Journal of Medical Systems, Vol. 14, No. 5, 1990
Measuring Technical Efficiency in Health Care Organizations Michael D. Rosko, Ph.D.
The rising cost of health care has created great interest in developing methods to increase the efficiency of health care organizations. Despite this interest most analyses of prospective payment and other programs designed to control expenditures have examined costs and not efficiency. This article examines a new technique--data envelopment analysis (DEA)--that facilitates the conduct of efficiency studies. The utility of DEA is analyzed by comparing this technique with other methods used to measure efficiency, by discussing the application of DEA in the health care industry and by assessing the validity of results from DEA studies. The article concludes with an assessment of the strengths and weaknesses of DEA and suggestions for refining this technique.
INTRODUCTION An inflationary spiral has plagued the U.S. health care industry since the 1960s. During this period the proportion of GNP spent on health care has more than doubled--going from 5% in 1960 to over 11% in 1989. In response to this problem a number of cost containment efforts have been proposed and implemented. Among these initiatives are the stimulation of competition, controls on capital formation, utilization review, managed care, and rate regulation. Currently, rate regulation is the most prominent approach by the government to stem the rising tide of health care expenditures. The federal government launched the Medicare Prospective Payment System (PPS) in 1983. By 1988 care-based prospective payment systems regulated rates of compensation for hospital patients in 18 states. 1 It is common to argue that by placing the health care organization (HCO) at financial risk for profit or loss prospective payment will cause hospitals to operate in a more efficient manner, thereby restraining cost increases. 2 On the other hand, HCOs may respond to prospective payment by reducing the quality of care. It is ironic that although rate regulation is intended to increase efficiency, there is little evidence that researchers have attempted to document this result. A recent review of empirical studies of rate From the Department of Health and Medical Services Administration, School of Management, Widener University, Chester, Pennsylvania 19013. 307 0148-5598/90/1000-0307506.00/0 © 1990 Plenum Publishing Corporat2on
308
Rosko
regulation programs reported that 32 studies examined the impact of rate-setting on costs while only one study examined the effect of rate-setting on efficiency) The emphasis on cost analysis can be attributed, in part, to the ease of conducting cost function studies relative to structural studies of production. However, the recent development and refinement of new techniques to measure efficiency will allow more studies to be conducted in this area. The purpose of this article is to demonstrate the utility of the application of an efficiency measurement technique, data envelopment analysis, in the health care field. This will be done by reviewing the literature of efficiency analysis in HCOs and by describing possible refinements and extensions of these techniques.
EFFICIENCY MEASURES Technical and allocative efficiency of health care organizations have been examined. The former measures the extent to which a given combination of inputs produces as much output as is feasible in an engineering sense. For example, the production function Q = 2L.SK .5 implies that the input combination L = 16, K = 4 will result in no more than 16 units of output. If the health care organization uses this combination of inputs and produces only 10 units of output, its efficiency rating is 10/16 or 0.625. The concept of technical efficiency is also shown in Figure 1. Operating at point A with 4 units of capital and 16 units of labor on the isoquant QI (a curve depicting a locus of points in which different combinations of capital and labor are capable of producing the same amount of output) the HCO is capable of producing at most 16 units of output. HCOs producing this level of output are classified as efficient and are assigned an efficiency rating of 1.0. If fewer units are produced with this combination of inputs, the HCO is classified as relatively inefficient and will be assigned an efficiency rating of less than 1. Allocative efficiency, on the other hand, measures the extent to which a firm is minimizing the cost of producing a desired level of output. Using the terminology of production theory, allocative efficiency measures the extent to which the optimal combination of inputs is employed by considering the relative marginal productivity and prices
C Capital
- 16
D Labor Figure 1. Graphicalrepresentationof technical and economicefficiency.
Measuring Technical Efficiency
309
of the inputs. For example, given a simple two input situation, allocative efficiency occurs when the ratio of the marginal product of capital to the price of capital equals the ratio of the marginal product of labor to the price of labor. As shown in Figure 1, this is equivalent to operating at point A which is the point of tangency between the isocost line (the firm's budget line for two inputs, depicted in Figure 1 as CD) and the isoquant. A firm operating at point B is allocatively inefficient. To produce 16 units of output at point B, it would incur greater expenses than if it were operating at point A. Thus, the firm should move away from point B and toward point A by using less capital and hiring more labor. Since studies of allocative efficiency in health care organizations have been reviewed comprehensively this paper focuses on technical efficiency.2
DATA ENVELOPMENT ANALYSIS Data envelopment analysis (DEA) is a technique, developed by Charnes et al.3 in 1978, that employs linear programming to measure the relative technical efficiency of decision-making units. A DMU may be defined as narrowly as an individual or as broadly as an organization. In order to apply DEA correctly, the comparison group of DMUs must be homogenous--i.e., they use common inputs to produce the similar outputs. Accordingly, it is inappropriate to use DEA to compare the efficiency of different types of providers. For example, a comparison of acute care hospitals and psychiatric hospitals is not a valid use of DEA. DEA has been used to evaluate the efficiency of DMUs producing similar outputs in a variety of industries including health care, education, mining, and electricity production. 3'4 Pareto-Koopnass Efficiency, derived from the well-known social welfare criterion of Pareto optimality, is used to define efficiency in DEA analysis. The construct, technical efficiency, is evaluated by using input and output criteria: (a) input criterion: a DMU is not efficient if it is possible to decrease any input without increasing any other input and without decreasing output; (b) output criterion: a DMU is not efficient if it is possible to increase any output without decreasing any other output and without increasing any input. A DMU will be characterized as perfectly efficient only when both criteria are satisfied. 3 A brief example illustrates how DEA applies the Pareto-Koopnass concept of efficiency. For simplicity assume that there are four DMUs producing the same type of output. Table 1 summarizes the input and output levels of the DMUs. Table 2 presents normalized input levels (i.e., input divided by output) for each Table 1. Summary of Input and Output Levels
DMU
Quantity of input 1
A B C D
6 15 21 16
Quantity of input 2 12 5 14 15
Quantity of output 30 25 35 26
310
Rosko
Table 2. Normalized I n p u t Levels DMU
Input 1/output
Input 2/output
A B C D
0.20 0.60 0.60 0.62
0.40 0.20 0.40 0.58
DMU. These are plotted in Figure 2. The Best Practice Production Frontier (BPPF) can be derived from the normalized input plots. Consistent with the Pareto-Koopnass efficiency criteria, any DMU in Figure 2 that is lower and to the left of another DMU is more efficient than that DMU because it is using fewer inputs to produce the same amount of output. As shown in Figure 2, DMUs A and B dominate DMUs C and D. Accordingly, DMUs A and B, which are not dominated by any other DMUs, lie on the BPPF and are designated point A and B, respectively. The BPPF can be constructed from a set of piecewise linear curves. The first component of this set is the segment drawn from point A to point B. The second member of the set is constructed by drawing a ray, parallel to the horizontal axis, and originating at point A. This segment is designated AA'. The final part of the BPPF is a ray drawn from point B through B', parallel to the vertical axis. Given the BBPF we can measure the relative technical efficiency of each DMU. Point A and B are on the frontier and, thus, DMU A and B are assigned an efficiency rating of 1.0. The efficiency score of DMU D, which is inefficient, can be measured by constructing a line segment from the origin to point D, representing DMU D. This line segment crosses the BPPF at point D'. The efficiency rating of DMU D is equal to the
INPUT 1 / OUTPUT
0.8
B'
0.7
D
0.6 0.5 0.4 0.3 0.2 0.1 0 0
0.1
0.2
0.3
0.4
INPUT 2 / OUTPUT Figure 2. Plot of normalized input levels.
0.5
0.6
0.7
Measuring Technical Efficiency
311
ratio of the length of line segment OD' to the length of OD. Since the numerator OD' is less than the denominator OD, the efficiency rating of DMU D will be less than 1.0. In addition to identifying inefficient DMUs, DEA provides guidelines for eliminating inefficiency. For example, DMU D could become technically efficient by maintaining its output level and reducing its employment of input 1 and input 2. However, there are an infinite number of ways in which this could be done. A by-product of DEA is the construction of a technically efficient composite DMU. In the case of DMU D the composite is D', which reflects the input use of DMU D's reference DMUs--A and B. DMU D' can be used to establish target levels of input use for DMU D. Although trivial problems can be solved graphically, most realistic problems require a mathematical formulation that can be solved by using linear programming. The theoretical base and mathematical model of DEA has been presented elsewhere, therefore only a brief treatment of the mathematical model will be presented in this article. 3'5'6 A general model to estimate technical efficiency can be expressed as follows:
•
UrYrk
r=l Maximize
Zk m
i=i
subject to: Z k ~< 1, k = 1. . . .
n;
Ur 1> 0 ;
Vi ~ O;
where:
Yrk is the rth output from the kth DMU; Xik is the ith input used by the kth DMU; u and v are artificial weights generated from the model; Zk is the ratio of weighted outputs to the weighted inputs, the weights are selected in a way that makes DMU k as efficient as possible compared to all other DMUs. For the analysis of an industry characterized by multiple output production processes, one of the especially appealing features of DEA is that it is capable of convetting multiple output and input information into a single measure of efficiency. Table 3 provides a summary of inputs and outputs used in health care applications of DEA. As this table shows, DEA has been applied to a variety of HCOs, including hospitals, nursing homes, pharmacies, and ambulatory care facilities. DEA studies of HCOs have defined the DMU as broadly as the entire organization (i.e., the hospital or the nursing home) and as narrowly as the individual physician.
U T I L I T Y O F DEA The utility of DEA can be assessed by (a) comparing DEA with other techniques used to measure efficiency; (b) examining the potential uses of DEA; and, (c) demonstrafing the comparative validity of DEA results.
312
Rosko
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Measuring Technical Efficiency in Health Care Organizations Michael D. Rosko, Ph.D.
The rising cost of health care has created great interest in developing methods to increase the efficiency of health care organizations. Despite this interest most analyses of prospective payment and other programs designed to control expenditures have examined costs and not efficiency. This article examines a new technique--data envelopment analysis (DEA)--that facilitates the conduct of efficiency studies. The utility of DEA is analyzed by comparing this technique with other methods used to measure efficiency, by discussing the application of DEA in the health care industry and by assessing the validity of results from DEA studies. The article concludes with an assessment of the strengths and weaknesses of DEA and suggestions for refining this technique.
INTRODUCTION An inflationary spiral has plagued the U.S. health care industry since the 1960s. During this period the proportion of GNP spent on health care has more than doubled--going from 5% in 1960 to over 11% in 1989. In response to this problem a number of cost containment efforts have been proposed and implemented. Among these initiatives are the stimulation of competition, controls on capital formation, utilization review, managed care, and rate regulation. Currently, rate regulation is the most prominent approach by the government to stem the rising tide of health care expenditures. The federal government launched the Medicare Prospective Payment System (PPS) in 1983. By 1988 care-based prospective payment systems regulated rates of compensation for hospital patients in 18 states. 1 It is common to argue that by placing the health care organization (HCO) at financial risk for profit or loss prospective payment will cause hospitals to operate in a more efficient manner, thereby restraining cost increases. 2 On the other hand, HCOs may respond to prospective payment by reducing the quality of care. It is ironic that although rate regulation is intended to increase efficiency, there is little evidence that researchers have attempted to document this result. A recent review of empirical studies of rate From the Department of Health and Medical Services Administration, School of Management, Widener University, Chester, Pennsylvania 19013. 307 0148-5598/90/1000-0307506.00/0 © 1990 Plenum Publishing Corporat2on
308
Rosko
regulation programs reported that 32 studies examined the impact of rate-setting on costs while only one study examined the effect of rate-setting on efficiency) The emphasis on cost analysis can be attributed, in part, to the ease of conducting cost function studies relative to structural studies of production. However, the recent development and refinement of new techniques to measure efficiency will allow more studies to be conducted in this area. The purpose of this article is to demonstrate the utility of the application of an efficiency measurement technique, data envelopment analysis, in the health care field. This will be done by reviewing the literature of efficiency analysis in HCOs and by describing possible refinements and extensions of these techniques.
EFFICIENCY MEASURES Technical and allocative efficiency of health care organizations have been examined. The former measures the extent to which a given combination of inputs produces as much output as is feasible in an engineering sense. For example, the production function Q = 2L.SK .5 implies that the input combination L = 16, K = 4 will result in no more than 16 units of output. If the health care organization uses this combination of inputs and produces only 10 units of output, its efficiency rating is 10/16 or 0.625. The concept of technical efficiency is also shown in Figure 1. Operating at point A with 4 units of capital and 16 units of labor on the isoquant QI (a curve depicting a locus of points in which different combinations of capital and labor are capable of producing the same amount of output) the HCO is capable of producing at most 16 units of output. HCOs producing this level of output are classified as efficient and are assigned an efficiency rating of 1.0. If fewer units are produced with this combination of inputs, the HCO is classified as relatively inefficient and will be assigned an efficiency rating of less than 1. Allocative efficiency, on the other hand, measures the extent to which a firm is minimizing the cost of producing a desired level of output. Using the terminology of production theory, allocative efficiency measures the extent to which the optimal combination of inputs is employed by considering the relative marginal productivity and prices
C Capital
- 16
D Labor Figure 1. Graphicalrepresentationof technical and economicefficiency.
Measuring Technical Efficiency
309
of the inputs. For example, given a simple two input situation, allocative efficiency occurs when the ratio of the marginal product of capital to the price of capital equals the ratio of the marginal product of labor to the price of labor. As shown in Figure 1, this is equivalent to operating at point A which is the point of tangency between the isocost line (the firm's budget line for two inputs, depicted in Figure 1 as CD) and the isoquant. A firm operating at point B is allocatively inefficient. To produce 16 units of output at point B, it would incur greater expenses than if it were operating at point A. Thus, the firm should move away from point B and toward point A by using less capital and hiring more labor. Since studies of allocative efficiency in health care organizations have been reviewed comprehensively this paper focuses on technical efficiency.2
DATA ENVELOPMENT ANALYSIS Data envelopment analysis (DEA) is a technique, developed by Charnes et al.3 in 1978, that employs linear programming to measure the relative technical efficiency of decision-making units. A DMU may be defined as narrowly as an individual or as broadly as an organization. In order to apply DEA correctly, the comparison group of DMUs must be homogenous--i.e., they use common inputs to produce the similar outputs. Accordingly, it is inappropriate to use DEA to compare the efficiency of different types of providers. For example, a comparison of acute care hospitals and psychiatric hospitals is not a valid use of DEA. DEA has been used to evaluate the efficiency of DMUs producing similar outputs in a variety of industries including health care, education, mining, and electricity production. 3'4 Pareto-Koopnass Efficiency, derived from the well-known social welfare criterion of Pareto optimality, is used to define efficiency in DEA analysis. The construct, technical efficiency, is evaluated by using input and output criteria: (a) input criterion: a DMU is not efficient if it is possible to decrease any input without increasing any other input and without decreasing output; (b) output criterion: a DMU is not efficient if it is possible to increase any output without decreasing any other output and without increasing any input. A DMU will be characterized as perfectly efficient only when both criteria are satisfied. 3 A brief example illustrates how DEA applies the Pareto-Koopnass concept of efficiency. For simplicity assume that there are four DMUs producing the same type of output. Table 1 summarizes the input and output levels of the DMUs. Table 2 presents normalized input levels (i.e., input divided by output) for each Table 1. Summary of Input and Output Levels
DMU
Quantity of input 1
A B C D
6 15 21 16
Quantity of input 2 12 5 14 15
Quantity of output 30 25 35 26
310
Rosko
Table 2. Normalized I n p u t Levels DMU
Input 1/output
Input 2/output
A B C D
0.20 0.60 0.60 0.62
0.40 0.20 0.40 0.58
DMU. These are plotted in Figure 2. The Best Practice Production Frontier (BPPF) can be derived from the normalized input plots. Consistent with the Pareto-Koopnass efficiency criteria, any DMU in Figure 2 that is lower and to the left of another DMU is more efficient than that DMU because it is using fewer inputs to produce the same amount of output. As shown in Figure 2, DMUs A and B dominate DMUs C and D. Accordingly, DMUs A and B, which are not dominated by any other DMUs, lie on the BPPF and are designated point A and B, respectively. The BPPF can be constructed from a set of piecewise linear curves. The first component of this set is the segment drawn from point A to point B. The second member of the set is constructed by drawing a ray, parallel to the horizontal axis, and originating at point A. This segment is designated AA'. The final part of the BPPF is a ray drawn from point B through B', parallel to the vertical axis. Given the BBPF we can measure the relative technical efficiency of each DMU. Point A and B are on the frontier and, thus, DMU A and B are assigned an efficiency rating of 1.0. The efficiency score of DMU D, which is inefficient, can be measured by constructing a line segment from the origin to point D, representing DMU D. This line segment crosses the BPPF at point D'. The efficiency rating of DMU D is equal to the
INPUT 1 / OUTPUT
0.8
B'
0.7
D
0.6 0.5 0.4 0.3 0.2 0.1 0 0
0.1
0.2
0.3
0.4
INPUT 2 / OUTPUT Figure 2. Plot of normalized input levels.
0.5
0.6
0.7
Measuring Technical Efficiency
311
ratio of the length of line segment OD' to the length of OD. Since the numerator OD' is less than the denominator OD, the efficiency rating of DMU D will be less than 1.0. In addition to identifying inefficient DMUs, DEA provides guidelines for eliminating inefficiency. For example, DMU D could become technically efficient by maintaining its output level and reducing its employment of input 1 and input 2. However, there are an infinite number of ways in which this could be done. A by-product of DEA is the construction of a technically efficient composite DMU. In the case of DMU D the composite is D', which reflects the input use of DMU D's reference DMUs--A and B. DMU D' can be used to establish target levels of input use for DMU D. Although trivial problems can be solved graphically, most realistic problems require a mathematical formulation that can be solved by using linear programming. The theoretical base and mathematical model of DEA has been presented elsewhere, therefore only a brief treatment of the mathematical model will be presented in this article. 3'5'6 A general model to estimate technical efficiency can be expressed as follows:
•
UrYrk
r=l Maximize
Zk m
i=i
subject to: Z k ~< 1, k = 1. . . .
n;
Ur 1> 0 ;
Vi ~ O;
where:
Yrk is the rth output from the kth DMU; Xik is the ith input used by the kth DMU; u and v are artificial weights generated from the model; Zk is the ratio of weighted outputs to the weighted inputs, the weights are selected in a way that makes DMU k as efficient as possible compared to all other DMUs. For the analysis of an industry characterized by multiple output production processes, one of the especially appealing features of DEA is that it is capable of convetting multiple output and input information into a single measure of efficiency. Table 3 provides a summary of inputs and outputs used in health care applications of DEA. As this table shows, DEA has been applied to a variety of HCOs, including hospitals, nursing homes, pharmacies, and ambulatory care facilities. DEA studies of HCOs have defined the DMU as broadly as the entire organization (i.e., the hospital or the nursing home) and as narrowly as the individual physician.
U T I L I T Y O F DEA The utility of DEA can be assessed by (a) comparing DEA with other techniques used to measure efficiency; (b) examining the potential uses of DEA; and, (c) demonstrafing the comparative validity of DEA results.
312
Rosko
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