fontenc}
\usepackage[ngerman,greek,polish,english]{babel}



\usepackage{float}








\begin{document}

\title{The Stochastic Frontier Analysis Technique in Measuring the Technical
and Economic Efficiency of Hospital Diagnostic Laboratories: A Case
Study in Iran}



\author[1]{Siamak  Aghlmand}%
\author[2]{Sadegh  Feizollahzadeh}%
\author[3]{hasan yusefzadeh}%
\author[2]{Mina  Alinejhad}%
\affil[1]{Urmia University of Medical Sciences School of Health and Paramedicine}%
\affil[2]{Urmia University of Medical Sciences}%
\affil[3]{Affiliation not available}%


\vspace{-1em}



  
  \date{June 13, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
Rationale, aims, and objectives An inefficient health system wastes
scarce resources even if it makes considerable gains in accountability
and equity. Such a system is expected to perform better. Therefore, it
is vital to examine the current performance of health systems and their
constituents as well as assess how to reach their full potential. The
aim of this study was to evaluate the technical and economic efficiency
of medical diagnostic laboratories in hospitals affiliated with Urmia
Medical Sciences University (UMSU) in 2016. Methods In this
descriptive-analytical study, the data of all diagnostic laboratories of
the hospitals of UMSU were inputted into Frontier 4.1 software after
taking the logarithm. Then, the technical and economic efficiency of the
laboratories were obtained by estimating the production and cost
function using the stochastic frontier analysis method, assuming input
minimization for 2016. Results The average technical and economic
efficiency of the diagnostic laboratories was obtained as 0.931\selectlanguage{ngerman}±0.34 and
0.519±0.33, respectively. These laboratories must reduce their inputs
and costs to achieve full efficiency without changing the amount of
their output. Conclusion Although the average economic efficiency of the
diagnostic laboratories of the studied hospitals was high, there is
still an increase in the efficiency of these units given the cost of
inputs at the time of allocating resources. In addition, it is possible
to improve the technical efficiency of the clinical laboratories of
hospitals affiliated with UMSU by 48.1\% by applying the same level of
inputs and without increasing the costs.%
\end{abstract}\selectlanguage{ngerman}%



\sloppy


\textbf{The Stochastic Frontier Analysis Technique in Measuring the
Technical and Economic Efficiency of Hospital Diagnostic}

\textbf{Laboratories: A Case Study in Iran}

Siamak Aghlmand\textsuperscript{1}, Sadegh
Feizollahzadeh\textsuperscript{2}, Mina Alinejhad\textsuperscript{1},
Hasan Yusefzadeh\textsuperscript{1}

\textsuperscript{1}Health Economics and Management Department, School of
Public Health, Urmia University of Medical Sciences, Urmia, Iran

\textsuperscript{2}Laboratory Sciences Department, School of Allied
Medical Sciences, Urmia University of Medical Sciences, Urmia, Iran

\textbf{Correspondence:}

Hasan Yusefzadeh, Iran, Urmia, Sero Street, Nazloo Paradise, School of
Public Health, Postal Code: 5756115198, Tel: +9832752300. Fax:
+9832752309. E-mail: hyusefzade2010@gmail.com

\textbf{Rationale, aims, and objectives}

An inefficient health system wastes scarce resources even if it makes
considerable gains in accountability and equity. Such a system is
expected to perform better. Therefore, it is vital to examine the
current performance of health systems and their constituents as well as
assess how to reach their full potential. The aim of this study was to
evaluate the technical and economic efficiency of medical diagnostic
laboratories in hospitals affiliated with Urmia University of Medical
Sciences (UUMS) in 2016.

\textbf{Methods}

In this descriptive-analytical study, the data of all diagnostic
laboratories of the hospitals of UUMS were inputted into Frontier 4.1
software after taking the logarithm. Then, the technical and economic
efficiency of the laboratories were obtained by estimating the
production and cost function using the stochastic frontier analysis
method, assuming input minimization for 2016.

\textbf{Results}

The average technical and economic efficiency of the diagnostic
laboratories was obtained as 0.931\selectlanguage{ngerman}±0.34 and 0.519±0.33, respectively.
These laboratories must reduce their inputs and costs to achieve full
efficiency without changing the amount of their output.

\textbf{Conclusions}

Although the average economic efficiency of the diagnostic laboratories
of the studied hospitals was high, there is still an increase in the
efficiency of these units given the cost of inputs at the time of
allocating resources. In addition, it is possible to improve the
technical efficiency of the clinical laboratories of hospitals
affiliated with UUMS by 48.1\% by applying the same level of inputs and
without increasing the costs.

\textbf{Key Words} : hospital, diagnostic laboratory, Stochastic
Frontier Analysis, economic efficiency

\textbf{Introduction}

Measuring the performance of hospitals' clinical laboratories as an
important and costly unit is essential for their
managers\textsuperscript{1} as they can demonstrate its strengths and
weaknesses, identify areas that need improvement, and increase
productivity in the hospital.\textsuperscript{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.\textsuperscript{3} In this
regard, medical diagnostic laboratories play an important role in
diagnosing and providing high-quality care to
patients.\textsuperscript{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.\textsuperscript{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. \textsuperscript{6} In this regard, economic
efficiency demonstrates the ability of the laboratory to obtain maximum
benefit according to price and input levels. \textsuperscript{7}
Economic efficiency is associated with a combination of technical
efficiency and allocative efficiency. \textsuperscript{8}Technical
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.
\textsuperscript{9} Allocation efficiency is also the allocation of
limited resources to different inputs in order to maximize
output.\textsuperscript{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.\textsuperscript{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.\textsuperscript{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. \textsuperscript{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.\textsuperscript{14,15}

The 2017 study by Alinejad et al. entitled ``The economic efficiency of
clinical laboratories in public hospitals: A case study in
Iran''\textsuperscript{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''\textsuperscript{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''\textsuperscript{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.

\textbf{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 \textsuperscript{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 \textsuperscript{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
\textless{}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.\textsuperscript{18}

\textbf{Results}

Table 1 summarizes the results of the stochastic frontier cost function
estimation in Frontier 4.1. Since the index of the likelihood ratio (LR)
test was high in this estimate for the Cobb-Douglas function, there was
no need to estimate the translog function. In order to calculate the
economic efficiency, it is necessary to estimate the cost function
through the cost of inputs and the total cost of the laboratory unit. In
this study, the total costs of construction, consumables, property,
equipment, and staff salaries of the relevant laboratory were used to
calculate the total cost of the hospitals' laboratory units.

\textbf{Table 1} : Estimation of Frontier Cost Function Parameters (SFA)
from the Maximum Likelihood Method (ML)

In Column 2 of Table 2, the amount of economic efficiency obtained from
the cost function estimation is greater than one, because Frontier 4.1
does not consider a constraint in cost function estimation such as the
economic efficiency range between zero and one. In order to compare the
calculated SFA efficiencies, the economic efficiency figures obtained
from the SFA method were divided into the highest cost efficiency figure
in Table 2 (1.124) until the numerical values of economic efficiency
fall between zero and one (Column 3 in Table 1). In this method, the
average economic efficiency of the laboratory units of hospitals
affiliated with the UUMS was 0.931 (SD=0.034). Also, the lowest
cost-efficiency belonged to Hospital Laboratory 9 (value=0.89), and the
highest cost efficiency was related to Hospital 13 (value=1).

\textbf{Table 2} : Economic efficiency of clinical laboratories of
hospitals affiliated with the UUMS through the SFA method

In Table 3, no significant relationship is observed between output, i.e.
the number of admissions, with expert, ELISA, cell counters, incubators,
centrifuges, microscopes, and microbial culture medium inputs. In other
words, these inputs do not have a considerable impact on the output
level, which may be due to the high similarity of data collected from
hospitals' laboratories and, therefore, a reduced fluctuation between
data and their low variance. Also, in Table 3, the sum of the partial
elasticity coefficients of the inputs was 1.94, so the return to scale
among the laboratory units of the studied hospitals was ascending. The
negative production elasticity of some production factors indicated that
the laboratories under study were in the third and non-economic stages
of production in terms of applying these factors. Also, the production
elasticity relative to specialist input was 3.82, which was greater than
the other elasticities. This means that a 1\% increase in this
production factor leads to the highest increase in the return of
laboratories by 3.82\%. According to the final results of the maximum
likelihood estimation regarding the accuracy of using the Cobb-Douglas
function, since the LR value was 7.93, the Cobb-Douglas function form
was chosen. In other words, due to the high LR value of the Cob-Douglas
function rather than the translog function, this form was suitable for
the SFA for the studied laboratory units. The gamma variable that shows
the contribution of inefficiency variance in the production function
also equaled 1 with a standard error of 0.0000006. That is, the share of
random factors in the inefficiency of clinical laboratories in hospitals
affiliated with the UUMS was equal to zero, and the observed
inefficiency component had the major contribution. The significance of
the \selectlanguage{greek}γ \selectlanguage{english}parameter confirms that inefficiency plays an important role in
the model.

\textbf{Table 3} : Estimation of stochastic frontier production function
(SFA) parameters from the maximum likelihood method (ML)

According to the results of Table 4, the average technical efficiency of
medical diagnostic laboratories affiliated with the UUMS was 0.519
(SD=0.33). According to the SFA model, the lowest technical efficiency
belonged to Hospital 17 (value=0.049) and the highest technical
efficiency belonged to Hospitals 2 and 3 (value=0.999).

\textbf{Table 4} : Technical efficiency of the clinical laboratories of
hospitals affiliated with the UUMS through the SFA method

\textbf{Discussion}

The technical and economic efficiency of medical diagnostic laboratories
of hospitals affiliated with the UUMS was estimated via SFA under VRS
and input-oriented minimization assumption by estimating production and
cost functions in order to evaluate their performance.

The low technical efficiency of medical diagnostic laboratories of the
hospitals indicated the high capacity of inputs in these units. While
using the same level of inputs, these units can increase their outputs
and thus their technical efficiency by 48.1\% without any increase in
costs.

The average economic efficiency of the above-mentioned units was 0.931.
Therefore, the efficiency of these units can be improved by reducing
costs by 6.9\% without decreasing the value of outputs by increasing the
profit. In other words, the managers of these laboratories must reduce
their costs by optimally combining and distributing inputs, while taking
into account the prices of the used inputs to approach the profitability
frontier.

The average economic efficiency of laboratory units was higher than the
average technical efficiency, which demonstrates the high allocative
efficiency of these units; that is, the combination of inputs in these
units is appropriate. However, service providers in these units can make
the most of this combination to increase service delivery without
changing the amount of inputs in order to increase technical efficiency.
Therefore, in order to reduce costs and increase their profits, the
above-mentioned laboratory units should avoid wasting resources by
enhancing the motivation of the staff and the awareness of the general
principles of medical diagnostic laboratories.

Furthermore, medical diagnostic laboratories of university hospitals had
an increasing return to scale. In other words, the coefficient of
function or degree of homogeneity was \textgreater{}1; that is, if
inputs are increased by 1\%, the output of laboratories will increase by
more than 1\%. Therefore, the laboratories under study should increase
their supply of services.

Alinejhad et al. in a study entitled ``Evaluating the economic
efficiency of clinical laboratories in Iranian public hospitals via DEA
method'' achieved the average economic efficiency of
0.676.\textsuperscript{1} The results of examining the economic
efficiency of laboratory units in hospitals affiliated with the UUMS by
using DEA and SFA methods showed that the average economic efficiency of
the units differed in the two methods (0.255). This difference could be
due to neglecting random effects, measurement errors, etc. in the DEA
method. In general, however, the average economic efficiency of the
studied units in the province is medium to high, indicating that in the
studied units, it is possible to increase economic efficiency by
reducing costs without affecting output values.

After examining the efficiency of Australian hospitals by using DEA and
SFA, Mortimer et al. concluded that each method of efficiency
measurement has its own characteristics, and there is no single method
for measuring the efficiency whose results would be more precise and
reliable compared to other methods.\textsuperscript{13}

In a study entitled ``Analyzing the efficiency changes of Irish
hospitals'', Gannon concluded that the technical efficiency values
obtained from the DEA method were higher than the SFA method; that is,
the inefficiency in the DEA method was
underestimated.\textsuperscript{19}

In a study entitled ``Evaluating the economic efficiency of CCU in
hospitals affiliated with Tehran University of Medical Sciences'',
Zahavi et al. used both SFA and DEA methods and concluded that these two
methods do not necessarily have the same results in calculating
efficiency, and greater efficiency in one of these methods is not
sustainable for all sectors.\textsuperscript{20}

Lamovsek et al. determined the optimal size of medical laboratories at
the primary healthcare level by using DEA. The average technical
efficiency of the laboratories with the VRS assumption was obtained as
0.9333. The authors concluded that increasing the automation and
consolidation of laboratory activities can affect the efficiency of
laboratories and, thus, costs.\textsuperscript{4}

In evaluating the technical efficiency of the clinical laboratories of
Shiraz University of Medical Sciences, Taheri et al. reported the
average technical efficiency of laboratory units to be
0.924\textsuperscript{16}, which indicates a high level of technical
efficiency in hospital units of Shiraz compared to Urmia.

In general, SFA is a useful tool for analyzing the efficiency of medical
diagnostic laboratories, and its information may be useful for
policy-making and performance evaluation of these units. The DEA and SFA
methods are also complementary in efficiency measurement, but for
efficiency measurement, it is recommended that the SFA method be first
performed in order to identify the variables having a negative effect
and to exclude them from the model.

One of the limitations of this study was the lack of participation of
the private sector diagnostic laboratories. Better analysis and
conclusions could be obtained from the efficiency status of provincial
laboratories had these laboratories cooperated, and the health planners
in the province could have used better data for decision making.

\textbf{CONCLUSION}

The findings of this study can provide a tool for better policy-making
in clinical laboratories by helping the management of laboratory
resources as a costly unit of the healthcare system. In addition,
performance evaluation allows inefficient hospitals to compare their
performance with that of similar but efficient hospitals and identify
their promotion capabilities.

\textbf{ACKNOWLEDGEMENTS}

This article is part of a master's thesis with the IR.UMSU.REC.1397.160
code of ethics at Urmia University of Medical Sciences. The authors
offer their sincere gratitude to the deputies of treatment and research
of said university.

\textbf{CONFLICTS OF INTEREST}

No potential conflicts of interest relevant to this article were
reported.

\textbf{REFERENCES}

1. Alinejhad M, Aghlmand S, Feizollahzadeh S, Yusefzadeh H. The economic
efficiency of clinical laboratories in public hospitals: A case study in
Iran. \emph{Journal of clinical laboratory analysis.} 2019:e23067.

2. Arah OA, Klazinga NS, Delnoij DM, Asbroek At, Custers T. Conceptual
frameworks for health systems performance: a quest for effectiveness,
quality, and improvement.\emph{International journal for quality in
health care.}2003;15(5):377-398.

3. Ketabi S, Ahmadi-Ahwaz N, Moazzam E, Mobasherizadeh S, Alizadeh V.
Efficiency evaluation of medical diagnostic laboratories using data
envelopment analysis in Isfahan, Iran. \emph{Medical Laboratory
Journal.} 2015;9(3):102-109.

4. Lamovsek N, Klun M, Skitek M, Bencina J. Defining the Optimal Size of
Medical Laboratories at the Primary Level of Health Care with Data
Envelopment Analysis: Defining the Efficiency of Medical Laboratories.
\emph{Acta Informatica Medica.}2019;27(4):224.

5. Pagana KD, Pagana TJ. \emph{Mosby's Manual of Diagnostic and
Laboratory Tests-E-Book.} Elsevier Health Sciences; 2017.

6. Hudson J. \emph{Principles of clinical laboratory management: a study
guide and workbook.} Pearson Prentice Hall; 2004.

7. Hollingsworth B. The measurement of efficiency and productivity of
health care delivery. \emph{Health economics.} 2008;17(10):1107-1128.

8. Murillo-Zamorano LR. Economic efficiency and frontier techniques.
\emph{Journal of Economic surveys.}2004;18(1):33-77.

9. Athanassopoulos A, Gounaris C. Assessing the technical and allocative
efficiency of hospital operations in Greece and its resource allocation
implications. \emph{European Journal of Operational Research.}
2001;133(2):416-431.

10. Yusefzadeh H, Ghorbani A, Lotfi F. Efficiency and productivity in
health system. \emph{Yuban Publishing, First Edition, Tehran.} 2017.

11. Peacock S, Chan C, Mangolini M, Johansen D. Techniques for measuring
efficiency in health services.\emph{Productivity Commission: Staff
Working Paper.} 2001.

12. Kujawska J. Measurement of healthcare system efficiency in OECD
countries. \selectlanguage{polish}\emph{Metody Ilościowe w Badaniach Ekonomicznych.}\selectlanguage{english}
2015;16(2):23-32.

13. Mortimer D, Peacock S.\emph{Hospital efficiency measurement: simple
ratios vs frontier methods.} Citeseer; 2002.

14. Emami Meibodi A. Efficiency and productivity measurement (in theory
and practice). \emph{Institute for trade studies and research press,
Tehran, Iran.{[}In Persian{]}.} 2006.

15. Worthington AC. Frontier efficiency measurement in health care: a
review of empirical techniques and selected applications. \emph{Medical
care research and review.}2004;61(2):135-170.

16. Taheri A, Jahromi SAS, Lotfi F. Efficiency of Clinical Laboratories
Affiliated Shiraz University of Medical Sciences in 2015: an Application
of Data Envelopment Analysis.\emph{International Journal of Health
Studies.} 2017;2(4).

17. Coelli TJ. \emph{A guide to FRONTIER version 4.1: a computer program
for stochastic frontier production and cost function estimation.} CEPA
Working papers;1996.

18. Aigner D, Lovell CK, Schmidt P. Formulation and estimation of
stochastic frontier production function models. \emph{Journal of
econometrics.} 1977;6(1):21-37.

19. Gannon B. Testing for variation in technical efficiency of hospitals
in Ireland. \emph{The Economic and Social Review.} 2005;36(3):273-294.

20. Zahavi M, Arab M, GOUDARZI GR, Hoseini M, Akbarisari A,
Akbarihaghighi F. Measurement of economic efficiency of CCUS of Tehran
university of medical sciences hospitals, using Data Envelopment
Analysis (DEA) and Stochastic Frontier Analysis (SFA) methods:
2006-2009. 2014.

\textbf{Hosted file}

\verb`Tables.docx`  available at \url{https://authorea.com/users/331403/articles/458070-the-stochastic-frontier-analysis-technique-in-measuring-the-technical-and-economic-efficiency-of-hospital-diagnostic-laboratories-a-case-study-in-iran}

\selectlanguage{english}
\FloatBarrier
\end{document}

