an intelligent system for prioritisation of organ transplant patient waiting lists using

7/29/2019 An Intelligent System for Prioritisation of Organ Transplant Patient Waiting Lists Using

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An Intelligent System for Prioritisation of Organ Transplant Patient Waiting Lists Using

Fuzzy LogicAuthor(s): T. Perris and A. W. LabibReviewed work(s):Source: The Journal of the Operational Research Society, Vol. 55, No. 2, Part Special Issue:Intelligent Management Systems in Operations (Feb., 2004), pp. 103-115Published by: Palgrave Macmillan Journals on behalf of the Operational Research SocietyStable URL: http://www.jstor.org/stable/4101862 .

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Journal of the Operational Research Society (2004) 55, 103-115 ? 2004 OperationalResearchSocietyLtd.All rightsreserved.0160-5682/04 $25.00www.palgrave-journals.com/jors

An intelligent system for prioritisation of organtransplant patient waiting lists using fuzzy logicT Perris and AW Labib*Universityof Manchester Institute of Science and Technology (UMIST), Manchester, UKThe objective of this paper is to investigate the effectivenessof using fuzzy logic in a complex decision-makingcapacity, and in particular,for the prioritisationof kidney transplant recipients. Fuzzy logic is an extension toBoolean logic allowing an element to have degrees of true and false as opposed to being either 100% true or100%false. Thus, it can account for the 'shades of grey'found in manyreal-world ituations.In this paper,two fuzzylogic models are developed demonstrating ts effectivenessas a model for vastly improvingthe currentprioritisationsystem used in the UK and abroad. The first model converts an element of the current kidney transplantprioritisation system used in the UK into fuzzy logic. The result is an improvementto the currentsystem and ademonstration of fuzzy logic as an effective decision-making approach. The second model offers an alternativeprioritisationsystemto overcomethe limitationsof the currentsystemboth in the UK and abroad,as brought up byresearch reviewed in this paper. The current UK transplant prioritisation system, adapted in the first model,uses objectivecriteria(age of recipient,waitingtime, etc) as inputs into the decision-makingprocess.This alternativemodel takes advantageof the facilityfor infinitelyvaryinginputs into fuzzy logic and a systemis developedthat canhandle subjective(humanistic)criteria(pain level, quality of life, etc) that are key to arrivingat such importantdecisions. Furthermore, he model is highly flexibleallowing any number of criteria to be used and the individualcharacteristicsof each criterion to be altered. The resultis a model that utilises the scope of fuzzy logic's flexibility,usabilityand effectiveness n the field of decision-makingand a transplantprioritisationmethodvastlysuperior o theoriginal system, which is constrainedby its use of only objectivecriteria. The 'humanistic'model demonstrates heability of fuzzy logic to considersubjectiveand complex criteria.However,the criteriaused are not intended to beexhaustive. It is simplya templateto which medicalprofessionalscan apply limitless additional criteria.The model isproducedas an alternative o anycurrentnationalsystem.However,the model can also be used by individualhospitalsto decideinitiallywhethera patientshould be placedon the transplantor surgerywaitinglist. The model canbe furtheradaptedand usedfor the transplantof otherorgansor similardecisions n medicine.Concurrentlywiththe researchandworkcarriedout to developthe two models the investigation ocused on the constraintsof the currentsystemsused inthe UK and the US and the seemingly impossibledilemmasexperiencedby those having to make the prioritisationdecisions. By removing the parametersof objective-only inputs the 'humanistic' model eradicates the previouslimitationson decision-making.Journalof the OperationalResearchSociety (2004) 55, 103-115. doi:10.1057/palgrave.jors.2601552Keywords: uzzy logic;waitinglists; organ transplants;prioritisation

IntroductionWithin engineering, fuzzy logic has been used in manyindustries ranging from complex robotic control' to themore mundanetraffic ightcontrol.2Withinmanufacturing,fuzzy logic has been used in developing arc sensors3 andon a systems level is popular in failure mode and effectanalysis (FMEA).4 Fuzzy logic has been successfullyimplemented in many engineering applications includingthe recent work of Vanegas and Labib5'6 in engineeringdesign, and Sudiarso and Labib7 in maintenance and

productionschedulingas well as in intelligentmaintenancemodelling in Labib et al.8

Fuzzy logic is also becoming increasingly popular inmedicine for use in fields such as diagnosis,9 expert systems'0and monitoring." It is proposed that fuzzy logic's ability tomimic human thinking, in its ability to deal with bothqualitative and quantitative measures, lends itself perfectlyto decision-making situations, especially decisions as com-plex and sensitive as transplant prioritisation.

Kidney transplant operations have been available in theUK under the NHS for 40 years. In year 2000, about 1820kidney transplants took place, but at the end of the sameyear, 6284 patients were still awaiting a transplant. On anaverage, patients have to wait about 11 months for atransplant. Prioritisation decisions are therefore extremelysensitive. (Data from www.uktransplant.org.uk.)

*Correspondence.: W Labib, ManufacturingDivision, Department ofMechanical, Aerospace and ManufacturingEngineering, University ofManchesterInstituteof Science and Technology, (UMIST), PO Box 88,ManchesterM60 1QD, UK.E-mail: [email protected]

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104 Journalf heOperationalesearchocietyol. 5,No.The paper is structured as follows: the following sectionpresents the current UK transplant prioritisation system.Two models are then proposed by the authors in order toaddress deficiencies and challenges in the current system.Discussion of results are presented followed by a Conclusionsection.

Current UK transplant prioritisationsystemThe kidney waiting list prioritisation system is highlycomplex involving medical, social and political factors. Thedetailed prioritisation process is run and maintained by the'United Kingdom Transplant Support Service Authority'(UKTSSA)12 and can be found at the UK Transplant website (www.uktransplant.org.uk). Essentially, when a kidneybecomes available, potential recipients are assessed on theirsuitability for that kidney using the following criteria(Figure 1).The test results for a patient's compatibility of tissue typeresults in a 'perfect match', 'favourable match', 'non-favourable match' or 'no match'. The kidney is allocatedto the patient with the best match. Within each match, thekidney always goes to paediatrics before adults and then tothe patient in the same district as the donor before going onthe national list. In the event of equally matched patients atany level of the decision-making process (as is often the case)the scoring system as shown in Table 1 is used. (Each patientis evaluated on the six criteria and the kidney is allocated tothe person obtaining the highest score.)

Compatibilityf tissue ype

Perfectatch Favourableatch on-favourableatchNo atchP a e d i a t r i c a d u l t P a e d i a t r i c a d u l P a e d i a t r i c a d u l t

L o c a l n a t i o n a l L o c a l n a t i o n a l L o c a l n a t i o n a l

Figure 1 Currentprioritisationsystem.

Information obtained from the UK transplant web sitewww.uktransplant.org.uk. ransplantation s a modern daysuccessstory.Thedevelopmentsn this specialityof medicinein the last 50 yearshavebeenphenomenal,withthousandsofpatients benefitingfrom a successful transplant. But thissuccess has broughtnew problems.Waitinglists have grownsteadily, with an increasing number of patients beingconsidered suitable candidates for transplantation.At thesame time the numberof organs becoming available eachyearhas fallenas deaths from road traffic accidentsdecreaseand the techniques for managing critically ill patientsimprove. It is therefore mperativethat all available donororgans are allocated to recipients ensuring that the bestpossible outcomefor each is achievedfrom this scarce andpreciousresource.12The UKTSSA was established in 1991 to run and

maintain the whole transplant system. We have alreadyseen the system that is successfully implemented forthe prioritisation of kidney transplant waiting lists.The following discussion highlights the fact that thereare many variables that could be considered. It could beargued that the current system does not take these intoaccount.

Complications in the decisionIf it were up to you to choose who should be treated n thepublichealth servicehow would you decide?Wouldyou treatthe sickest first? The poorest? Young people before old?Perhaps you would hold a lottery to select patients- firstprize,a hearttransplant.13The above quote is a very cynical view of decisions thatare made in the health service; however, it throws up some

very important issues. How do you decide who shouldreceive treatment first and, perhaps more significantly, whoshould not receive treatment? These issues are no differentwith regard to transplant decisions. Initially, it may seemobvious that the youngest and sickest patient should receivethe available kidney. However, 'Sicker people are more likelyto die after their transplants, or to need 2nd and even 3rdtransplants'.14The kidney could have gone to somebody elsewith a much better chance of survival. In effect it has beenwasted.

Table 1 Currentpoint scoring systemFactor Scale Points available Whobenefits?Recipient age Old to young 1-10 Favours younger recipientsDonor/recipient age difference Large to small 1-10 Avoids large age differenceWaiting time Short to long 0.5-5 Favours longest waitingMatchability Easy to hard 1-10 Favours rarer HLA typesSensitisation High to low 0.5-3.5 Favours low sensitisation andavoids cross matchesBalance of exchange Low to high 1-10 Favours higher centre balanceTotal between and48.5points.



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TPerrisndAW abib-Prioritisationforganransplantatientaitingists 105The situation is furthercomplicatedwhen we introducemedical science. As we have seen, a kidney from donor torecipientcan be classifiedas a perfectmatch, a favourablematch or a non-favourable match. All situations havethepotential or successbut withvaryingdegrees.Currently,the kidney goes to the most favourable match. Again,

this seems a sensible decision. However, what if theclosest match is somebody with a non-life-threateningcondition and there is somebody else, weeks awayfrom death, whose match may be close but just not asclose. Thekidneywouldcurrentlybe allocatedto thepatientin less need. It would be more realisticto assessall criteriatogether.The point system (Table1) suggests hat waitingtime andsensitisationare less important han the other criteriawith amaximum of only 5 or 3.5 points achievable.Somethoughthas obviouslygone into theseweightingsbutjust how much?Are we to assume that recipient age, age difference,matchability and balance of exchange are exactly asimportantas eachother?Furthermore, o these six variablesconstitute an exhaustive ist of considerations n matters asimportantas kidneydonation?Thecurrent ystemcannot beassumed to be the best.Gordon'5 calls for the need to take 'sociocultural'factors into consideration such as the patients' lifestyleand pain level. 'Should those in more pain get highera consideration han those who aren't?'If so, should theystill get higher prioritisationif the tissue match is lessfavourable?The situation is complicated further still in Americawherea NationalHealth Service omparable o the UK doesnot exist. In this system, insurancecompanies and theirpolicies are a major factor. Finally, Ham'6 calls for morejustification of the decisions that are made in transplantwaitinglists.

Entry onto the waiting listJohnson et a1'7 looks at the problems associated withdeciding whether a patient should be added to thewaiting list or not. The paper looks at the UK system,which currentlyleaves the decision up to the individualdoctor and the patient. The doctor asks questions suchas would this person like a transplant?Is it possible?Would it seem reasonable to give them a chance? Thepaper calls for the need to take more explicit andquantitative criteria into consideration as the currentapproach 'may not make best use of a scarce nationalresource'such as kidneys.The systemused to prioritise hesewaiting ists must be asaccurate as possible due to the sensitivityof the decisions.What is the best systemand what criteriashould be takeninto consideration?Arethe systemscurrentlyused in the UKand abroad capable of taking into consideration more

criteria,and assess them at the same time, or do they havelimits?The problemsassociated with such decisions are highlycomplex and sensitive. At the end of the day, theseissues affect peoples lives, aiming to improve the qualityand/or the survival of that life. Dr Robert D Gibbons,from the University of Illinois in Chicago conducted ananalysis of approximately68 000 patients on the livertransplantwaiting ist between1995and 1999.He concluded'currentallocation policies fail to provide organs to theneediest patients'.18 The current prioritisation systemscould do better and an alternative s needed. This paperoffers two models using fuzzy logic with the flexibilityto include the more sensitive and humanistic criteriadiscussed above. Fuzzy logic has been chosen due to itscapabilityof dealingwith qualitativemeasures, he storageand provision of knowledge in the form of rule-baseand its decision support and visualisation capabilities.Neither model explores the full range of criteria thatshould be considered.They simply present the possibilityof using fuzzy logic in such a sensitive decision-makingsituation and offer an example of how other, morehumanistic criteria can be used. The result is a flexibletemplate by which medical professionalscan apply therelevant criteria based on medical researchand their ownknowledgeand experience.

The modelsModel one, simply applies fuzzy logic to the currentpointscoringsystem,demonstratingheeffectiveness f fuzzy logicin makingsuch decisions while improving he sensitivityofthe point scoring system.Model two utilises fuzzy logic's full potential bydemonstrating he applicationof humanisticcriteriato theprioritisationproblem.The models are only an exampleofwhat is possibleusing fuzzy ogic. Theyhave beendevelopedto allowprofessionals o adapt readily he actual criteriaandweightings of the criteria using knowledge from theirexperience.

Model One (fuzzy appliedto the currentsystem)By applying fuzzy logic to the current point scoringmechanism(Table 1), great advantagesare achieved andfuzzy logic's flexibilityand usabilityare well demonstrated.The rules devised in this model demonstrate an original,highly systematic process. The model is developed in anumberof stages.The model (Stage One)Membershipunctions: Each of the six attributes in thepoint scoring system is used as inputs into a fuzzy



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106 Journalf heOperationalesearchocietyol. 5,No.

system resulting in a single output function. Initially, allsix inputs are given two membership functions, eachwith the same characteristic (shape); this is shown inFigure 2 for the 'Age' input.Notice that the first membership unction (MF) in eachcase represents he favourable choice from the mechanism(Table 2). For example, the highest prioritywill go to therecipientwho is the youngest, with the least age differencebetweendonor and recipient,who has been on the waitinglist for the longest, with a difficultmatchabilityrating,lowsensitisation and from a region which has the highestbalance of exchange.The outputhas sevenMFs. The reasonfor this relates to the rule-makingprocedureand will beexplainedbelow.

Degreeof membership

Age

~ K:~C?

Figure 2 MFs for the age input.Table 2 MF names

Input MF1 MF2Age Young OldAge difference Small LargeWaiting ime Long ShortMatchability Hard EasySensitisation Low HighBalanceof exchange High Low

Rules: If an AND rule is made for every combinationof input MF then there will be 64 (26) rules. This willbecome clear. The system used for deciding the rules is asystematic seven-step procedure:

Step 1: The highest priority (top) is allocated when allinputs have the favourable MF. There is only onecombination in this scenario (number 1 represents thefavourable MF) (Table 3).So the rule is as follows:

IF (Age is Young) AND (Age Difference is Small) AND(Waiting Time is Long) AND (Matchability is Hard) AND(Sensitisation is Low) AND (Balance of Exchange is High)THEN (Output is Top).

Step 2: The next highest priority (very high) is allocatedwhen five of the six inputs have the favourable MF. Thereare six combinations in this scenario (number 0 representsthe unfavourable MF; these cells are highlighted to clearlydifferentiate them) (Table 4).Step 3.: The next highest priority (high) is allocated whenfour of the six inputs have the favourable MF. There are 15combinations in this scenario. MFs will be represented bytheir number only from now on (1 for favourable and or

unfavourable). Table 8 in the Appendix shows the high-priority permutations.

Step 4: The next highest priority (medium) is allocatedwhen three of the six inputs have the favourable MF. Thereare 20 combinations in this scenario. Table 9 in theAppendix shows the medium-priority permutations.

Step 5: The next highest priority (low) is allocated whentwo of the six inputs have the favourable MF. There are 15combinations in this scenario. Table 10 in the Appendixshows the loil'-prioritypermutations.Step 6.: The next highest priority (very low) is allocatedwhen one of the six inputs have the favourable MF. Thereare six combinations in this scenario. Table 11 in theAppendix shows the very-low'-prioritypermutations.

Table 3 Top-priority permutationsRule no. Age Age difference Waitingtime Matchability Sensitisation Balance of exchange Output (priority)1 Young (1) Small (1) Long (1) Hard (1) Low (1) High (1) Top

Table 4 Very-high-priority permutationsRule no. Age Age difference Waiting teatchabiitinge Matchaility Sensitatsation Balance of' exchange Output (priority)2 Young (1) Small (1) Long (1) Hard (1) Low (1) Low (0) Very high3 Young (1) Small (1) Long (1) Hard (1) High (0) High (1) Very high4 Young (1) Small (1) Long (1) Easy (0) Low (1) High (1) Very high5 Young (1) Small (1) Short (0) Hard (1) Low (1) High (1) Very high6 Young (1) Large (0) Long (1) Hard (1) Low (1) High (1) Very high7 Old (0) Small (1) Long (1) Hard (1) Low (1) High (1) Very high



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T PerrisndAW abib-Prioritisationforganransplantatientaitingists 107Bottom V.Low Low Med High V.High Top

Degreeofmembership

0 10 Output Priority)Figure3 Output MFs.

Table 5 MF weightingsInput Points acailable WeiqhtincjAge 10 1Age difference 10 1Waiting time 5 0.5Matchability 10 1Sensitisation 3.5 0.35Balance of exchange 10 1

Step 7: The next highest priority (bottom) is allocatedwhen none of the six inputs have the favourable ME. Thereis only one combination in this scenario. Table 12 in theAppendix shows the bottonm-priorityermutations.

The doctor will allocate points as normal to the sixinputs. The fuzzy system will manipulate the inputs toproduce a degree of membership for the output functionsresulting in a single output number representing thepriority number. As described by the rule devising systemabove, there are seven output MFs as shown in Figure 3.The output (priority) is given on a scale of 0-10 as canbe seen.

This concludes the first stage of the model. It is extremelysimplistic; there are only two MFs for each input, the shapesof every MF are the same and no weightings have been takeninto account. Subsequent stages in the model will deal withthese issues starting with the weightings.The model (Stage Two) - weightingsFor the moment we will just look at the weightings that havealready been applied to the current prioritisation system.Additional weightings will be discussed in subsequent stages.The weightings shown in Table 5 are currently used (takenfrom Table 1).Some of the inputs in the mechanism allow points to beallocated as low as 0.5, while others only allow points as lowas 1. One of the advantages of fuzzy logic is its acceptance ofdecimal numbers, that is, 7.5 would be an acceptable score.Therefore, this model allows points to be allocated as low asrequired (eg 0.1-9.9).

Every rule is initially given a weighting of 1 (Table 6).If a rule includes the favourable MF for 'Waiting Time'(ie 'High'), then the rule's weighting is multiplied by 0.5(the weighting for 'Waiting Time'). Similarly, if therule includes the favourable MEF for 'Sensitisation'(ie 'Low'), then 0.35 multiplies the rule's weighting. Forexample:

Rule 43.: IF (Age is Old) AND (Age Difference is Large)AND (Waiting Time is Short) AND (Matchability is Easy)AND (Sensitisation is Low) AND (Balance of Exchange isHigh) THEN (Output is Low) WEIGHTING=0.35(1 x 0.35).Rule 44. IF (Age is Old) AND (Age Difference isLarge) AND (Waiting Time is Short) AND (Matchabilityis Hard) AND (Sensitisation is High) AND (Balance ofExchange is High) THEN (Output is Low)WEIGHTING = 1.

Rule 45.: IF (Age is Old) AND (Age Difference is Large)AND (Waiting Time is Long) AND (Matchability is Easy)AND (Sensitisation is High) AND (Balance of Exchangeis High) THEN (Output is Low) WEIGHTING=0.5(1 x 0.5)If further research discovered that the weightings shouldbe altered, the model can easily be adjusted to cater for these

changes by adapting the rule weightings.Figures 4 and 5 show a sample of the surface views

developed. The surface views simply show a three dimen-sional representation of two of the inputs compared withthe output. Figure 4 (Age difference versus age) showsa moderately smooth surface model, this is representativeof the majority of the surfaces produced in this particularfuzzy model. Figure 5 (Weighting time versus sensitisation)has a slight bulge. This occurs when one or both ofthe inputs are weighted as both weighting time andsensitisation are.

The mnodelStmge Three) - MF shiapesThe model has chosen the shapes of the MFs arbitrarilyto prove the effectiveness of fuzzy logic in such situations.



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108 Journalf heOperationalesearchocietyol. 5,No.Table 6 Example of rules

Rule no. Age Age difference Waitingtime Matchability Sensitisation Balance of exchange Output (priority)43 0 0 0 0 1 1 Low44 0 0 0 1 0 1 Low45 0 0 1 0 0 1 Low

.. ? -'-- .___

264524

S 2..

..- . . .T .~?.:: _ "..:Cc(~ :...: : .... Y

~F.... ...A g e ~

?~D~'r -.,,. . ..,

R 2

loe1igure 4 Age differenceversus age surface model.

In reality, each of the six inputs to this priority decisionwill have different characteristics. For example, youmay want the age MF to favour any recipient under theage of 18 years equally. This would give the MF as shown inFigure 6.There are many ways that the shape can be changedto represent a particular characteristic. As doctorsbecome familiar with the technique, they will be able touse their judgement to alter the shapes accordingly.Alternatively, a medical professional may have a verygood idea of how he or she expects the decisions toaffect the outcome. Therefore, they will have a good ideaof how the surface model should look. MFs could bealtered appropriately in order to achieve the desired effect.This may involve an element of trial and error but withincreasing fuzzy experience the process would become moresystematic and accurate. Further examples of the effect ofshape changes can be seen in the second model. Withappropriate medical expertise and experience, the shapes ofall the MF can be adapted very easily to produce a moreaccurate decision-making model.

The model (Stage Four) - No. of MFsThe greater the number of labels (MFs) assigned to describean input variable, the higher the resolution of the resultantfuzzy control system, resulting in a smoother control system.However, it is unusual to have more than nine MFs.

Currently, each input has only two MFs. This is probablytoo low and does not allow for any great degree of resolutionor smoothness. In reality, one would hope for smoothersurface views. However, we already have 64 (26) rules. Thevalue 26 describes the number of combinations of two MFsin six inputs. If we were to slightly increase the number ofMFs to three per input, then we would have 36 (72 9) rules.Even then, the surface may not be as smooth as we wouldlike. Maybe six MFs would produce a better system;however, this would then require 66 (46 656) rules. This isan NP-hard problem.Implementing the modelMFs that model the real-life characteristics of the criteriaare set up by medical professionals with knowledge



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T PerrisndAW abib-Prioritisationforganransplantatientaitingists 109

30

24--

0.51.5 .

2 33.5 5

Figure 5 Waiting time versus sensitisation surface model.Young MiddleAged Old

Degree fMembership

18 AgeFigure 6 Effect of MF shapes.

and experience in the transplant field by adjusting therules, rule weightings and MF shapes. For each patient,the relevant information is then simply input into thesystem.

Model Two (the 'humanistic'fuzzy model)Belief or attitude emphasizingcommon human needs andseeking solely rational ways of solving human problems;system of thought concernedwith human matters... OxfordDictionarydefinitionof humanisticDoes the current system offer an exhaustive list ofinputs? In light of the many debates that occur in suchdecisions(someof which were discussedearlier) t seemsthatperhapsmore considerationscould be taken into account,in particularsocioculturalor humanistic elements.15 Thisis a purely scientific paper and despite the medical

researchcarried out it does not pretendto be an authorityon medical decisions. It is argued,however, that decisionsof such importance (somebody's life or death incertainsituations)should take into account morehumanisticissues.Currently,the criteria are purely objective considering

only real things that can be easily measured(age, waitingtime, etc). This section offers an alternative system thatconcentrates on the humanisticelements involved in suchdecisions. Fuzzy logic 'blurrs' input boundaries allowingsmooth transitionbetweenMFs. It also allowsevaluationofmultiple inputs.The fuzzy logic model has been designedwith the view toaid the decision-makingthat takes place to prioritisethekidney recipientwaiting list. When a kidney is donated, allthe patientsfor whom the kidney s suitableareanalysedandput throughthe program.The programasks the doctor toclassifycertainfactors,such as patients'pain level,and thenprovidesa prioritypercentageof how criticalthe need for akidneyis.CriteriaThree ssues(criteria) re looked at specifically;hese are'lifeexpectancy', pain level' and 'quality of life'. These criteriaare representative of some of the issues and debatespreviouslydiscussed.However, t is by no meansexhaustiveand many more will be added as a result of professionalinput.The modeldeveloped s only aimed at highlighting hepossibilityof such a model existingand working.



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110 Journalf heOperationalesearchocietyol. 5,No.Table 7 'Pain level' criteria

'Pain level' Best description o/fpatient10 Patient is in no pain9 Patient rarelysuffers from pain, but when they do it does not requiremedication8 Patient suffers from regular(daily) discomfort that does not requiremedication7 Patient is in constant discomfort, but not to the extent that it requiresmedication6 Patient occasionally (one to two times a week) experiencesdiscomfort that requires'over the counter' medication.5 Patient regularly(daily) requires'over the counter' medication.4 Patient constantly taking 'over the counter' medication.3 Patient occasionally (one to two times a week) experiences pain that requires prescriptionmedication.2 Patient requiringconstant doses of a mixture of prescriptionand non-prescriptionmedication.1 Patient regularly(daily) requires prescription strength medication.0 Patient is in constant pain that requires prescription strength medication to control.

Life ExpectancyV.Short Short Medium Long NotLifeThreatening

DegreeofMembership

2 LifeExpectancymonths)Figure 7 'Life expectancy' MFs.

Life expectancy.:Life expectancy is defined as the length oftime that the patient is expected to live, should a transplantbe unavailable.Pain level. A number between 0 and 10 is assignedindicating the amount of pain a patient is suffering. Number10 is no pain and 0 is excruciating. A doctor will assess thislevel. Table 7 shows possible criteria that could be used when

allocating a value. It should be noted that pain level does nothave to be an integer, allowing room for medical discretion.The aim is to make the determination of the amount of paina patient is in less subjective and therefore a crisp input tothe system.Quality of life: This indicates how much the quality of lifeof the patient would change if they received a kidney.The shape of the MFs controlling each input can be

changed to put more or less emphasis on any of these inputvariables. Much thought has been put into the shape of theMFs, but as this method is subjective, consultancy withexperts will be required to ensure that the functions chosenare appropriate. The shapes decided upon are describedbelow.

MFsThe shape of the MFs controlling the three inputs can bechanged to put more or less emphasis on any of the inputvariables.

The MFs are measured in months (Figure 7). The scopeof each MF increases as they move from 'very short' to'not life threatening'. (The shapes get bigger.) Thisimplies that changes in life expectancy become increasinglyinsignificant. For example, a difference of 1 month whena patient has 6 weeks to live has a far more drastic effectthan if life expectancy is 3 years. After 48 months, it isassumed that the condition of the patient is not lifethreatening.The trapezoidal shape of the 'very short' MF is important.This initial level platform lasts for 2 months. If the lifeexpectancy is within this time, it will belong to the 'veryshort' MF to a degree of 1. Therefore there is no distinctionbetween life expectancies of less than 2 months. The timeperiod during which it is level can be altered easily,demonstrating the flexibility of the program.Three membership functions are used, all being symme-trical about the centre. This allows smooth transitionbetween each of the MFs. The inputs were purposelysimplified in this way due to the subjective nature of pain(Figure 8). There are no rules stating how critical pain isother than 'humanistic' common sense. By leaving the MFslike this, it is left to the rules to portray a common senseapproach and attribute any exceptions to the current smoothnature of the input. Of course, any future research into painlevel may enable the MFs to be adapted. The model isflexible so as to allow for such improvements.



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TPerrisndAW abib-Prioritisationforganransplantatientaitingists 111Patientsrequirea kidneymoreurgently f theyarein greatpain than if they are only in some pain. Pain may bemeasuredon a scale of 1-10, and great painassigneda valueof 2 and below. Without fuzzy logic. a personwith a painlevel of 2 would have a much higher prioritythan a personwith 3 (all other things remainingthe same), although in

realitythey may actuallybe experiencingvery similarpain.This discrepancymay be further highlighted if different

Pain LevelGreatPain Some Pain No Pain

DegreeofMembership

Pain LevelFigure8 'Pain level' MFs.

Qualityof LifeVast Improvement Beneficial Change No Chanige

Degree ofMembership

Qualits of Life

Figure9 'Quality of life' MFs.

doctors are assessing the pain level. Fuzzy logic allowsblurringof theseboundariesenablinga smoothertransitionbetween two pain levels. Fuzzy logic also allows multipleinputs to be evaluatedsimultaneously.The MFs that determine the recipients' quality of life'havebeenspecifiedas havingthesameshapeas thoseusedin'painlevel'.The sameanalysiscan be made of 'qualityof life'as that of 'pain level' (Figure9).

RulesEverycombination of input functions was analysed usingonly AND commands, and an appropriatepriority level(very high, high,mediumand so on) was established.In thiscase the total numberof possiblerules is 45 (5 x 3 x 3). Thedecisions reached are subjectiveand open for change bymedical professionals. This model does not use thesystematicrule method as used in model one, insteadeachrule is analysed and devised separately.This benefits thesystem by giving it a humaninput.An exampleof the decisions reachedwhendevelopingtherules is describedfor the 'life expectancy'input. Here therules have been set to give the 'very short' MF overallpriority over the other inputs and MFs. A sample of therulesis shown in Figure 10. As can be seen, everyrule thathas 'life expectancy'set at 'very short' has the top output.Combined with the 'very short' MFs level platform(discussedabove), this means that if patientshave less than2 months to live, they get priorityover everythingelse. Thisisjust one exampleof how humandecisionscan influence herules.

33. IF(Life Expectancy s 'Short')and(Pain Level is 'Some Pain')and(Qualityof Life is 'Vast Improvement') hen (Priority sV.High)34. IF (Life Expectancy s 'Short')and (Pain Level is 'GreatPain') and (Quality of Life is 'No Change') then (Priority sHigh)35. IF(Life Expectancy s 'Short')and(Pain Level is 'GreatPain')and (Qualityof Life is 'Beneficial Change') then (Priority sV.High)36. IF(Life Expectancy s 'Short')and(PainLevel is 'GreatPain')and(Qualityof Life is 'Vast Improvement') hen (Priority sExtremelyHigh)37. IF(Life Expectancy s 'V.Short') and (Pain Level is 'No Pain') and (Quality of Life is 'No Change') then (Priority sTop)38. IF(Life Expectancy s 'V.Short')and(Pain Level is 'No Pain')and(Qualityof Life is 'BeneficialChange') then (Priority sTop)39. IF(Life Expectancy s 'V.Short')and(PainLevel is 'No Pain')and(Qualityof Life is 'Vast Improvement') hen (Priority sTop)40. IF(Life Expectancy s 'V.Short')and (Pain Level is 'Some Pain') and (Qualityof Life is 'No Change') then (Priority sTop)41. IF(Life Expectancy s 'V.Short')and (PainLevel is 'Some Pain')and(Qualityof Life is 'Beneficial Change')then (Priorityis Top)42. IF(Life Expectancy s 'V.Short')and(PainLevel is 'Some Pain')and(Qualityof Life is 'Vast Improvement') hen(Priorityis Top)43. IF (Life Expectancyis 'V.Short')and (Pain Level is 'GreatPain') and (Qualityof Life is 'No Change') then (Priority sTop)44. IF(Life Expectancy s 'V.Short')and(Pain Level is 'GreatPain')and (Qualityof Life is 'Beneficial Change') then(Priorityis Top)45. IF(Life Expectancy s 'V.Short')and(Pain Level is 'GreatPain')and(Qualityof Life is 'Vast Improvement') hen (Priorityis Top)

Figure 10 Sample of the rules.



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. . . .

9 0 ~ - . ? G ~-~ ~ ~ ~ . . ? .? . . . _? --80

a 70

--

6068 '- -- "" - . -----

44 6 ele\flity1 2 - -

0 10

Figure 11 'Quality of life' versus 'pain level' surface model.

80 ........ .

eo,..........0,4030 --20

.- .........................10 \ .. .. . . . . ... . . . . ..

..

. . . . . . . .. . . . . . . .

.... . . ... . . . . . . . . . . . .1 :

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. . ..

.. . . .......4 -........ '.-.......i . .... ..............-

. . . . . . . . . . . . .. . . . . . . . . .

.. ...c! 2'." ............

' ......

.--_....-0 -0 040 200

120 1 00 80 c60Life Expectancy

Figure 12 'Life expectancy' 'versus quality of life' surface model.

Surface modelsA sample of the surface models is shown in Figures 11 and12. Figure 11 is almost perfectly flat representing the equalityof the shapes and rules involving 'quality of life' and 'painlevel'. Figure 12, however, includes the life expectancy'input. The bias towards 'life expectancy' can be clearly seen.

Discussion of resultsThe paper does not deal with the question of what makesone decision rule better than another. A completely separatemodelling exercise is required to assess the value of a specificdecision rule: an example in the case of liver transplants is

given by Ratcliffe et al.19 The current paper wouldacknowledge that such issues are beyond its scope.

ConclusionThis is a purely scientific paper and despite the medicalresearch carried out, it does not pretend to be an authorityon medical decisions. The models are devised as a tool to beapplied by medical professionals. The models can also beused to aid the many problematic issues as discussed above.The first model was produced to demonstrate theeffectiveness of fuzzy logic in making prioritisation decisions.This was successfully achieved by improving the existing



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kidneyprioritisation ystemused in the UK. The improvedmodeldistinguishesbetweensmallchanges n inputscreatinga muchmore reliableand realistic ystem(thesmoothnessofthe models can be seen in the surface models). This isessential when dealing with such sensitivedecisions wheresmalldiscrepanciesmay represent he differencebetween ifeand death. Furthermore,decisions can be more clearlyjustified,as the decision-makings highlysystematic.Owing to the systematicnatureof the rulespresented nthis first model, it is proposed that as further work, acomputer program could be written to devise the rulesautomatically.This would solve the problemsexperiencedwhen too many rules are required.The second model continues where the first modelfinished, extendingthe model to allow humanisticinputs.This model demonstrates the effectiveness of fuzzy logicwhen dealing with humanistic criteria by consistentlydetermining he priorityof patientswaiting for transplantand attemptingto remove some of the sharp boundaries.This follows the call for suchcriteria o be considered foundin an increasingnumber of papersresearchedand analysedin this paper).Both models developed improve the quality of theprioritisation decisions. The decisions are more realisticand more confidence can be placed in them. This in turnleads to a justificationof the decisionsas calledfor in manypaperssuch as Ham.16The models leave the door openfor medicalprofessionalsto add alternativecriterion and adjust the weightingsandcharacteristicsof the criteriaalready modelled. A furtherexampleof an inputto the modelcould be the doctors' owndecision-makingcharacteristics.For example, a hospitalmay use a number of doctors to assess the humanisticelementssuch as pain level. Thisproducesan inconsistency,as different doctors would allocate points differently.However,the doctors'previousdecisionscould be analysed,measuredagainstthe outcomes of those decisionsand used

as an input into the systemand used as an input into thesystem.The models are highly flexibleand can be adaptedintomanyforms. Further nputsand modifications an be easilyadded should medicalprofessionals ee fit or some analysisof the inputs(for example,measurement f pain or qualityof life)be published. nitially, heyareproducedas potentialalternativesto national transplantprioritisationsystems.However, they can be just as useful if used by individualhospitalsand evenindividualdoctorsto helpdecidewhethera patientshould be put on the waiting ist in the firstplace.Each hospital could cater the criteriaand input character-istics to suit theirparticular ituation.Much of the research arriedout in thispaperfocused onthe complications involved with such sensitive decision-making,should the sickestpatientsbe treated irst or last forexample.The models do not directlyanswer hesequestionsbut aredesigned o be flexibleenoughto cope with constantchanges in criteriaagreed on. Changes,which in the USoccur on almosta monthlybasis.The resultsof suchchangescan be easilyseen and thus analysed n the surfacemodels.Both models can be combined to produce an overallsystem. Other criteria could also be added to this withmedicalprofessional nput.For example, he currentsystemin the UK follows a step-by-stepprocedure (shown inFigure 1) assessingcriteria ndividuallybeforefinally usingthe points system.The modelsproduced n this paperallowall criteriato be consideredat the same time. So bloodmatches are analysedalongsidepain level and age, etc.The main conclusion of this research work is that theoptimal decisionrule selected from a largerset of possibledecision rules is likely to be better than the optimal ruleselectedfrom a more restricted et of possiblerules.

AppendixTables8-12 relate to model one.

Table8 High-priority ermutationsRule Age Age Waiting Matchability Sensitisation Balance of Outputno. difference time exchange (priority)8 1 1 1 1 0 0 High9 1 1 1 0 1 0 High10 1 1 0 1 1 0 High11 1 0 1 1 1 0 High12 0 1 1 1 1 0 High13 1 1 1 0 0 1 High14 1 1 0 1 0 1 High15 1 0 1 1 0 1 High16 0 1 1 1 0 1 High17 1 1 0 0 1 1 High18 1 0 1 0 1 High19 0 1 1 0 1 1 High20 1 0 0 1 1 1 High21 0 1 0 1 1 1 High22 0 0 1 1 1 1 High



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114 Journalf heOperationalesearchocietyol. 5,No.Table 9 Medium-prioritypermutations

Rule no. Age Age difference Waitingtime Matchability Sensitisation Balance of exchange Output(priority)23 1 1 1 0 0 0 Medium24 1 1 0 1 0 0 Medium25 1 0 1 1 0 0 Medium26 0 1 1 1 0 0 Medium27 1 1 0 0 1 0 Medium28 1 0 1 0 1 0 Medium29 0 1 1 0 1 0 Medium30 1 0 0 1 1 0 Medium31 0 1 0 1 1 0 Medium32 0 0 1 1 1 0 Medium33 1 1 0 0 0 1 Medium34 1 0 1 0 0 1 Medium35 0 1 1 0 0 1 Medium36 1 0 0 1 0 1 Medium37 0 1 0 1 0 1 Medium38 0 0 1 1 0 1 Medium39 1 0 0 0 1 1 Medium40 0 1 0 0 1 1 Medium41 0 0 1 0 1 1 Medium42 0 0 0 1 1 1 Medium

Table 10 Low-prioritypermutationsRule no. Age Age difference Waitingtime Matchability Sensitisation Balance of exchange Output(priority)43 0 0 0 0 1 1 Low44 0 0 0 1 0 1 Low45 0 0 1 0 0 1 Low46 0 1 0 0 0 1 Low47 1 0 0 0 0 1 Low48 0 0 0 1 1 0 Low49 0 0 1 0 1 0 Low50 0 1 0 0 1 0 Low51 1 0 0 0 1 0 Low52 0 0 1 1 0 0 Low53 0 1 0 1 0 0 Low54 1 0 0 1 0 0 Low55 0 1 1 0 0 0 Low56 1 0 1 0 0 0 Low57 1 1 0 0 0 0 Low

Table 11 Very-low-prioritypermutationsRule no. Age Age difference Waitingtime Matchability Sensitisation Balance of exchange Output (priority)58 0 0 0 0 0 1 Very low59 0 0 0 0 1 0 Very low60 0 0 0 1 0 0 Very low61 0 0 1 0 0 0 Very low62 0 1 0 0 0 0 Very low63 1 0 0 0 0 0 Very low

Table 12 Bottom-priority permutationRule no. Age Age difference Waitingtime Matchability Sensitisation Balance of exchange Output (priority)64 0 0 0 0 0 0 Bottom



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Acknowledgements-Wehank the referees or their valuablecom-ments.References

1 SaffiottiA (1997).The uses of fuzzy logic in autonomousrobotnavigation.Soft Comput.1: 180-197.2 ChoiW et al (2002).A traffic ightcontrollingFLCconsideringthe traffic congestion. The SpringerLink Forum Web-Site,www.link.springer.de.htm.ol. 2275, p 0069.3 KimY and RheeS (2001). Developmentof an arc sensormodelusing fuzzy controller in gas metal arc welding. Meas SciTechnol12: 534-541.4 ChangC, Wei C and Lee Y (1999). Failure mode and effectsanalysis using fuzzy method and grey theory. CyberneticsntJ Systems Cybernet 8: 1072-1080.5 Vanegas LV and Labib AW (2001). A FQFD model forderivingoptimumtargets.Int J Prod Res 39: 99-120.6 VanegasLV and LabibAW (2001). Applicationof new fuzzyweighted average (NFWA) method to engineering designevaluation. nt J Prod Res 39: 1147-1162.7 SudiarsoA and LabibAW (2002).A fuzzy ogic approach o anintegratedmaintenance/productionchedulingalgorithm. nt JProd Res 40: 3121-3138.8 Labib AW, Williams GB and O'Connor RF (1998). Anintelligent maintenance model (System): an application ofAHP and a fuzzylogic rule-based ontroller.J OplRes Soc 9:745-757.9 Adlassnig K-P and Akhavan-HeidariM (1989). An experi-mentalexpertsystem or thediagnosisof gallbladder ndbiliarytractdiseases.ArtifIntell Med 1: 71-77.

10 BanerjeeA, MajumbaAK and Basu A (1995).A fuzzyexpertsystemapproachfor real-timemonitoringof endemic diseases.Inf Sci Appl,3: 41-53.11 Barro S, Ruiz R, Mira J (1990). Fuzzy beat labelling forintelligent arrhythmiamonitoring. ComputBiomed Res 23:240-258.12 UKTSSA Web-Site. www.uktransplant.ors.uk,ast updated2002.13 Devlin N and HansenP (1999).Who shall live and who shalldie?Rationingpublicly undedhealthcare.OtagoJ (Universityof Otago, EconomicsDepartment)8: 117-126.14 Stolberg S (2001). Patients lives on the line in battle overtransplants. nsulin-freeworld foundationweb-sitewww.insu-linfree.org/articles.htm.15 Gordon EJ (2000). Preventingwaste: a ritual analysis ofcandidate selectionfor kidneytransplantation.AnthropolMed7: 351-372.16 Ham C (1999). The role of doctors,patientsand managers nprioritysettingdecisions.HealthExpect2: 61-68.17 Johnson JG, Firth J, Bird SM and Mander A (2001).The effect of alteringeligibilitycriteria or entryonto a kidneytransplant waiting list. Nephrol Dialysis Transplant 16:816-823.18 Kidney Source Web-Site.www.kidneysource.com./Trans-plant.htm,2001.19 Ratcliffe et al (2001). A simulationmodelling approach toevaluating alternative policies for the management of thewaitinglist for liver transplantation.Health CareMngt Sci 4:117-124.

Received June 2002;accepted January 2003 after one revision

an intelligent system for prioritisation of organ transplant patient waiting lists using

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