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benefit analysis and capital investment decisions in nuclear cardiology
0038~l21/83 $3 00 t w Pergamon Press Ltd
Socio-Econ Plan. SCI. Vol. 17, No. 4, pp. 177-180, 1983 Pnnted m Great Britain
COST/BENEFIT ANALYSIS AND CAPITAL INVESTMENT DECISIONS IN NUCLEAR CARDIOLOGY E. V. KOTLYAROV Department of Nuclear Medicine, George Washington University, Washington, DC 20010,U.S.A.
MARC J. SCHNIEDERJANS Department of Management, University of Nebraska-Lincoln, Lincoln, NE 68588,U.S.A. (Received 7 October 1982) Abstract-This paper demonstrates an application of Cost-Benefit Analysis as an aid in capital investment medical decision making. Specifically, a cost-benefit analysis is used to compare three nuclear cardiology instruments (i.e. Nuclear Stethoscope, Mobile Camera/Computer and Fixed Cardiac Computer). The study examined both non-quantitative and quantitative comparative factors. Results of the study show: (1) Conversion of the non-quantitative factors into a numerical system (via medical opinion) greatly delineates the relative merits of each instrument. (2) Simulating the stochastic economic and equipment utilization factors reveals instrument selection to be a function of patient flow and amortization procedures. (3) Adjusting the quantitative assessment of each instrument by the non-quantitative assessment (via the numerical system) aids in the capital investment decision.
INTRODUCTION
Cost/Benefit Analysis is increasingly being used as a decision aid in medical decision making[4]. As the need for this type of analysis grows, so does the need grow for alternative approaches to fit unique problem situations. This is particularly true for capital investment decision making. In surveying the cost/benefit literature pertaining to this area, it appears that most analyses can be grouped at one end or the other of the following continuum: Subjectively
Objectively <
Derived Analysis
> Derived Analysis.
The subjective end of the continuum represents a more theoretical or non-economic approach to cost/benefit analysis. This type of analysis is usually based on subjective input, such as opinions or judged data as opposed to empirical data[2-41. The objective end of the continuum represents an economic approach to cost/benefit analysis. This type of analysis is based on objective input, such as cost, usually in terms of dollars, units of time or labor, and benefits, usually in terms of revenue dollars of profit[l, 51. Unfortunately, many capital investment decisions in the medical area are arrived at by objective or economic criteria, and relevant subjective or non-economic criteria are considered secondary to the decision process. Thus, relevant non-economic criteria are not directly used in the actual decision. What is called for is a procedure that will combine the economic and non-economic decision making criteria into one over-all measure of cost/benefit effectiveness. The purpose of this paper, then, is to demonstrate how economic and non-economic decision criteria can be combined to provide a more precise measure of net-
benefits. In the process of achieving this objective, this paper will: (1) Illustrate the use of the Monte Carlo simulation method to aid in assessing the economic decision factors of a capital investment project under differing utilization rates. (2) Illustrate the use of rankings as a means of quantifying non-economic decision factors. (3) Illustrate how the economic and non-economic decision criteria can be combined via mathematically derived multipliers. This paper will not only describe the methodological procedure, but also provide an application of the procedure for a medical decision making capital investment problem. Specifically, a cost/benefit analysis of both economic and non-economic factors will be performed in an effort to evaluate which of three pieces of equipment (i.e. Nuclear Stethoscope, Mobile Camera/Computer, and Fixed Cardiac Computer) a hospital should purchase under differing rates of utilization. METHODOLOGY
The cost/benefit analysis procedure proposed in this paper requires three steps. The first step involves the analysis of economic factors via a Monte Carlo simulation. The second step involves a subjective ranking of non-economic factors. The third step involves the combination of the results obtained in steps one and two via the use of mathematical multipliers. Each of these three steps will be described as they relate to the hospital equipment decision problem. Step 1
The Monte Carlo simulation technique allows the recognition of stochastic economic behavior in modeling a problem situation. It will be assumed the reader is familiar with the basic procedure and application of this operations research technique. Generally, to perform this 177
E. V. KOTLYAROV and M. J. SCHNIEDERJANS
178
step, a decision maker must first identify the economic costs and benefits. For those costs and benefits that are variable, probability distributions based on that variable’s mean and standard deviation are developed. These distributions are then used as sampling distributions from which random samples of costs and benefits are selected. Having selected a specific set of cost/benefit values, a value for net-benefit (or net-cost) can be calculated under differing conditions as defined by the problem situation. It should be mentioned as a limitation on this step that if all of the costs or benefits are static the solution is deterministic and not stochastic. As such, the Monte Carlo simulation technique would not be applicable. For the specific hospital equipment problem, the economic costs and benefits need to be identified. The economic cost of the equipment falls into four categories: Labor, Supplies, Amortization, and Maintenance. The economic benefit of the equipment is the patient reimbursement for the service performed using the equipment. To determine the costs, a survey of eleven midwestern hospitals who utilize the equipment was conducted. From these responding hospitals, three used the Nuclear Stethoscope, four used a Mobile Camera/Computer, and four used a Fixed Cardiac Computer. Economic cost and benefit information was collected and is presented in Table 1. As can be seen on Table 1, each of the five types of economic factors have both a mean and standard deviation per subject examined from which a probability distribution is made up. The goal here is to model the net reimbursement or operating profilt. That is, if you subtract from the reimbursement the labor, supplies, amortization, and maintenance costs, you arrive at the net reimbursement or the net economic benefit (or loss) from purchasing and operating this particular piece of equipment. Having developed the probability distributions, the differing conditions under which the simulation model is to run needs to be stated. From the comments provided by the hospital survey, it appears three distinct utilization rates are most commonly used by the hospitals. The weekly utilization rates most commonly stated in the survey are five subjects per week, ten subjects per week, and fifteen subjects per week. Since the amortization and maintenance costs are a function of equipment utilization, these variables will be affected by the differing utilization rates.
To perform the actual simulation, a F.ORTRAN IV computer program was written and exercised on an IBM 370 at the University of Hawaii at Hilo. The simulation was designed to simulate the use of the three different types of equipment over a five year investment period under the three differing utilization rates mentioned above. This required nine separate computer runs to calculate the net-benefit (or loss) for each of the three pieces of equipment at the three differing utilization rates. Sfep 2 To generally evaluate non-economic factors, a number of techniques can be utilized. This paper recommends ranking as an efficient and effective means for evaluating non-economic factors. It is assumed the reader is familiar with ranking systems. In general, the non-economic costs and benefits need to be recognized. In many problem situations, a clear distinction between a factor being a “cost” or “benefit” is achieved by the ranking itself. Once the categories of costs and benefits are defined, a ranking system also needs to be defined. This system will usually be based on the number of alternatives being evaluated with the rank of “one” representing the most preferred alternative, rankings and subsequent representing subsequently less preferred alternatives. The rankings obtained can be used individually or as groups in assessing the differences in the alternatives for each category of non-economic factors being evaluated. Having determined the rankings by each alternative for each non-economic factor, a relative index can be developed by simply adding the ranks by alternatives and dividing the largest sum of the ranks into the sum of the ranks for the other alternatives. This relative index indicates the preference of the individuals who provided the rankings. Simply, the alternative with the smallest index is the preferred alternative based on non-economic factors chosen. In the hospital equipment problem addressed by this paper, five categories of non-economic factors were selected for comparison. These categories are: Patient Accessibility to Each Type of Equipment, Patient Flow In/Out, Flexibility of Application (e.g. clinical), Complexity in Usage, and Machine Set-Up Inconvenience. These categories were obtained from the hospital survey previously mentioned and represent the five most corn
Table 1. Economics factors* Mobile Camera/
costs/s Scp@les
6.37 17.37
Amorlization*i Maintenance**'
10.12 1.67
L.%b<,I
-
I.93 5.01 2.74 .6C
11.05 18.05 42.56 18.62
2.00
3.15 5.60 2. 0
Fixed Ce.rci!ac
11.75 18.05 38.58 20.30
1.50 3.00 4.65 2.30
*These average values were calculated from a sample survey of eleven hospitals that utilize this type of equipment. **Based on an average cost of $26,310.0c; $110,650.0c a five year period at ten subjects per week
ard $100,300.00 over
***Based cn ter subjects per week and an annual yearly maintenance cost of $800.00; $8,900.00 and $9,700.00, rapectiv+Ay, with a forecasted 796compounded increase starting in the third year. The resulting average yearly maintwance cost for the three types of equipment are $870.38; $9,681.10 and $10.553.49, respectively.
179
Cost/benefit analysis and capital investment decisions
Table 2. Non-economicfactors
-
___I--category
Mobile Camera/ Computer
Fixed Cardiac Computer
27
10
24 9
17 14
18
Patient Accessibility Patient Flow Flexibility of Applictmn Complexity in &.3ge Set-& Inccnvtrierce _.__ TOTAL
26
Pelative Index
130
Fmfit
I.
Iqultlpller
Sumof the Ranks (n=9\
NUClt?ZZ Stethoscope
14
11
26 20
9:
a4
89
a6 (a/97)
(9?/97)
GO( lGO/LOO(”1.16
monly suggested non-economic criteria for use in making a decision in the eleven hospitals surveyed. A second survey was conducted by phone of nine physicians who utilized or had some knowledge of all three alternative pieces of equipment. Each physician was asked to rank (where 1 = most preferred and 3 = least preferred) the three alternative pieces of equipment for each of the five categories. The results of these rankings is presented on Table 2. Adding the rankings by column (or alternative), they can be converted into a relative index. Step 3 Step 3 involves the combining of the economic results found in Step 1 with the non-economic results analyzed in Step 2. This is accomplished by converting the relative index measure computed in Step 2 into a profilt multiplier. The profit multiplier is simply the reciprocal of the decimal value equivalent of the relative index. Once the profit multiplier is derived, it is then used as an adjustment to the economic net-benefit or profit. The adjustment is achieved by multiplying the net-benefit or profit by the profit multiplier. The result will cause an increasing adjustment in net-benefit for those capital investment alternatives that were highly ranked in the non-economic analysis. It should also be mentioned that the adjusted net-benefit figure can only be used for comparative purposes and has no specific economic value. Also, if the net-benefit is negative (a loss situation) the adjustment can still be made, but does not require the profit multiplier. Instead, the decimal equivalent of the relative index and the net loss are multiplied. thus reducing the amount of the net loss. For the hospital equipment problem situation, the profit multipliers are given at the bottom of Table 2. In interpretting the meaning of the multipliers, it is clear that the net reimbursement or profit for the Mobile Camera/Computer and the Fixed Cardiac Computer will be increased by sixteen and seven per cent, respectively. RESULTS In addition to performing the required analysis in Step 1, validity tests were conducted on the Monte Carlo
92 (89/97)
(1~0,:&'6) 1.07
(lOC/92\
simulation results. Chi-square goodness-of-fit tests were used to compare input and output probability distribution similarity. Five chi-square tests were conducted for each of the nine simulation runs, and the results showed no significant difference (p > 0.001) between the hypothetical economic cost/benefit distributions input and the resulting distributions tallied in the output. Similarly, one-way analysis of variance tests were conducted for each of the nine simulation runs, and the results showed no significant difference (p >O.Ol) between the input mean cost/benefit values and the resulting tallied mean values in the output. It was concluded from these statistical tests and several others, that the simulation model validly assessed the economic factors for the cost/benefit analysis. The results of the simulation are summarized in Table 3. As can be seen, nine to total net reimbursement or profit figures are presented. These figures represent the summation of all the profit for each peice of equipment over the five year period of investment that will be achieved (on the average). These nrofit figures are also broken down by the rate of equipment utilization (i.e. five, ten, and fifteen subjects per week). Interpretting the results of the economic net-benefit presented in Table 3 is very simple. Regardless of equipment utilization, the Nuclear Stethoscope is clearly the best choice for the hospital. This choice is particularly true as the rate of utilization drops. The results of Step 2 are necessarily given in Table 2. They are described in the Methodology section of this paper. Step 3 involves the adjustment of the simulated netbenefit figures on Table 3 by use of the profit multipliers. These adjusted figures are presented in Table 4. CONCLUSIONS As can be seen on Table 4, the resulting combined net-benefit figures indicate that the level of equipment utilization does have an effect on the net-benefit of capital investments. Specifically, a medical decision maker would select the Mobile Camera/Computer over the Nuclear Stethoscope when the number of subjects utilizing the equipment per week is fifteen or above. At
Table 3. Simulated total net reimbursement Equipment Utilization Rate (S/W)
12
19 23
NUCl&3,7Y Stethoscope ($J
over a five year period
Mobile Camera/ computer ($j
Fixed Cardiac computer ($)
Five
110,312
Tt?n
248,842
184,948
185,634
Fifteen
391,525
381,6h2
355,744
12,297
17,831
180
E. V. K~LYAROV and M. 3. SCHNIE~ERJA~S Table 4. Combined economic and non-economic Equipmert Utilizstio~ Rate (S/W)
net benefit
NUClS3X Mobile Camera/ Stethoscope ($‘I Computer ($I
14,265
Fjxed Cardiac Corrputtr($1
19,o79
Five
118,312
Ten
246,WZ
214,*0
198,528
Fifteen
391,525
442 I705
380,
rates of equipment utilization, the Nuclear Stethoscope would still be used. but at higher rates of utilization, it appears that the Mobile Camera/Computer is preferred. Thus, it can be concluded that not only can economic and non-economic factors be combined into a ~ost/benefit measure for decision making, but also the product of the two analyses can result in differing conclusions. It should also be noted that the actual utilization rate, whereby the Mobile Camera/Computer has an adjusted net-benefit greater than the Nuclear Stethoscope, is between ten and fifteen subjects per week. Thus, hospitals which are facing this capital investment situation and have a mean utilization rate between ten and fifteen subjects per week might want to duplicate this study using rates between ten and fifteen to determine the exact break-even point. It can also be concluded that the Fixed Cardiac Computer will become a preferable choice to the Nuclear Stethoscope at utilization rates slightly higher than fifteen subjects per week. This can be easily forecasted by the observable difference in the rate of increase in adjusted net-benefits between the two pieces of equipment.
&6
SUNNY
lower
This paper demonstrates the use of the Monte Carlo simulation technique and a ranking procedure as a means by which economic and non-economic cost/benefit factors can be combined to generate a single measure of net-benefit. The three step cost/benefit procedure proposed is illustrated by an actual hosFLta1capital investment problem. This problem compares the cost and benefits between three alternative pieces of equipment: the Nuclear Stethoscope, Mobile Camera/Computer, and the Fixed Cardiac Computer. The results of the study show the combined netbenefit dictates that the investment decision is a function of equipment utilization. 1. L G. Anderson
REFERENCES and R F. Settle. Benefit-Cosf Analysis: A
Practical Guide. Lexington Books. Lexington. Mass. (1977). 2. A. K. Dasqupta and D. W. Pearce, Cost-Benefit An&is: Theov~and Practice. Macmillan, London (1972). 3. W Edwards, M. Guttentag and K. Snapper, A decrsiontheoretIe approach to evaluation research. In E. L. Struening and M. Guttentag (Eds.), ~~~~boo~ of ~~u~~afi~~ Resent&. Voi 1. pp. 139-81 Sage, Beverly Hills, California (1975). 4. C E Metz, Basic principles of ROC analysis. Seminars in Nuclear Medicine 8,283-298 (1978) 5. P. G. Sassone and W. A. Schaffer, Cost-Benefit Analysis: A Handbook. Academic Press, New York (1978).
Socio-Econ Plan. SCI. Vol. 17, No. 4, pp. 177-180, 1983 Pnnted m Great Britain
COST/BENEFIT ANALYSIS AND CAPITAL INVESTMENT DECISIONS IN NUCLEAR CARDIOLOGY E. V. KOTLYAROV Department of Nuclear Medicine, George Washington University, Washington, DC 20010,U.S.A.
MARC J. SCHNIEDERJANS Department of Management, University of Nebraska-Lincoln, Lincoln, NE 68588,U.S.A. (Received 7 October 1982) Abstract-This paper demonstrates an application of Cost-Benefit Analysis as an aid in capital investment medical decision making. Specifically, a cost-benefit analysis is used to compare three nuclear cardiology instruments (i.e. Nuclear Stethoscope, Mobile Camera/Computer and Fixed Cardiac Computer). The study examined both non-quantitative and quantitative comparative factors. Results of the study show: (1) Conversion of the non-quantitative factors into a numerical system (via medical opinion) greatly delineates the relative merits of each instrument. (2) Simulating the stochastic economic and equipment utilization factors reveals instrument selection to be a function of patient flow and amortization procedures. (3) Adjusting the quantitative assessment of each instrument by the non-quantitative assessment (via the numerical system) aids in the capital investment decision.
INTRODUCTION
Cost/Benefit Analysis is increasingly being used as a decision aid in medical decision making[4]. As the need for this type of analysis grows, so does the need grow for alternative approaches to fit unique problem situations. This is particularly true for capital investment decision making. In surveying the cost/benefit literature pertaining to this area, it appears that most analyses can be grouped at one end or the other of the following continuum: Subjectively
Objectively <
Derived Analysis
> Derived Analysis.
The subjective end of the continuum represents a more theoretical or non-economic approach to cost/benefit analysis. This type of analysis is usually based on subjective input, such as opinions or judged data as opposed to empirical data[2-41. The objective end of the continuum represents an economic approach to cost/benefit analysis. This type of analysis is based on objective input, such as cost, usually in terms of dollars, units of time or labor, and benefits, usually in terms of revenue dollars of profit[l, 51. Unfortunately, many capital investment decisions in the medical area are arrived at by objective or economic criteria, and relevant subjective or non-economic criteria are considered secondary to the decision process. Thus, relevant non-economic criteria are not directly used in the actual decision. What is called for is a procedure that will combine the economic and non-economic decision making criteria into one over-all measure of cost/benefit effectiveness. The purpose of this paper, then, is to demonstrate how economic and non-economic decision criteria can be combined to provide a more precise measure of net-
benefits. In the process of achieving this objective, this paper will: (1) Illustrate the use of the Monte Carlo simulation method to aid in assessing the economic decision factors of a capital investment project under differing utilization rates. (2) Illustrate the use of rankings as a means of quantifying non-economic decision factors. (3) Illustrate how the economic and non-economic decision criteria can be combined via mathematically derived multipliers. This paper will not only describe the methodological procedure, but also provide an application of the procedure for a medical decision making capital investment problem. Specifically, a cost/benefit analysis of both economic and non-economic factors will be performed in an effort to evaluate which of three pieces of equipment (i.e. Nuclear Stethoscope, Mobile Camera/Computer, and Fixed Cardiac Computer) a hospital should purchase under differing rates of utilization. METHODOLOGY
The cost/benefit analysis procedure proposed in this paper requires three steps. The first step involves the analysis of economic factors via a Monte Carlo simulation. The second step involves a subjective ranking of non-economic factors. The third step involves the combination of the results obtained in steps one and two via the use of mathematical multipliers. Each of these three steps will be described as they relate to the hospital equipment decision problem. Step 1
The Monte Carlo simulation technique allows the recognition of stochastic economic behavior in modeling a problem situation. It will be assumed the reader is familiar with the basic procedure and application of this operations research technique. Generally, to perform this 177
E. V. KOTLYAROV and M. J. SCHNIEDERJANS
178
step, a decision maker must first identify the economic costs and benefits. For those costs and benefits that are variable, probability distributions based on that variable’s mean and standard deviation are developed. These distributions are then used as sampling distributions from which random samples of costs and benefits are selected. Having selected a specific set of cost/benefit values, a value for net-benefit (or net-cost) can be calculated under differing conditions as defined by the problem situation. It should be mentioned as a limitation on this step that if all of the costs or benefits are static the solution is deterministic and not stochastic. As such, the Monte Carlo simulation technique would not be applicable. For the specific hospital equipment problem, the economic costs and benefits need to be identified. The economic cost of the equipment falls into four categories: Labor, Supplies, Amortization, and Maintenance. The economic benefit of the equipment is the patient reimbursement for the service performed using the equipment. To determine the costs, a survey of eleven midwestern hospitals who utilize the equipment was conducted. From these responding hospitals, three used the Nuclear Stethoscope, four used a Mobile Camera/Computer, and four used a Fixed Cardiac Computer. Economic cost and benefit information was collected and is presented in Table 1. As can be seen on Table 1, each of the five types of economic factors have both a mean and standard deviation per subject examined from which a probability distribution is made up. The goal here is to model the net reimbursement or operating profilt. That is, if you subtract from the reimbursement the labor, supplies, amortization, and maintenance costs, you arrive at the net reimbursement or the net economic benefit (or loss) from purchasing and operating this particular piece of equipment. Having developed the probability distributions, the differing conditions under which the simulation model is to run needs to be stated. From the comments provided by the hospital survey, it appears three distinct utilization rates are most commonly used by the hospitals. The weekly utilization rates most commonly stated in the survey are five subjects per week, ten subjects per week, and fifteen subjects per week. Since the amortization and maintenance costs are a function of equipment utilization, these variables will be affected by the differing utilization rates.
To perform the actual simulation, a F.ORTRAN IV computer program was written and exercised on an IBM 370 at the University of Hawaii at Hilo. The simulation was designed to simulate the use of the three different types of equipment over a five year investment period under the three differing utilization rates mentioned above. This required nine separate computer runs to calculate the net-benefit (or loss) for each of the three pieces of equipment at the three differing utilization rates. Sfep 2 To generally evaluate non-economic factors, a number of techniques can be utilized. This paper recommends ranking as an efficient and effective means for evaluating non-economic factors. It is assumed the reader is familiar with ranking systems. In general, the non-economic costs and benefits need to be recognized. In many problem situations, a clear distinction between a factor being a “cost” or “benefit” is achieved by the ranking itself. Once the categories of costs and benefits are defined, a ranking system also needs to be defined. This system will usually be based on the number of alternatives being evaluated with the rank of “one” representing the most preferred alternative, rankings and subsequent representing subsequently less preferred alternatives. The rankings obtained can be used individually or as groups in assessing the differences in the alternatives for each category of non-economic factors being evaluated. Having determined the rankings by each alternative for each non-economic factor, a relative index can be developed by simply adding the ranks by alternatives and dividing the largest sum of the ranks into the sum of the ranks for the other alternatives. This relative index indicates the preference of the individuals who provided the rankings. Simply, the alternative with the smallest index is the preferred alternative based on non-economic factors chosen. In the hospital equipment problem addressed by this paper, five categories of non-economic factors were selected for comparison. These categories are: Patient Accessibility to Each Type of Equipment, Patient Flow In/Out, Flexibility of Application (e.g. clinical), Complexity in Usage, and Machine Set-Up Inconvenience. These categories were obtained from the hospital survey previously mentioned and represent the five most corn
Table 1. Economics factors* Mobile Camera/
costs/s Scp@les
6.37 17.37
Amorlization*i Maintenance**'
10.12 1.67
L.%b<,I
-
I.93 5.01 2.74 .6C
11.05 18.05 42.56 18.62
2.00
3.15 5.60 2. 0
Fixed Ce.rci!ac
11.75 18.05 38.58 20.30
1.50 3.00 4.65 2.30
*These average values were calculated from a sample survey of eleven hospitals that utilize this type of equipment. **Based on an average cost of $26,310.0c; $110,650.0c a five year period at ten subjects per week
ard $100,300.00 over
***Based cn ter subjects per week and an annual yearly maintenance cost of $800.00; $8,900.00 and $9,700.00, rapectiv+Ay, with a forecasted 796compounded increase starting in the third year. The resulting average yearly maintwance cost for the three types of equipment are $870.38; $9,681.10 and $10.553.49, respectively.
179
Cost/benefit analysis and capital investment decisions
Table 2. Non-economicfactors
-
___I--category
Mobile Camera/ Computer
Fixed Cardiac Computer
27
10
24 9
17 14
18
Patient Accessibility Patient Flow Flexibility of Applictmn Complexity in &.3ge Set-& Inccnvtrierce _.__ TOTAL
26
Pelative Index
130
Fmfit
I.
Iqultlpller
Sumof the Ranks (n=9\
NUClt?ZZ Stethoscope
14
11
26 20
9:
a4
89
a6 (a/97)
(9?/97)
GO( lGO/LOO(”1.16
monly suggested non-economic criteria for use in making a decision in the eleven hospitals surveyed. A second survey was conducted by phone of nine physicians who utilized or had some knowledge of all three alternative pieces of equipment. Each physician was asked to rank (where 1 = most preferred and 3 = least preferred) the three alternative pieces of equipment for each of the five categories. The results of these rankings is presented on Table 2. Adding the rankings by column (or alternative), they can be converted into a relative index. Step 3 Step 3 involves the combining of the economic results found in Step 1 with the non-economic results analyzed in Step 2. This is accomplished by converting the relative index measure computed in Step 2 into a profilt multiplier. The profit multiplier is simply the reciprocal of the decimal value equivalent of the relative index. Once the profit multiplier is derived, it is then used as an adjustment to the economic net-benefit or profit. The adjustment is achieved by multiplying the net-benefit or profit by the profit multiplier. The result will cause an increasing adjustment in net-benefit for those capital investment alternatives that were highly ranked in the non-economic analysis. It should also be mentioned that the adjusted net-benefit figure can only be used for comparative purposes and has no specific economic value. Also, if the net-benefit is negative (a loss situation) the adjustment can still be made, but does not require the profit multiplier. Instead, the decimal equivalent of the relative index and the net loss are multiplied. thus reducing the amount of the net loss. For the hospital equipment problem situation, the profit multipliers are given at the bottom of Table 2. In interpretting the meaning of the multipliers, it is clear that the net reimbursement or profit for the Mobile Camera/Computer and the Fixed Cardiac Computer will be increased by sixteen and seven per cent, respectively. RESULTS In addition to performing the required analysis in Step 1, validity tests were conducted on the Monte Carlo
92 (89/97)
(1~0,:&'6) 1.07
(lOC/92\
simulation results. Chi-square goodness-of-fit tests were used to compare input and output probability distribution similarity. Five chi-square tests were conducted for each of the nine simulation runs, and the results showed no significant difference (p > 0.001) between the hypothetical economic cost/benefit distributions input and the resulting distributions tallied in the output. Similarly, one-way analysis of variance tests were conducted for each of the nine simulation runs, and the results showed no significant difference (p >O.Ol) between the input mean cost/benefit values and the resulting tallied mean values in the output. It was concluded from these statistical tests and several others, that the simulation model validly assessed the economic factors for the cost/benefit analysis. The results of the simulation are summarized in Table 3. As can be seen, nine to total net reimbursement or profit figures are presented. These figures represent the summation of all the profit for each peice of equipment over the five year period of investment that will be achieved (on the average). These nrofit figures are also broken down by the rate of equipment utilization (i.e. five, ten, and fifteen subjects per week). Interpretting the results of the economic net-benefit presented in Table 3 is very simple. Regardless of equipment utilization, the Nuclear Stethoscope is clearly the best choice for the hospital. This choice is particularly true as the rate of utilization drops. The results of Step 2 are necessarily given in Table 2. They are described in the Methodology section of this paper. Step 3 involves the adjustment of the simulated netbenefit figures on Table 3 by use of the profit multipliers. These adjusted figures are presented in Table 4. CONCLUSIONS As can be seen on Table 4, the resulting combined net-benefit figures indicate that the level of equipment utilization does have an effect on the net-benefit of capital investments. Specifically, a medical decision maker would select the Mobile Camera/Computer over the Nuclear Stethoscope when the number of subjects utilizing the equipment per week is fifteen or above. At
Table 3. Simulated total net reimbursement Equipment Utilization Rate (S/W)
12
19 23
NUCl&3,7Y Stethoscope ($J
over a five year period
Mobile Camera/ computer ($j
Fixed Cardiac computer ($)
Five
110,312
Tt?n
248,842
184,948
185,634
Fifteen
391,525
381,6h2
355,744
12,297
17,831
180
E. V. K~LYAROV and M. 3. SCHNIE~ERJA~S Table 4. Combined economic and non-economic Equipmert Utilizstio~ Rate (S/W)
net benefit
NUClS3X Mobile Camera/ Stethoscope ($‘I Computer ($I
14,265
Fjxed Cardiac Corrputtr($1
19,o79
Five
118,312
Ten
246,WZ
214,*0
198,528
Fifteen
391,525
442 I705
380,
rates of equipment utilization, the Nuclear Stethoscope would still be used. but at higher rates of utilization, it appears that the Mobile Camera/Computer is preferred. Thus, it can be concluded that not only can economic and non-economic factors be combined into a ~ost/benefit measure for decision making, but also the product of the two analyses can result in differing conclusions. It should also be noted that the actual utilization rate, whereby the Mobile Camera/Computer has an adjusted net-benefit greater than the Nuclear Stethoscope, is between ten and fifteen subjects per week. Thus, hospitals which are facing this capital investment situation and have a mean utilization rate between ten and fifteen subjects per week might want to duplicate this study using rates between ten and fifteen to determine the exact break-even point. It can also be concluded that the Fixed Cardiac Computer will become a preferable choice to the Nuclear Stethoscope at utilization rates slightly higher than fifteen subjects per week. This can be easily forecasted by the observable difference in the rate of increase in adjusted net-benefits between the two pieces of equipment.
&6
SUNNY
lower
This paper demonstrates the use of the Monte Carlo simulation technique and a ranking procedure as a means by which economic and non-economic cost/benefit factors can be combined to generate a single measure of net-benefit. The three step cost/benefit procedure proposed is illustrated by an actual hosFLta1capital investment problem. This problem compares the cost and benefits between three alternative pieces of equipment: the Nuclear Stethoscope, Mobile Camera/Computer, and the Fixed Cardiac Computer. The results of the study show the combined netbenefit dictates that the investment decision is a function of equipment utilization. 1. L G. Anderson
REFERENCES and R F. Settle. Benefit-Cosf Analysis: A
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