Efficiency Analysis of Healthcare Sector

- Hospital efficiency & Productivity analysis, is an important issue in the health economics. Furthermore, the study analyze the efficiency and productivity in the hospitals, from two viewpoints: firstly, Data Envelopment Analysis (DEA) used to measure the relative efficiency of the hospitals with applying (CCR) approach. Secondly, Luenberger Productivity Indicator (LPI) used to measure the change (progress) in productivity of consecutive time periods. The study model has been tested and implemented on four case studies based on changing in inputs and outputs variables, of three hospitals in the study district (Baghdad) to analyze their efficiency, in two years period (2014-2015), with three inputs variables and five outputs variables. The results of using DEA technique shows that Al-Alwaiya Children's hospital only still efficient in four cases, while, other hospitals (Ibn Al-Balady & Fatima Al-Zahraa) change their efficiency by changing the case, then by using LPI technique, the results indicate that the (Ibn Al-Balady) hospital has productivity growth in three cases. The Fatima Al-Zahraa hospital has productivity decline in two cases and has growth in one case only. Finally the Al-Alwaiya Children's hospital has productivity growth in all cases during period (2014 – 2015).


Introduction
Public hospitals represent an essential part in health care system in any society, and particularly in Iraq. They represent the most vital part for many reasons, such as the growth of urban settlements (medium and big cities) at the expense of rural settlements shrinkage, and also the nature of the services given by these hospitals, which are characterized by very high standard with high specialization [1]. Most of researchers agree that efficiency is related to the utilization of resources. According to (Lovell), the efficiency of a production unit is defined in terms of a comparison between actual and optimal quantity of inputs and outputs [2]. The efficiency measures are more accurate than of productivity in meaning that they employ a comparison with the most efficient frontier, and for that they can complete those of productivity, based on the ratio of outputs to inputs. (Pritchard), clarify some definitions which related with productivity: first, the productivity is output/input, in other term is measure of efficiency; second, the productivity refers to broader concept that makes the organization has a better function; and another definition states that Productivity is composition of both, effectiveness and efficiency [3]. Figure (1) shows the relation between productivity, efficiency and other similar terms as (profitability, performance, and effectiveness), that explained by (Triple p) model [4]. There are many measurement approaches to estimate the productivity and efficiency [5] such as: partial factor productivity, total factor productivity, index number approaches, parametric & non parametric approaches. In this research two methods are used, non parametric Data Envelopment Analysis (DEA) to estimate relative efficiency for each Decision Making Unit (DMU) & Luenberger Productivity Indicator (LPI) to measure the change (progress) in productivity of consecutive time periods. I. Data Envelopment Analysis (DEA) (DEA) evaluates the relative technical efficiency with "linear programming model" by using (input & output) variables from similar and homogeneous DMUs. In (DEA) model there are two models approaches are: (CCR approach) & (BCC approach). The CCR approach [5], assume a constant returnsto-scale (CRS), strong disposability of inputs and outputs, and convexity of the production possibility set. Under the assumption of CRS, any scaled-up or scaled-down versions of the input combinations are also involved in the production possibility set. However, the constraint over returns-to-scale may be relaxed to allow units to be compared given their scale of operations. So, to allow returns-to-scale to be variable (constant, increasing or decreasing), develop (BCC) model, called variable returns-to-scale (VRS) [6]. Also, (DEA) model has two assumptions: (1) Input oriented (outputs are held constant and inputs are decreased). (2) Output oriented (inputs are held constant and outputs are increased) [7]. In this research CCR (minimization problem) dual form is used rather than primal form, due to fewer constrains. The models (1) and (2)

Where:
 are inputs and outputs for each DMU;  representing the inputs and outputs for ;  is the factor by which an: (1) (input set is adjusted to attain the minimum input level in county hospital i, in order to reach the efficient frontier) in input oriented, (2) (output set is adjusted to attain the maximum output level in county hospital i, in order to reach the efficient frontier) in output oriented.  λ = variables weights. Based on input oriented model if θ = 1, the relative technical efficiency is efficient; and if θ < 1, is inefficient, while in output oriented model if θ = 1, the technical efficiency is efficient; and if θ > 1, is inefficient.

II. Luenberger Productivity Indicator (LPI)
The second technique Luenberger productivity indicator (LPI) introduced by (Chambers) [8], used to determine the change in productivity over consecutive years. It is based on (Directional distance function). The directional distance function calculates the smallest changes in a given direction in inputs & outputs, which are needful for a maker to reach the production frontier. The Luenberger productivity indicator is defined as: ), are directional distance function values as described in models (3), (4), (5) and (6).
= ( ) denotes inputs and outputs in period p, and g = ( ) is the directional vector indicating that the inputs are to be contracted and the outputs increased simultaneously. A direction vector g = (x, y) is use in this study research, to measures the smallest changes in inputs & outputs. Thus, the (directional distance function) is comparable to the (proportional-distance-function), that introduced by (W. Briec) [9]. Productivity improvement is represented by a positive value of the index (L), and productivity declines by negative value. The Luenberger productivity indicator (L) can be decomposed in to terms: efficiency change (catch -up) and technological change (frontier shift). The efficiency change (EFFCH) measures efficiency change between time periods (p) and (p+1), and expresses as:

Literature Survey
Hospital productivity and efficiency analysis, is a significant issue in the health economics. Furthermore there are many studies that deal with productivity and efficiency analysis in the hospitals using different measurement approaches in different countries. Barros et al. (2007) [10] applied Luenberger productivity indicator (LPI), to estimate the efficiency and the change in productivity of Portuguese hospitals over seven periods from (1997 to 2004). They found the selected sample of hospitals didn"t meet productivity growth through the study periods. Abou El-Seoud (2013) [11]

The Study Methodology
The methodology of the study in general consists of a relevant model, as shown in Figure (2), which consists of three modules: The first module (Specify the Goal and Related Data), includes: (1) Define the goal of the study. (2)

Data and Results
The study model is implemented on three hospitals (Al-Alwaiya Children's Hospital, Fatima Al-Zahraa Hospital and Ibn Al-Balady Hospital) in study district (Baghdad). By using four case studies are shown in Table (1).  (1) and (2) respectively. The relative efficiency score for each hospital was obtained by running the linear programing formula in Excel software as in Figure  (3). The summary of efficiency scores and reference sets of each hospital are presented in Table (2).

Figure 3: Spreadsheet of DEA model implementation using excel software
From the Table (2), the efficiency score in input oriented case (I) of the three hospitals are equal to (1), this is because the hospitals have the average inputs convergent to each other, signifying all are relatively efficient. Except the Ibn Al-Balady hospital in 2015, it has efficiency score equal to (0.999). This may be caused from the average of inputs in Ibn Al-Balady hospital is relatively slightly higher than other hospitals. In output oriented case I, very small amount of inefficiency appears in Fatima Al-Zahraa hospital, caused from the outputs average is relatively slightly lesser than its peers. In spite of this small amount of inefficiency, there is no reference sets, denoting that the Fatima Al-Zahraa hospital is very close to efficiency frontier.   The output oriented case III as in input oriented, the amount of inefficiency of Fatima Al-Zahraa hospital increases if compared with amount of inefficiency in case (II). In case IV, select only one input, with three output variables, the input oriented results show that Ibn Al-Balady hospital is inefficient, has relative efficiency score less than one (0.99323), with efficient Fatima Al-Zahraa and Al-Alwaiya Children's hospitals in year 2014, but the inefficiency in Ibn Al-Balady hospital is small if compared with inefficiency in year 2015 (0.87446). In output oriented case IV, the Ibn Albalady hospital has relative efficiency score more than one (1.00682) in 2014, (1.14356) in 2015. The Fatima Al-Zahraa hospital also is inefficient (1.17483) in year 2015, but, the Ibn Al-balady hospital is more efficient than Fatima Al-Zahraa hospital, which in output oriented, the hospital be more efficient whenever the efficiency score closer to one.

II. LPI Module
LPI technique used to determine the change in productivity over consecutive time periods, first find the values of directional distance functions by applying models (3)   Case (II) shows that, the "Fatima Al-Zahraa" revealed the productivity progress (-1.445%) in negative, which means that there is decline in productivity in year 2015, while the two hospitals "Ibn Al-Balady" and "Al-Alwaiya Children's" hospitals have a growth in productivity, which revealed productivity change in positive (0.299 %, 1.32%) respectively, as in case (I) the "efficiency change" of "Fatima Al-Zahraa" in case (II), plays a major role in productivity progress than technological change, due to the score of efficiency change in negative (-10.489%) is higher than the score of technological change in positive (9.044). While the two other hospitals revealed no change in the efficiency as in case (I), because they are relatively efficient in both years (2014) and (2015). In case (III), the three hospitals revealed positive productivity progress. The Al-Alwaiya Children's hospital has highest positive productivity change (2.4708 %), then Fatima Al-Zahraa hospital (1.087 %), and Ibn Al-Balady hospital (0.299%). In this case, the three hospitals have growth in productivity, the efficiency change scores are equal to zero in "Ibn Al-Balady" and Al-Alwaiya Children's hospitals, and "Fatima Al-Zahraa" hospital has a small negative change (-5.425%). while the Technological change has the positive values in all hospitals (0.299%), (2.4708 %), and (6.512%) respectively. Finally, in case (IV), only ("Al-Alwaiya Children's") has positive productivity change (3.874%), indicating, it has productivity growth during year 2015, while, the two hospitals "Fatima Al-Zahraa" and Ibn Al-Balady have the change in productivity in negative (-6.1%), (-7.621%) respectively, indicating, that there was decrease in productivity during year 2015.
From previous results indicate that the (Ibn Al-Balady) hospital has productivity growth in all cases unless in case (IV) has decline in productivity. The Fatima Al-Zahraa hospital has productivity decline in two cases (II, IV) and has productivity growth in case (III) only, with no change in case (I). Finally the Al-Alwaiya Children's hospital has productivity growth in all cases during period (2014-2015).

Conclusion
From the results highlighted in previous sections, the following conclusions are drawn: 1.
This research using (two techniques DEA and LPI), gives a comprehensive analysis of hospital efficiency, which determines if the hospital is efficient or not by DEA, determines the change of productivity over consequence time periods using LPI. 2.
The study model can be developed in all hospital wards and healthcare centers, but each hospital should be supplied with peer systems. 3.
Using (DEA) technique, the results show that Al-Alwaiya Children's hospital still efficient in four cases (combination of different inputs & outputs), while, other hospitals change their efficiency by changing the case. 4.
Using (LPI) technique, the results show that there is a clear decline in efficiency of Fatima Al-Zahraa hospital over the period (2014)(2015) in all cases, while in Al-Alwaiya Children's hospital there is no change in efficiency.

5.
U sing the Luenberger indicator with DEA gives insightful results of the change in productivity and causes of the change of either declined or increased, to achieve better indicators.