Socio-Economic Planning Sciences 41 (2007) 130–146 A decision support system to improve the efficiency of resource allocation in healthcare management Emel Aktas - a , Fu¨sun U ¨ lengin b, ,S - ule O ¨ nsel S - ahin b a Istanbul Technical University, Faculty of Management, Industrial Engineering Department, Macka, 34357 Istanbul, Turkey b Dogus University, Engineering Faculty, Industrial Engineering Department, 34722 Kadikoy, Istanbul, Turkey Available online 20 December 2005 Abstract Limitations in healthcare funding require hospitals to find more effective ways to utilize resources. An effective patient management system is critically dependent on the accurate analysis of individual patient outcomes and resource utilization. In the current paper, a management-oriented decision support model is thus proposed to assist health system managers in improving the efficiency of their systems. In the first stage of the model, the key variables affecting system efficiency, as well as their causal relationships, are identified through causal maps. Efficiency is measured by the total time spent in the system. In the second stage, a Bayesian Belief Network (BBN) is employed to represent both the conditional dependencies and uncertainties of the key variables. In the third stage, a sensitivity analysis is performed using a BBN to determine the most critical variable(s) in terms of impact on the system. Finally, strategies to improve system efficiency are proposed. The suggested decision support system is applied to the tomography section in the radiology department of a private hospital in Turkey. r 2005 Elsevier Ltd. All rights reserved. Keywords: Healthcare management; Decision support system; Bayesian belief network 1. Introduction Effective utilization of limited resources is a vital problem for healthcare management [1,2]. The scarcity of healthcare resources is particularly important in developing countries where poor health conditions is one of the most important obstacles in the fight for economic development and welfare [3]. However, healthcare systems are complex and depend on a variety of economic, structural, and organizational factors, and their interdependencies. For example, a change in a clinical action may affect treatment cost, while a change in activity scheduling may influence treatment procedure. Additionally, many of the factors that influence healthcare system efficiency are uncertain. In order to increase such efficiency, we thus seek insight into the system by highlighting its most critical variables [4]. Although, efficiency is often measured by the cost of providing a given level of service, generally, quality of service and the desire to not wait in queues are of critical importance to the users of health services [5,6]. In this ARTICLE IN PRESS www.elsevier.com/locate/seps 0038-0121/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.seps.2005.10.008 Corresponding author. Fax: +902122407260. E-mail address: [email protected] (F. U ¨ lengin).
Limitations in healthcare funding require hospitals to find more effective ways to utilize resources. An effective patient
management system is critically dependent on the accurate analysis of individual patient outcomes and resource utilization.
In the current paper, a management-oriented decision support model is thus proposed to assist health system managers in
improving the efficiency of their systems. In the first stage of the model, the key variables affecting system efficiency, as well
as their causal relationships, are identified through causal maps. Efficiency is measured by the total time spent in the
system. In the second stage, a Bayesian Belief Network (BBN) is employed to represent both the conditional dependencies
and uncertainties of the key variables. In the third stage, a sensitivity analysis is performed using a BBN to determine the
most critical variable(s) in terms of impact on the system. Finally, strategies to improve system efficiency are proposed. The
suggested decision support system is applied to the tomography section in the radiology department of a private hospital in
Turkey.
r 2005 Elsevier Ltd. All rights reserved.
Keywords: Healthcare management; Decision support system; Bayesian belief network
1. Introduction
Effective utilization of limited resources is a vital problem for healthcare management [1,2]. The scarcity ofhealthcare resources is particularly important in developing countries where poor health conditions is one ofthe most important obstacles in the fight for economic development and welfare [3]. However, healthcaresystems are complex and depend on a variety of economic, structural, and organizational factors, and theirinterdependencies. For example, a change in a clinical action may affect treatment cost, while a change inactivity scheduling may influence treatment procedure.
Additionally, many of the factors that influence healthcare system efficiency are uncertain. In order toincrease such efficiency, we thus seek insight into the system by highlighting its most critical variables [4].
Although, efficiency is often measured by the cost of providing a given level of service, generally, quality ofservice and the desire to not wait in queues are of critical importance to the users of health services [5,6]. In this
e front matter r 2005 Elsevier Ltd. All rights reserved.
ARTICLE IN PRESSE. Aktas- et al. / Socio-Economic Planning Sciences 41 (2007) 130–146 131
paper, efficiency is thus measured by the total time spent in the system. In fact, length of stay (LOS) inhospitals is a challenging task and essential to operational success in terms of reducing costs while maintaininghigh quality of care [2].
Having to wait is caused by a scarcity of resources while more effective use of existing resources can helpreduce LOS in the system.
This paper thus aims:
1.
To provide insight into the complexity of the healthcare system by analyzing interactions of key variablesaffecting time spent in the system.
2.
To provide a useful guide for healthcare managers in improving the efficiency of their systems by evaluatingthe consequences of selected strategies.
To these ends, we propose a management-oriented decision support system (DSS) based on (for reasons notedbelow) a Bayesian Belief Network (BBN). In the first stage, the key variables affecting system efficiency areidentified and their causal relationships revealed through causal maps.
In the second stage, a BBN is used to represent the conditional dependencies as well as the uncertainties ofthese variables. In the third stage, a sensitivity analysis is performed using the BBN to determine impacts ofthe most critical variables affecting system efficiency. The proposed model is then applied to the case of atomography section in the radiology department of a private hospital in Turkey.
In the following section, a literature review helps identify basic advantages of the proposed DSS model.Section 3 discusses major stages of the proposed model in some detail. Results of the model application to ourcase study facility are given in the fourth section, where important strategies are revealed through selectedanalyses of earlier results. Finally, conclusions and suggestions for further research are presented to generalizeuse of the proposed model on a nationwide basis.
2. State of the art
2.1. General considerations
The approaches available to evaluate the efficiency of resource utilization in a healthcare facility are varied[7]. If the interaction effects of multiple variables on resource requirements are to be investigated, a simulationmodel is generally seen as desirable [8]. Simulation may be used to mimic the behavior of a healthcare systemin order to evaluate its performance and analyze the outcomes of various scenarios [9]. For example,simulation-based applications are well-suited to estimate and evaluate the potential effects of changes to afacility’s environment [6].
There has been substantial research using discrete event simulation to describe and analyze the behavior ofhealthcare systems, e.g., asking what-if questions in providing guidance for the design of management policies.In [10] and [11], such simulation was used to analyze waiting lists and resource utilization in a hospital. Cote[6], for example, considered the relationship between examining room capacity and patient flow across fourclinic-based performance measures. Blake and Carter [12] investigated the impact of surgical schedule onresources throughout the hospital. Zaki et al. [2] developed a simulation model which is easy to understandand employ by system administrators in the allocation and management of resources for emergency services.
Another approach to evaluating the efficiency of resource utilization in healthcare systems involvesmathematical optimization models [40]. These explicitly represent the functioning of the system, generallyresulting in large linear/nonlinear and integer models with significant numbers of variables and constraints[13,14]. Optimization applications in health care address a variety of issues such as the efficient use ofresources [15], the cost-effectiveness of selected interventions [15,16], portfolio analysis for policy/decision-making [17], and nursing home and hospital in-patient expenditures on heart failure [18].
A significant number of papers involving the optimization of healthcare management activities deal witheconomic aspects of the subject. Ferri et al. [19], for example, discuss selected issues of healthcare resourceallocation in developing countries. They propose an object-oriented system, and illustrate its implemented
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prototype. Bretthauera and Shetty [20] present a survey of algorithms and applications for the nonlinearknapsack problem, including those in health care.
De Angelis et al. [1] present a model combining simulation and optimization for healthcare management. Intheir formulation, the manager can evaluate the budget against average time spent by users in decidingwhether a budget increase should be pursued to keep system performance at a given level.
Data envelopment analysis (DEA) has been used to investigate the technical efficiency of healthcareresource use among OECD (Organization for Economic Co-operation and Development) countries [21]. DEAwas also used to investigate the efficiency of a set of small-scale hospitals in Greece [22]. In another study,nonparametric DEA was employed to document empirical evidence on the relationship between hospitalownership and operating efficiency in Taiwan [5].
A few attempts have also been made to use neural networks to predict patient LOS [e.g., 2,23 and 24].Morrison et al. offer a prediction model of the total treatment cost for a patient using artificial neuralnetworks (ANNs). They also contrast results from using both ANNs and traditional regression analysis [25].
2.2. Stochastic considerations
Healthcare management systems are complex networks involving a variety of factors that influence theirefficiency. Additionally, the factors may be uncertain, and the information incomplete. According to Srinivasand Shekar [26], due to the stochastic nature of factors that influence the performance of healthcare systems,uncertainty-based networks may be more suitable for purposes of representation and analysis.
Among such networks, BBNs influence diagrams, and qualitative probabilistic networks constitute some ofthe more prominent formalisms found in applied research. In medical informatics and other domains, forexample, BBNs and influence diagrams are efficient tools that have been used for knowledge representationand decision analysis under uncertainty [27]. BBNs, in particular, have been widely used in probabilisticreasoning. The formalism of BBNs is generally considered an intuitively appealing and powerful element forcapturing the knowledge of a complex problem domain that includes uncertainties [28]. Using BBNs, theimpact(s) of a number of potential actions, or combination of actions, can be effectively simulated with anyuncertainties explicitly represented.
Thus far, BBNs have apparently been used only in medicine to assist in the diagnosis of disorders, and topredict the natural course of disease following treatment [29]. Although it has become clear that managers, aswell as physicians, can benefit from the advantages of BBNs, attempts to apply the approach to healthcaremanagement scenarios remain in the early stages of research and thus require further investigation [13].
A possible reason for why BBN applications in management-oriented medical domains have lagged behindtheir use in diagnosis and follow-up type analyses is the difficulty of determining which variables are truly themost relevant/impacting. In particular, using experts’ judgments would seem critical in helping identify thosevariables that could, in any way, contribute to total LOS and to specifying cause and effect relationshipsamong the factors.
Causal maps are considered useful in constructing BBNs in that they are better able to capture expertknowledge that is particularly important within the context of decision-making [30].
In general, the relations represented in a BBN do not have to be causal. Thus, where the dependencerelations are causal, BBNs may also be referred to as causal belief networks, causal probabilistic networks, etc.
The research reported herein attempts to reduce problems encountered in specifying both the key variablesand their causal relationships by initially using causal maps in the problem structuring phase. A management-oriented decision support model, based on BBNs, is then constructed to provide dynamic representation of thevariables, and to introduce learning about any causal relations impacting the making of complex decisions.
Developed as such, and as noted below, the proposed model is expected to provide important assistance tohealthcare managers in their attempt to improve efficiency in the delivery of healthcare services.
3. The proposed model
The proposed decision support model has three stages. The first is concerned with knowledge acquisitionand problem structuring, during which the basic/key variables of the system to be modeled are identified
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through causal maps. In the second stage, a BBN representing the system variables and their interactions isconstructed under the supervision of available domain experts. The developed BBN represents conditionaldependencies between/amongst those variables affecting total time spent in the system, and thus provides aframework for representing the uncertainty of variables in the map. In the third stage, a sensitivity analysis isconducted using the BBN to determine the impact of those variable(s) considered critical to systemperformance. Finally, based on an analysis and evaluation of the BBN, strategies for improvement areproposed to the decision-maker.
The detailed framework of the proposed decision support model is given in Fig. 1.
3.1. Knowledge acquisition and problem structuring using causal maps
In the first stage of the proposed model, in order to capture knowledge expertise and assumptions about thesystem, and to better understand the system’s behavior, we employ a causal map. Such maps represent domainknowledge in the form of directed cause–effect relationships between variables. Since they do so moreeffectively than alternative models such as regression and structural equations, we consider them more usefuldecision tools within the current context [31].
There are three components of a causal map: nodes representing causal concepts, links representing causalconnections among causal concepts, and strengths representing causal value of a causal connection. Different
Step 2: Conversion of causal map to BBN -Elimination of loops -Variable states -Conditional probabilities
Validation Does the BBN
represent reality correctly?
Redesign according to experts’ opinion
Sensitivity analysis
Strategy suggestions for health care managers.
Yes
No
Survey- Previous data - Current situation - System variables
Resolve differences of opinions - Final causal map
No
Yes
Redesign according to experts’ opinion
Fig. 1. Framework of the proposed methodology.
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methods are used to construct causal maps, depending on the purpose and theory guiding the research.Thus, the self-Q method is designed especially for minimal intrusion and maximal disclosure ofnodes, links and loops [32]. Axelrod [33] devised a mapping technique to represent the causal assertionsembedded in decision-makers’ argumentations about policy- and the decision-making environment. Inanother approach, proposed by Eden and Ackermann [34], a deliberately open structure is used forinterviewing.
3.1.1. Specification of the basic variables
In the proposed model, Axelrod’s sense of mapping is regarded as suitable [33]. Mapping in Axelrod’s senseis designed to be a systematic, reliable way of measuring and analyzing the structure of an entire argument, notjust its separate parts [33]. The purpose of this type of unstructured approach is to inductively explore a new orunfamiliar domain by posing questions such as: ‘‘What are the concepts relevant to the decision?’’ [30]. Theunstructured approach yields a richer understanding of those processes individuals engage in during decision-making, while gathering important insights into the general knowledge they possess regarding the domainbeing evaluated.
In order to obtain a mutually exclusive and selectively exhaustive list of basic variables from the causal map,interviews are conducted with insider domain experts. The experts are encouraged to identify concepts thatmight be relevant to the decision. This process is continued until a comprehensive and exhaustive list ofconcepts is generated.
3.1.2. Determination of the causal relationships
Once variables related to the problem of interest are specified, a second interview should be heldwith experts to help reveal key causal relationships within the system. The experts will compare theconcepts in a pairwise matrix wherein the rows represent causes and the columns effects. They specify whetherthe relation between each pair was ‘‘positive’’, ‘‘negative’’ or ‘‘zero (no relation)’’. A ‘‘+,’’ ‘‘�,’’ or ‘‘0,’’respectively, is entered in each cell to specify the given relationship. In order to merge the group map fromthese notes, the union set of all concepts is used, thus capturing the various points of view. The resultingpairwise comparison matrix of the map can then be prepared by aggregating the relationships based onmajority rule.
As a result, a graph can be drawn where variables are represented by nodes, and the causal relationsbetween these variables represented by the arcs between the nodes.
3.2. Construction of the Bayesian Belief Network
In order to represent the dynamic nature of the causal relations, and to draw inferences based on theuncertainty concerning the states of the variables, a BBN will be used. In the BNN, variables of the system arerepresented by nodes, and the causal relations among the variables with arcs directed from the parent(affecting) variable to the child (affected) variable.
3.2.1. States of the variables
In order to construct a BBN, initially, a finite set of states is defined for each variable. This set represents thepossible behaviors that a variable can exhibit. Both historical data and the subjective evaluation of experts areneeded for this purpose.
3.2.2. Calculation of the conditional probabilities
A basic assumption of a BBN is that when the conditionals for each variable are multiplied, the jointprobability distribution for all variables in the network results. For example, suppose that variable A is seriallyconnected to variable C through variable B. The chain rule for BBNs then yields
PðA;B;CÞ ¼ PðAÞ � PðB\AÞ � PðC\BÞ.
ARTICLE IN PRESSE. Aktas- et al. / Socio-Economic Planning Sciences 41 (2007) 130–146 135
In theory, the posterior marginal probability of a variable can be computed from the joint probability bysumming all other variables one by one:
PðAijBÞ ¼PðAiÞPðBjAiÞ
PðA1ÞPðBjA1Þ þ � � � þ PðAnÞPðBjAnÞ
¼PðAiÞPðBjAiÞPni¼1PðAiÞPðBjAiÞ
.
Fig. 2 provides a simple example of Bayes’ rule.The example in Fig. 2 shows that if the time spent by a physician is short, and the time spent by a medical
secretary is long, then reporting will be short with 80% probability and medium with 20% probability.In practice, such an approach is not computationally tractable when there is an extensive number of
variables since the joint distribution will have an exponential number of states and values. Although BBNscreate an efficient language for building models of domains with inherent uncertainty, it may be timeconsuming to calculate conditional probabilities, even for a very simple BBN [35]. Fortunately, there areseveral commercial software tools such as Hugin [36] and Netica [37] that can perform this operation.
In the current research, Netica version 1.12 was used. It is a complete software package designed towork with BBNs, decision networks, and influence diagrams. In particular, it can be used to identifypatterns in data, create diagrams encoding knowledge or representing decision problems, and thenutilize those patterns to answer queries, find optimal decisions, and create probabilistic expert systems. It issuitable for application in the areas of diagnosis, prediction, decision analysis, sensor fusion, expert systembuilding, reliability analysis, probabilistic modeling, risk management, and selected types of statistical analysisand data mining [37].
3.3. Sensitivity analysis
Once the conditional probabilities of the states of each variable are calculated using the BBN, the next stageis to determine the relative importance of the variables in achieving the desired system output(s). In theproposed methodology, a sensitivity analysis is used for this purpose.
In general, sensitivity analysis is used to investigate the effect(s) of varying model inputs on a model’soutcome(s), where the inputs can be parameters or real inputs. The technique can be used to evaluate theimportance of inputs and/or possible inaccuracies in the model. Sensitivity analysis consists of answeringquestions such as ‘‘What are the crucial findings?’’; ‘‘What if one of the findings was changed or removed?’’ or‘‘What set of findings would be sufficient for the conclusion?’’ [35].
Reporting (R)
Time spent by physician (P)
Time spent by medical secretary (S)
P(R | P, S) Short Medium Short, Short 1 0 Short, Medium 0.9 0.1 Short, Long 0.8 0.2 Medium, Short 0.9 0.1 Medium, Medium 0.4 0.6 Medium, .Long 0.3 0.7 Long, Short 0.6 0.4 Long, Medium 0.5 0.5 Long, Long 0.2 0.8
P(P) Short Medium Long 0.428 0.359 0.213
P(S) Short Medium Long 0.4 0.4 0.2
Fig. 2. Example of Bayes’ rule.
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The most common form of analysis is to consider values of user selected observables, allowing distinctionbetween more and fewer important observables. Sensitivities related to observables allow for distinguishingbetween more and fewer important user inputs. The case where an important observable is associated with anode containing highly sensitive parameters should thus be classified as a critical point in the network [38].
Netica can perform extensive utility-free, single-finding sensitivity analysis by selecting a node (called the‘‘query node’’) and choosing ‘‘Network-Sensitivity to Findings’’ from the menu. A report displaying howmuch the beliefs, mean value, etc. of the query node could be influenced by a single finding at each of the othernodes in the network (each is called a ‘‘findings nodes’’) is given in the ‘‘Messages’’ window. The first part ofthis report has a section for each findings node, showing how much it can affect the query node using severaldifferent sensitivity measures. The second part provides a summary table that compares the sensitivities foreach of the findings nodes [37].
4. A case study in a private hospital
The proposed decision support model is now applied to the tomography section in the radiology departmentof a private hospital in Turkey [39], where the objective is to improve management system performance. Thehospital operates 42 branches, including clinical research, diagnostics, and outpatient and inpatient care, with279 expert physicians and 1038 healthcare and support staff. The facility has an ISO 9001 quality certificateand serves 162,423 polyclinic patients annually with a bed capacity of 210. A total of 36,000 radiological testsare conducted per annum.
4.1. Development of the causal map in the tomography section
4.1.1. Specification of the basic variables
Specification of the basic variables for the tomography section was carried out via interviews with theinsider domain experts as well as with data recently collected by the hospital’s quality improvementdepartment.
In order to specify the basic variables that influence (or are influenced by) the total time spent in the system,three experts, two doctors from the tomography section and the head of the Quality Department, were selectedas domain experts.
In the first series of interviews, experts were asked to specify the most critical variable(s) of the system aswell as the basic system variables affecting and/or affected by the critical variable(s). These initial interviewsshowed that, for the tomography section, the most important issue is time spent for scrutiny. When this time islonger than expected it can cause problems since the purchase and operating costs of the computedtomography (CT) machine are high. Further, long queues of waiting patients create dissatisfied customers,which is most undesirable to a private hospital enterprise.
The first column of Table 1 shows that the basic variables affecting time spent for scrutiny are type of
scrutiny (some types last very long); (behavior of the) patient (e.g., nervous patients cause the time spent for
scrutiny to last longer since, some such patients are less able to follow the technicians’ directives); technician (inthe radiology department, there are 20 technicians, six of whom are considered ‘‘primary’’); sometimes,technicians of other techniques such as magnetic resonance (MR) can be present and make the time spent forCT scrutiny last longer; and medical treatment. (Sometimes, CT scrutiny requires medical treatment, forexample, if a drug is taken before the scrutiny. In this case, time spent for scrutiny is increased.)
In the second column of Table 1, the states of these variables are given. The third column lists the datacollection methodology.
4.1.2. Determination of the causal relationships
Once the system variables are revealed, the experts are asked to compare them in a pairwise matrix and tospecify whether a positive, negative, or no relation exists between each pair of variables. The final mapstructure is obtained through several revisions based on feedback received from the experts.
During this stage, the experts were interviewed six times in order to ensure a stable final structure of themap. As noted earlier, the resulting pairwise comparison matrix was prepared by aggregating the relations
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Type of scrutiny
Time spent from arrival to scrutiny
Patient Re-imaging
Scrutiny
CT machine Suspicious findings
Reporting
Report typing
Doctor’s workload
Medical secretary’s workload
Delivery of report
to patient
Fig. 3. Preliminary causal map.
Table 1
Basic variables of the tomography section
Variable State Data collection
Time spent from arrival to scrutiny Short, medium, long Historical data
Type of scrutiny Thorax, cranial, whole abdomen, urinary Historical data
Patient Calm, nervous Expert knowledge
Technician Primer tomography technician (PTT), not PTT Expert knowledge
Time spent for scrutiny Short, medium, long Historical data
Medical treatment Present, absent Expert knowledge
Time spent by physician for scrutiny and report Short, medium, long Historical data
Time spent by medical secretary Short, medium, long Historical data
Reporting Short, medium Historical data
Report’s delivery to the patient Short, medium, long Historical data
E. Aktas- et al. / Socio-Economic Planning Sciences 41 (2007) 130–146 137
based on majority rule. Since the number of experts was odd (3), majority rule was used to address conflictingviews about the types of relations. A positive signed arrow was used if at least two of the experts suggested apositive relationship between two concepts. The resulting preliminary map is given in Fig. 3.
In the first few interviews, the experts were asked to specify those variables they saw as affecting thetomography system. The variables in Fig. 3 were thus revealed. The type of scrutiny affects the time spent from
arrival to scrutiny because selected preparations (e.g., drinking water, injection of medical liquids etc.) arenecessary for each type of scrutiny. Type of scrutiny also affects the scrutiny process as it determines the natureof the operation. Scrutiny process is also affected by time spent from arrival to scrutiny, patient, re-imaging,computed tomography (CT ) machine, and suspicious findings.
For some cases, medical treatment is necessary before scrutiny since treatment is thought to be partof time spent from arrival to scrutiny. When there is medical treatment, the scrutiny process lasts longer. Anychange in the position of the patient can put at risk success of the scrutiny. The process must then be repeatedto obtain clear and meaningful results. If the patient is nervous and/or changes his/her position unwillingly,then re-imaging (repeat the operation) must be done immediately. Thus, re-imaging affects the scrutinyprocess.
CT machine is the core of the scrutiny process; if it is out of order, then, no scrutiny can be done. Suspiciousfindings enter when such findings are made by the doctor. He/she may ask that scrutiny last longer in order toidentify the underlying phenomena. In terms of reporting, the doctor reads the results of the scrutiny to a taperecorder. This process is thus affected by the scrutiny process, by re-imaging (as it affects scrutiny), and bydoctor workload. If the doctor’s workload is high, then reporting may wait for his/her availability (not busy,or idle). Reporting affects report typing as this is done by a medical secretary. The medical secretary types
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what is recorded by the doctor about the patient’s CT process as well as key results. Like the doctor’sworkload, medical secretary’s workload also affects the report typing process. Finally, the doctor reads what istyped by the medical secretary and verifies that the content is correct. This is why the doctor’s workload alsoaffects delivery of the report to patient.
4.2. Construction of the Bayesian Belief Network
Drawing inferences about concepts in causal maps may be insufficient as they do not model any uncertaintyassociated with the decision variables. Further, the maps provide only a static representation of the decisionconcepts [31]. Since BBNs utilize a probabilistic approach in making inferences about the concepts, our secondstep involves conversion of the causal map into BBNs.
The existence of loops is an indicator of the dynamic structure of the map [34]. However, the circularrelationships, or loops, violate the acyclic structure that is required by a BBN. The loops may be due to codingmistakes that must be corrected, or they may represent dynamic relationships between concepts acrossmultiple time frames. In such cases, parts of the loop linkages pertain to a current time frame while othersrelate to some time frame in the future [30]. When this occurs, disaggregating the concepts into two timeframes can often solve the problem of circularity. Additionally, the loops can be eliminated if a distinction ismade between direct–indirect relationships. The experts should thus be informed that, if two concepts havereciprocal influences, then the one with the more dominant causal influence must be determined.
After additional interviews, the structure in Fig. 3 is modified to appear as in Fig. 4. A global variable(average time in system (by the patient)—(ATS)) is now defined; it is affected by all other variables in thesystem, directly or indirectly. ATS increases the doctor’s workload which, in turn, increases ATS; that is, aloop between ATS, reporting, and doctor’s workload. In this study, this loop problem is overcome with thefinal causal map. The structure is changed to that shown in Fig. 5.
In the final causal map, ATS was viewed as a variable that makes the system more complex. The expertssuggested that the critical variable here is the time spent for scrutiny since it is the core of the tomographyprocess. Further, the goals of the system are to examine as many patients as possible for economic/efficiencyreasons, and to enhance customer satisfaction.
Type of scrutiny
Time spent from arrival to scrutiny
Patient
Re-imaging
Scrutiny
Reporting
Report typing
Doctor’s workload
Medical secretary’s workload
Delivery of report
to patient
Average time spent in the
system
Fig. 4. Revised causal map.
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Type of scrutiny
Patient Technician
Time spent for scrutiny
Time spent from arrival to scrutiny
Medicine treatment
Time spent by physician for scrutiny and report
Report’s delivery to the patient
Reporting
Time spent by medical secretary
Fig. 5. Final causal map and BBN of the tomography section.
E. Aktas- et al. / Socio-Economic Planning Sciences 41 (2007) 130–146 139
Medical treatment was seen as a different variable since it has a direct impact on the time spent for scrutiny.The arc between time spent from arrival to scrutiny and time spent for scrutiny was thus removed. The patientvariable affects time spent for scrutiny because of the aforementioned reasons.
Reporting and report typing was combined under the variable reporting. It is not affected by workloads somuch as by time spent by the physician for scrutiny and reporting, and time spent by the medical secretary. Wealso chose to change the names of these variables because of the database created by the quality department.In that database, time spent by doctor and medical secretary is recorded. This final causal map was thenconverted to a BBN, as given in Fig. 5.
Initially, the states related to each variable were specified. Due to this circumstance, the database preparedby the hospital’s quality department was investigated early on. It contained 165 records from September 09,2002, to December 24, 2003. Some of the data were recorded when the patient entered the system, while otherinformation was obtained once the patient had been treated. As a result, it was possible to use historical datafor a good number of our variables: time spent from arrival to scrutiny, type of scrutiny, time spent forscrutiny, time spent by physician for scrutiny and report, time spent by medical secretary, reporting, andreport’s delivery to the patient.
Discretization of the variables was accomplished by taking into account breakpoints in the data (see Fig. 6).For those variables on which it was impossible to secure historical data, experts’ judgments were obtained
through a second series of interviews. The second and third columns of Table 1 summarize the possible statesof these variables, and how they were specified. Thus, for the variable labeled time spent from arrival to
scrutiny, the states are short (less than 30min), medium (between 30 and 90min), and long (more than 90min).Type of scrutiny and its states were determined using both the data set and experts’ knowledge. The most
common types of scrutiny in the tomography section are thorax, cranial, whole abdomen and urinary. Thesewere then set as the states of type of scrutiny.
The patient variable has two states: calm and nervous. These refer to the behavior of the patient duringscrutiny which, in fact, has a direct impact on time spent for scrutiny.
Technician has two states: primer tomography technician and not primer tomography technician.The time spent for scrutiny variable has three states, defined as: short (less than 10min), medium (between 10
and 20min), and long (more than 20min). The time spent by physician for analysis and report variable has threestates; namely, short (less than 10min), medium (between 10 and 20min), and long (more than 20min).
Medical treatment refers to the patient taking some medication before scrutiny, or not. It thus has twostates: present and absent. Time spent by physician for scrutiny and report has the states short (less than 10min),medium (between 10 and 20min), and long (more than 20min).
Time spent by medical secretary has three states: short (less than 10min), medium (between 10 and 20min),and long (more than 20min). Reporting has two states: short (up to 20min) and medium (between 20 and40min). Very rarely does reporting last more than 40min; hence, the long state, initially considered, was latereliminated (based on feedback from the experts).
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Fig. 6. Discretization of the variables.
E. Aktas- et al. / Socio-Economic Planning Sciences 41 (2007) 130–146140
For the variable known as report’s delivery to the patient, the three revealed states were short (less than halfan hour), medium (between half an hour and an hour), and long (more than an hour).
Note: States of the time-related variables differ due to their varying structural characteristics.
4.2.1. Calculation of the conditional probabilities
The final step in the development of our BBN for the tomography section involved calculation of theconditional probabilities. As was explained in Section 3.2.2, during this step, whenever a variable was found tobe affected by several others, joint probabilities were used to estimate the probabilities of its states.
As can be seen from Fig. 7, time spent for scrutiny is affected by the type of scrutiny, patient, technician, andmedicine treatment. In fact, there are 11 different types of scrutiny in the radiology department where theprimer tomography technician is involved 90% of the time while a technician of some other section (such asmammography) is involved the other 10% of the time. On the other hand, according to the experts’ opinions,95% of the patients are calm, while only 5% of them are nervous; further, a medical treatment is necessarybefore scrutiny 50% of the time.
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Fig. 7. Compiled BBN.
E. Aktas- et al. / Socio-Economic Planning Sciences 41 (2007) 130–146 141
Reporting is directly influenced by the time spent by physician and time spent by medical secretary. Alsobased on the experts’ opinions, the time spent by medical secretary is short 40% of the time, while theprobabilities of being medium and long are 40% and 20%, respectively.
Based on the above figures, the conditional probabilities of the various states for each variable werecomplied using Netica 1.12 (see Fig. 7). It can be seen that, based on a priori information, time spent for
scrutiny will be short with a probability of 42.7%, while its probabilities of being medium and long are 29.5%and 27.8%, respectively.
Obviously, the probabilities of affected states will change based on any additional information that becomesavailable over time, e.g., whenever type of scrutiny is known to be ‘‘whole abdomen.’’ In this situation, time
spent for scrutiny cannot be short, but it can be medium with 49.2% probability and long with 50.8%probability. Fig. 8 shows the compiled posterior probabilities based on this additional information.
Similarly, Fig. 9 shows how the probabilities would change based on additional information about medical
treatment. For example, when it is known that such treatment is not applied, the time spent for scrutiny will bemedium with 98.3% probability. Under these circumstances, there is clearly no chance that the time will beshort.
4.3. Sensitivity analysis
The developed BBN of the tomography section was used to analyze the complex conditional dependenciesamongst the system’s variables. The network’s visual characteristic allows easy what-if and sensitivity analysesby simply changing variable states and observing the automatically updated decision outcomes. In fact, ourdata analysis shows that time spent for scrutiny is longer than it is supposed to be, and is accepted, by theexperts to be the most critical variable in the system. Accordingly, a sensitivity analysis was done in order toidentify the relative importance of those variables affecting time spent for scrutiny.
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Fig. 8. The case where type of scrutiny is known.
E. Aktas- et al. / Socio-Economic Planning Sciences 41 (2007) 130–146142
This analysis considered the parent variables (type of scrutiny, patient, technician, and medical treatment) oftime spent for scrutiny using Netica. The value describing the degree of sensitivity of one node to another isgiven in the ‘‘Mutual Info’’ column of Table 2. For continuous nodes, or nodes with state values defined, thiscolumn corresponds to the variance reduction; otherwise, it represents entropy reduction. The ‘‘QuadraticScore’’ column is a measure of distance between target and approximations. Basically, the scoring reflects howmuch information is obtained from observing an event with probability (P). The more the information (andthe quadratic score of parent variables), the more sensitive the time spent for scrutiny to that variable.
The ‘‘Mutual Info’’ column of Table 2 shows how much the variable can affect the query node (time spent
for scrutiny here) using the mutual info sensitivity measure. The higher the mutual info sensitivity measure, themore effective the parent variable. The ‘‘Quadratic Score’’ column of Table 2 compares the sensitivities foreach of the findings nodes. For example, as can be seen from the table, time spent for scrutiny is most sensitiveto type of scrutiny, followed by medical treatment, patient and, finally, technician.
5. Conclusions and further suggestions
One of the basic problems of healthcare managers is making good decisions dealing with the pressures ofcost control while, at the same time, maintaining high-quality care. However, in healthcare managementjudgment often has to be made under incomplete or imprecise information.
The proposed DSS, which is based on the BBN, provides results that can be analyzed and interpreted byhealth managers without an operational research background. Using this methodology, a manager canevaluate the system under consideration, and specify the variables that have the greatest impact on the criticalvariable(s) of the system. Developed as such, the methodology can provide important guidelines on strategiesdesigned to make improvements in the critical variable(s), and on ways to use a limited budget to implementthese strategies.
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Fig. 9. The case where type of scrutiny and medicine treatment is known.
Table 2
Sensitivity of ‘‘time spent for scrutiny’’ based on findings at another node
Node Mutual ınfo Quadratic score
Type of scrutiny 0.67718 0.104473
Medicine treatment 0.33299 0.034178
Patient 0.01682 0.002208
Technician 0.00026 4.74E�05
E. Aktas- et al. / Socio-Economic Planning Sciences 41 (2007) 130–146 143
In fact, choosing one strategy over another is a difficult task for healthcare managers. This study does notclaim to prescribe a single best strategy; rather, it offers a picture of the current system and provides someinsights for managers into making choices about where they should allocate primary resources. Thosestrategies having the greatest weight will appear as those having the highest impact on the overall performanceof the critical variable(s) when used independently. The examples from the case study can provide a better,more practical understanding.
If, initially, the full picture of the system is taken into account, one of the biggest problems is found to beexcessive time spent for scrutiny. The hospital manager thus wishes the time spent for scrutiny variable to beshort 90% of the time due to the high cost of CT machines. However, based on a priori information, for a new/incoming patient, the probability of time spent for scrutiny being short was predicted to be 42.7% undercurrent circumstances (see Fig. 7).
If additional information was obtained for this (new) patient, it would then be possible to revise the stateprobabilities. For example, analysis shows that, if the new patient is to have a whole abdomen scrutiny, there isno chance of time spent for scrutiny to be short. Rather, it will be medium with probability 49.2%, and long
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Fig. 10. Target values for the parent variables of time spent for scrutiny.
E. Aktas- et al. / Socio-Economic Planning Sciences 41 (2007) 130–146144
with probability 50.8%. Similarly, if the patient were to have a urinary scrutiny, then time spent for scrutiny
would be short with probability 34.2%, medium with probability 15.8%, and long with probability 50%.Additionally, using a sensitivity analysis, suggestions to remedy the problem can be generated. For example,
in the case study, it can be seen that in the tomography section, time spent for scrutiny is most sensitive to type
of scrutiny. Therefore, different types of this service may be offered on different days. Thus, time spent for
scrutiny is especially long for whole abdomen scrutiny. As can be seen from Fig. 10, it is impossible to have ashort state for time spent for scrutiny variable if the type of scrutiny is whole abdomen. Therefore, it may bewise to propose different days of service for each scrutiny type unless there is an emergency. In fact, even aseparation of 1 day may be worthwhile.
Another improvement might involve separating the scrutiny according to the medical treatment since time
spent for scrutiny is sensitive to medical treatment in the second place. Therefore, it can be suggested toseparate scrutiny with and without medical treatment.
Although it is generally difficult to control the behaviors of patients, if they are informed about the scrutinyprocess beforehand, the process may become less problematic. Finally, we note that time spent for scrutiny isleast sensitive to the technician variable. Thus, any attempt to improve the technicians will likely not make anoticeable difference on the time spent for scrutiny variable.
The accuracy of our causal model may be improved by taking into account perspectives/preferences of thenurses, as well as those of the patients themselves, in addition to expert opinion. The proposed system should,therefore, incorporate multiple levels of detail and multiple decision-makers’ perspectives. On the other hand,the knowledge bases employed should be monitored so as to reflect the most up-to-date literature-based,practice-based, and patient-based research and practice.
In order to generalize use of the proposed model, future research may also investigate differences resultingfrom the use of local vs regional vs national data sources. In such situations, the proposed framework shouldact as a useful guide for policy-makers in developing strategies to improve the performance of selectedhealthcare systems, as well as in the allocation of scarce resources, subject to budget and other systempriorities.
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