Applications of gray relational analysis in gastroenterology

PO Box 2345, Beijing 00023, ChinaWorld JGastoenterol 205112):3457 3460www .wignet.comWorld Jourmal of Gastroenterology ISSN 1007-9327wjg@wignet.com◎2005 The WJG Press and Elsevier Inc. All rights reserved.ELSEVIER●BRIEF REPORIS●Applications of gray relational analysis in gastroenterologyXue-Rui Tan, Yu-Guang Li, Ming-Zhe ChenXue-Rui Tan, Yu-Guang Li, First Affiliated Hospital of Shantouconsulting sequence, x;∈X(i= 1,2..... m, m≥2, as theUniversity MedicalCollege, Shantou 510041,Guangdong Province, Chinacomparative factors) be the comparative sequence, x andMing-Zhe Chen, Medical School of Tsinghua University, Beijingx; are named factor sequences. The x0(问) and x(k) are the100083, ChinaSupported by the National Natural Science Foundation of China,values of xo and xat k point(k= 1,2.... 街n≥3). Thus,the formulae of gray relational coefficient Y(xo(k), x:(k))No. 30271158Correspondence to: Xue Rui Tan, MD, PhD, First Affiliatedand gray relational grade Y(xo,x) are the following:Hospital of Shantou University Medical College, Shantou 510041,Guangdong Province, China. tanxuenui@ vip.sina.comF(k)-x(kN+ζ maxmat.()-x(Q)and x1-中_2.()Telephone: +86-754-8552841 Fax: +86-754-861 1690Received: 2004-02-02 Accepted: 2004-02-21The gray relational order, based on the gray relationalgrade Y(xo,x) which represents the strength of relationshipbetween x0 and x, can be constructed. In the formula,min min|xo(k)-x,(k) and max max |xo(k)-x;(k)| are the absoluteAbstractvalues of the minimum and maximum from the differencesAIM: To introduce the basic methods of gray relational analysisbetween x(l) and xo(). x(k) and x0() are the values at(GRA) and to ilustrate its applications in gastroenterology.point k in the x and x the sequences without dimension.Here,ζ = 0.5.METHODS: With the essential formulae of GRA andDis-dimension method Let x=(x(1), 2).... x() beseveral typically practical examples, the procedure ofthe sequence with dimension. Thus,fx- * x,GRA was introduced. Examples were drawn from thegastroenterological studies. Thus the trait of GRA couldbe demonstrated.Consider parameter sequence x=(x(1),x(2), ... wherei=1, 2...N;RESULTS: The superiority of GRA in gastroenterological=(x()(10..();. .study was proved by the examples.阳=(+(2--.(2);CONCLUSION: GRA can be applied mechanically or fexiblyYn =(+)*.x..);.x(k)- min y(k)in gastroenterology.Thus,fx- *X, f(x,(k))=max y(k)- min y(k)= x(k).x,(k)∈s(1).⑥2005 The WJG Press and Elsevier Inc. All rights reserved.Here, max y(k)= max x(k), min y(k)= min x(k),k∈K,K = 12.k...Key words: Gray relational analysis; GastroenterologyEvaluation matrix of GRA Suppose xay∈xo be a groupTan XR, uYG, Chen MZ. Applications of gray relational analysisof the consulting factors,j= 1, 2... e. Thus, there is thein gastroenterology. World J Gastroenterol 2005; 11(22):gtay relational matrix R about向and x; as the following:3457-3460http://www.wjgnet.com/1007-9327/11/3457.aspR(x)=y(x0x) r(x021x2) .. y(x。,x2) r(,x)[rex,xm) r(x02.xm) .. Yax,.xm)}rqe,xm)GRA model of clinical trial Let x;∈X, x:=(x<(1), x:(2),，INTRODUCTIONx(1) be the observing parameter sequences of group iGray relational analysis (GRA) was initiated by Professoror case;i=1, 2.... m m≥2, as the number of trial group orJu-I ong Deng, the famous scientist and founder of gray systemtrial case.theory, Huazhong University of Science and Technology'".Let x∈X, xo= (x0(1), x>()... x(m)) be the idealPrevious applications of GRA in medical researches wereparamostly in cardiology2n. In our viewpoint, it is very usefulx0 ar中国煤化工1, 2...n. n≥3, as the .to introduce GRA to gastroenterologists.numlIYHCNMH(uences. Hence, the grayrclati: 2eflcction of approachingthe ideal effects. Then, the formulae:MATERIALS AND METHODSr(axk)x()-min minx()- x(kX+ζ max mlka(k)- x0(x)Essential formulae of GRALet X be the gray relational factor set, x∈X be theare called GRA model of clinical trial.3458ISSN 1007-9327CN 14-1219/ RWorld J GastroenterolJune 14, 2005 Volume 11 Number 22Table 1 Baseline values in four patients before treatmentAfyr)Course of jaundiceToughness degreeLiver below costalL iver belowSplenomegaly(mo) (x)of liver (x)arch (cm) (x)xiphoid (cm) (x)P (cm)(2)585.0304320270.7481Table 2 Hepatic functions in four patients before and after albendazole treatment(u BirtinOne muinute bingbinALPGU)GOTA/G&(L)No.(K)BeforeAfter89211.32.1176.628.430.045.5/37544.2/27.5602898.0558.0510.76.03041.0/56.045.1/33.9620923.4481.0280/54.048.0/36.02129129.2194630470.135.033.0/45.0 .45 0/227.0Examplesrx7,网) Yx8,x) Y(x9,x) Y(x10,x) YXx11,网)GRA on small sample data backgtound The objectiveY(x0x) -0.83086 0.84450 0.68009 0.59362 0.68935 70.72768Y(x0,x2)| 0.65564 0.63919 0.58232 0.57313 0.56608 0.60327of this study was to evaluate the relationship between the20x3)| 0.82607 0.82195 0.68418 0.56399 0.75575 0.73039baseline condition of patients with alveococcosis and theR(0x= r(r0,x0)| 0.75198 0.78167 0.75162 0.49046 0.77538 0.71112therapeutic effects by using albendazole regularly. FourY(x0,x)| 0.66376 0.67106 0.64311 0.58631 0.52690|0.61823patients with complete data who were diagnosed clinicallyr(x0x6) L -0.65423 0.65564 0.62717 0.59336 0.76081 - 0.658240.73042 0.73567 0.66217 0.56681 0.67905and complicated by obstructive jaundice were entrolled inthis study. Albendazole was orally given twicc daily for overThe GRA results revealed in the gray relational factor1 year with a dosage of 20 mg/kg each day in all cases.set that the superior consulting factors were对and鸡theBaseline values of the observation parameters are shownsuperior comparative factors were x1, x and X4.in Table 1. The effects of albendazole on hepatic functionsare shown in Table 2.Analysis Step 1: To calculate the improved ratio of hepaticGRA for four therapeutic strategies of duodenal ulcer relatedto Helicobacter pylorifunctions.The improved ratio was calculated by using theformula:|a-bBackgtound The purpose of this project was to evaluatethe effects of four therapeutic strategies on duodenal ulcerHere, r = improved ratio, a = parameter value before(DU) related to Helicobacter pylori (H pylor). Forty-nine maletreatment, b = parameter value after treatment.and nine femalc patients with DU were complicated byThe calculated values of the improved ratio are listedH pylori positivities proved by endoscopic examination andin Table 3.H pylori test, and had no gastric or complex ulcer. TheirStep 2: Correlation analysis Let -X11 be the dependentages were 24-62 years (average 37.1士6.5 years). All thevariables, let x1X。be the independent variables, correlationsubjects had no obvious complications or other systemicanalysis was petformed using the statistical analysis systemdisorders. They did not take antibiotics, bismuth agents or(version 6.12). The results of correlation analysis are shownrestrain acids/ antacids for 2 wk preceding the study.in Table 4, indicating that the correlation between dependentvariables and independent variables was not significant.Step 3: GRA Let x,Exo be a group of the consultingTable 4 Results of correlation analysisfactors,j= 7,8, 9, 10, 11 as the consulting factors, let x1-Xx%x知∈xi= 1,2, 3, 4, 5, 6 be the comparative factors. GRAwas operated by using GRA program that we edited in the-0.81774-0.279070.10911-77759statistical analysis system (version 6.12). Dis-dimension0.18230.40690.72090.89090.224process was the averaging method. Thus, the gray relationalx2-0.786660.980540.15755-0.56181-0.989540.21330.01950.43820.0105matrix R about x and x; is as follows:-0.31909-0.377370.154630.06341-0.454980.68090.62260.84540.93660.5450xe0.665730.126520.63044-0.592130.40379Table 3 Improved ratio of hepatic functions after treatment中国煤化工%60.4079X0Xuxs-0.52589-0.57561YHCNMHG1o0.47410.42440.840810.814160.00000.324680.978140.722190.383170.034760.900900.852160.937500.120690.605260.817110.02190.27780.96520.09910.980740.961540.977960.125001.571410.92010.985290.4665207777781.27274Note: The upper numbers are the crrelationocoffcients between correspondingvariables and the lower numbers are the P values.Tan XR et al. Gray relational analysis in gastroenterology3459Table 5 Raw data in four groupsDisappearance of symptomsEradication of H pyloriActive mucitis fadingUlcer cureGroupnkRate(%)Timg(d)”Ratg(%)A(x)1410378.69/1369.285.7B (x2)1553.6066.7733C(x)147146.i19/127564.3DCE)13.3b3/1225Ideal (xo)1003.5.7P<0.05, bP<0.01 us other groups;i=A, B,C,D=1,2,3,4;k=1,23,4,5.Table 6 Gray relational cofficients between ideals (x) and other groups (x)Eradication of H pylori Active mudtis fadingGroup 0Time(d)Rate(%) .A(1)0.91750.8481B(2)0.73280.7547C3)0.63020.40990.6407D(4)0.95690.33330.39320.6013Materialsunchanged in color were defined as negative.Step 1: Data collection Grouping and therapeuticEstimation criteria Al patients were asked to return forstrategies: All the subjects were randomly divided into foura check-up in a month after treatment. They were evaluatedgroups. Group A had 14 cases that were treated with aunder four aspects: (1) Disappearance of symptoms (alltriple therapeutic strategy of tinidazole (Livzon), Lizhubaseline symptoms including pyrosis, epigastric pain,Dele/ colloidal bismuth subcitrate (Livzon Pharmaceuticalabdominal distension, acid suffusion and belching of gas,Factory, Zhuhai) and omeprazole (Sanye Pharm). Group Betc. disappeared). (2) Eradication of H pylori (the specimennad 14 cases that were treated with a triple therapeuticmuter representatives in H pylori test double boxes becamestrategy of metronidazole (Tongji Meiji), amoxicillinnegative, and one of them being positive was thought that(Baiyunshan, Guangzhou) and omeprazole (Sanye Pharm).eradication of H pylori infection was not achieved). (3) ActiveGroup C had 14 cases that were treated with a triplemucitis fading (the original byperemia, erosion, edema intherapeutic strategy of mctronidazole (Tongji Meii)，the duodenal mucosa were not seen endoscopically). (4)amoicllin (Baiyunshan, Guangzhou) and De Nol/ colloidalUlcer cure (the duodenal ulcer vanished or pitted, andbismuth subcitrate (Yamanouchi Europe). Group D hadabated, dilated or unchanged ulcers in the ulcer arca were15 cases that were treated with a single therapeutic stratcgydefined as uncured).of omeprazole (Sanye Pharm). There were no significantStep 2: Raw data of four gtoups are listed in Table 5.differences between groups in age or sex distribution. TheStep 3: GRA Let the ideal sequence如xo(k)∈xqk= 1,2,dose of tinidazole was 1.0 mg b.id, Lizhu Dele/ colloidal3, 4, 5, be the consulting factor sequences. Let x x() E xbismuth subcitratc 110 mg qid, omeprazole 20 mg q.d,i= 1, 23, 4, 5, 6, be the compacative factor sequences. GRAamoxicilin 0.5 mg q.i.d, metronidazole 0.2 mg t.i.d,was operated using GRA program that we edited in the statisticalDe-Nol/ colloidal bismuth subcitrate 120 mg qid. Lizhuanalysis system (version 6.12). Thus, the gray relationalDele/ colloidal bismuth subcitrate and De-Nol/ colloidalcoefficients between x and x are as follows (Table 6).bismuth subcitrate were taken orally 30 min ante cibum orThe gray relational grades to ideals of four groups were:before sleep. The others were taken orally 30 min post cibum.%A,i.e. 7%1= 0.95312; %B, i.e. %z = 0.86712; %c, i.e.Lizhu Dele/ colloidal bismuth subcitratc, De-Nol/ colloidal%3= 0.73616; 7%D, i.e. %4= 0.65694.bismuth subcitrate and omeprazole were given for 2 wkThus the gray relational order was x>x2>x3>x4; ie.and the others for 1 wk.strategy A> strategy B > strategy C > strategy D.Endoscopic examination and H pylori test All thesubjects underwent endoscopic examination and H pyloriGRA on serum markers ofliver fibrosistest. After pharynx local anesthesia, gastroduodenalBackgtound Serum procollagen type I (PC II), prolidaseendoscopy was performed in all subjects taking a left lateral(PLD), and hyaluronic acid (HA), are of diagnosticposition by Q30 electronic endoscope system. Images weresignificance in liver fbrosis. To find out the markers withscreened and rinsed, washing-cell specimen muterearly中国煤化，Tis via GRA, 100 patientsrepresentatives were taken from the site of ulcer lesionwithE 28 patients with chronicduring endoscopy. At normal temperature, the specimenpersisMHC N M H Gants with chronic activemuter representatives were put in the H pylori fast test boxhepatitis (CAH), and 51 patients with liver citthosis (LC),containing reagents (the PLA Higher Medical School,were studied. Thirty HBVM- ncgative subjects with normalLanzhou, China). After 24 h, the reagents that appeared inliver biochemical test served as controls. The clinical materialsrose were defined as positive, and those that remainedof the subjects are listed in Table 7.3460ISSN 1007-9327CN 14-1219/ RWorld J Gastroenterol June 14, 2005 Volume 11 Number 22Table 7 Clinical materials of the subjects (mean+SD)with early diagnostic value of liver fbrosis. This exampleGroups Number of subjectsAge(yr) _Number of malesprovides a new insight into the study of liver diseases andControls3031.7+729ilustrates a practical application of GRA.IH2835.2+9.1Since the discovery of H pylori in 1983, a wealth ofCAH234.9+6.916data about DU related to H pylori has been accumulated,c5145.1+11.41and the therapeutic strategies of duodenal ulcer have beenchanged. There is evidence that ulcer cure and reductionof recurrence could be achieved by effective antibioticClinical materials Examination of PC II, PLD and HAtherapy. Such colloidal bismuth subcitrates as Lizhu DelePC III was assayed by using a commercially availableor De-Nol can form a protective bismuth-protein membraneradioimmunoassay (Chongqing Institute of Phymatosis,which can promote healing of the ulcer and preventChongqing). The activity of PLD was assayed by using arecurrence of ulcer. The results of GRA showed that thecommercially available ultraviolet spectrophotometry (Thirdgray relational order of the comprehensive effects in termsMilitary Medical University, Chongqing). Serum HA wasof the symptomi disappearance, eradication of H pylori,assayed by using a commercially available radioimmunoassayactive mucitis fading and ulcer cure is strategy A > strategy(Shanghai Institute of Navy Medicine, Shanghai). PC II,B> strategy C> strategy D, and strategy A is the best ofPLD and HA in conttols were regarded as the normal upperfour strategies which showed no differences from thelimits, and the sensitivity of each market was calculated.previous reports.The results are shown in Table 8.Alveococcosis is as harmful as a malignant tumor.Untreated cases had a 5-year mortality rate of 70% and10-year of 93%. The severity is related to jaundice. PatientsTable 8 Sensitivity of serum PC lI. PLD and HAwith alveococosis had a low diagnostic and hospitalizationMarkerCPHLCrate. There is a shortage of clinical samples, and not suitablefor statistical analysis. The first time report on alveococcosis28.6100.088.2PLD0.090.2had no statistical analysis. The GRA results indicated thatA7.176.294.2jaundice parameter bilirubin and 1- min bilirubin were thesuperior consuling factors, which suggest the main effectof albendazole on alveococcosis. The relevant factors withGRA Step 1: To construct the ideal sequence Theseverity of the discase such as age, degree of liver toughnessideal sequence was constructed according to the pathologicaland liver below costal arch were the superior comparativechanges of liver diseases. There was no liver fibrosis infactors, which suggest that the eects of albendazolc onCPH, and so the sensitivity of an ideal marker value foralveococcosis were partially restricted by the baselinethe diagnosis of CPH should be zero. Whereas there wasconditions of patients. This example provides objectiveearly liver fibrosis in CAH, and so the sensitivity of an idealevidence and demonstrates that GRA is superior to statisticalmarker value for CAH should be 100%. The averageanalysis for small sample data.value of the sensitivity of PC II, PLD and HA in LCwas 90.9%, which can be chosen as the sensitivity of anREFERENCESideal marker value for LC. So, the ideal sequence was x=Deng JL. Introduction to grey system theory. J Grey System(0, 100, 90.9).Step 2: To identify the comparative sequencesTheHuang WD, Shi HR, Tan XR. A grey relational study on de-observed parameter sequencesof i(i= 1, 2, 3 = sensitivitytermination of stroke volume with D and M echocardi-of PC II, sensitivity of PLD and sensitivity of HA) wereography. I Grey System 1994; 6: 203-211Tan XR, Deng JL, Huang WD, Wang ZL. GRA on plasma ET-x x x x∈x Thus, the parameter sequences were x =1, PAP, PaOz and PaCO2 in the elderly patients with PHD. In:(28.6, 100, 88.2), x2二(0, 57.1, 90.2), x3= (7.1, 76.2, 94.2),Liu SF, Xu ZX. Huise Xitong Yanjiu Jinzhan Huazhong Li Gongwhich served as the comparative sequences.的x∈X, wasDaxue Chubanshe Wuhan China 1996: 133-135the GAR factor set.Xu rC, Tan XR. Grey relational analysis of a trial of trental 0sStep 3: GRA operation GRA was performed using theantiaggregants. J Grey System 1997; 9: 365-370Tan XR, Yang YH, Deng JL. Grey relational analysing factorsGRA progtam that we edited in the statitical analysis systemin hypertensive with cardiac insufficiency. J Grey System 1998;(version 6.12). The tresults were: Y (xo,x) = 0.7733, r (x0,x2)10: 75-80= 0.7667, Y (xm,x3) = 0.7. So the gray relaional order was: 6 Tan XR, Deng JL, Chu YJ. Grey relational analysis of(Y(ax)>Y(xx2)> Y(xu,x); i.c. x1>x>好circadian variation of plasma renin activity, angiotensin llIn conclusion, The GRA showing superiority to statisticaland blood pressure in hypertensives. I Grey System 1999; 11:41-46methods in some cases can be applied mechanically orTan XR. Yane HS. Chu YI. Sunerior grey relational analysisflexibly in gastroenterology.中国煤化工with blood pressure in sys-Ciymposium on HypertensionC N M H Gnsion League Chinese SocietyDISCUSSIONHof Caraiorogy & Cnmese Acaaemy of Medical Science Bejjing-Through GRA, scrum PC III was identified as the markerLangfang China 1999: 135Science Editor Zhu LH, Wang XL and Li WZ Language Editor Elsevier HK