Research Article Predicting Renal Failure Progression in

Research ArticlePredicting Renal Failure Progression in Chronic KidneyDisease Using Integrated Intelligent Fuzzy Expert System

Jamshid Norouzi1 Ali Yadollahpour2 Seyed Ahmad Mirbagheri3

Mitra Mahdavi Mazdeh4 and Seyed Ahmad Hosseini5

1Department of Environmental and Energy Islamic Azad University Science and Research Branch Tehran Iran2Department of Medical Physics School of Medicine Ahvaz Jundishapur University of Medical Sciences Ahvaz 61357-33118 Iran3Department of Civil and Environmental Engineering K N Toosi University of Technology Tehran Iran4Iranian Tissue Bank amp Research Center Tehran University of Medical Sciences Tehran Iran5Nutrition and Metabolic Diseases Research Center Ahvaz Jundishapur University of Medical Sciences Ahvaz 61357-33118 Iran

Correspondence should be addressed to Ali Yadollahpour yadollahpouragmailcom

Received 12 October 2015 Accepted 13 December 2015

Academic Editor Ezequiel Lopez-Rubio

Copyright copy 2016 Jamshid Norouzi et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Background Chronic kidney disease (CKD) is a covert disease Accurate prediction of CKD progression over time is necessary forreducing its costs and mortality rates The present study proposes an adaptive neurofuzzy inference system (ANFIS) for predictingthe renal failure timeframe of CKD based on real clinical dataMethodsThis study used 10-year clinical records of newly diagnosedCKDpatientsThe threshold value of 15 cckgmin173m2 of glomerular filtration rate (GFR)was used as themarker of renal failureA Takagi-Sugeno type ANFIS model was used to predict GFR values Variables of age sex weight underlying diseases diastolicblood pressure creatinine calcium phosphorus uric acid andGFRwere initially selected for the predictingmodel ResultsWeightdiastolic blood pressure diabetes mellitus as underlying disease and current GFR

(119905)showed significant correlation with GFRs and

were selected as the inputs of model The comparisons of the predicted values with the real data showed that the ANFIS modelcould accurately estimate GFR variations in all sequential periods (Normalized Mean Absolute Error lower than 5) ConclusionsDespite the high uncertainties of human body and dynamic nature of CKD progression our model can accurately predict the GFRvariations at long future periods

1 Introduction

Chronic kidney disease (CKD) is a growing health problemworldwide (about 10 to 15 percent of the adult population inUSA 112 in Australia 101 in Singapore 187 in Japanand 83 to 189 in Iran) [1 2] It is a progressive diseaseassociated with a high risk of cardiovascular diseases mortal-ity andmorbidity rates and high health care costsThereforeearly detection of the disease to control and manage theconsequences is of prime significance [3 4]The world healthorganization has estimated an amount of 11 trillion dollarsas the cost of dialysis in the last decade [5] Because of thedynamic nature of renal disease its covert nature in the earlystages and heterogeneity of patients predicting the renal

failure progression with reasonable accuracy is necessary [6]The renal failure progression can be considered as a functionof various parameters including underlying renal diseasesblood pressure hypertension proteinuria and age [7 8]

In recent years early diagnosis of the disease especiallydetermining the appropriate time to apply medical treat-ments for CKD has received great attention among cliniciansand researchers [9ndash11] Researchers through epidemiologicaland registry-based studies try to diagnose CKD in high riskpatients as soon as possible and to control identified risk fac-tors aggravating the disease progression to End Stage RenalDisease (ESRD) like hypertension proteinuria and hyper-phosphatemia [9 10 12] Based on the evaluations of thesevariables different models have been developed to accurately

Hindawi Publishing CorporationComputational and Mathematical Methods in MedicineVolume 2016 Article ID 6080814 9 pageshttpdxdoiorg10115520166080814

2 Computational and Mathematical Methods in Medicine

predict progression to ESRD in CKD stages [9 12] Howeverthey cannot quantitatively predict the variations of glomeru-lar filtration rate (GFR) in the patients Aguilar et al evaluatedthe effective factors associated with CKD on 103 patients withmean age of 708plusmn13 yearsThe CKD associated factors wereage gt65 years old male sex positive history of cardiovasculardisease anemia and obesity (BMI gt 30) Their findingsshowed that age and anemia were the strongest factors associ-ated with CKD in their population [13] There have been sev-eral studies on the GFR variations among different popula-tions of CKD patients [9 10 14ndash16] In this regard intelligentand machine learning methods have been increasingly usedin the context of health and disease forecasting Gaspari et al(2004) compared renal function derived from 12 predictionequations with GFR measurement by plasma iohexol clear-ance as reference method in a group of 81 renal transplantrecipients [16] They concluded that all models overestimaterenal function However Modification of Diet in RenalDisease (MDRD) and Walser formulas showed the best per-formance with the lowest bias and the highest precision [16]Brier et al (2003) compared artificial neural networks withtraditional logistical regression in the prediction of delayedgraft function (DGF) in kidney transplant patients Theycompared the results of neural network with logistic regres-sion method and founded more sensitivity of logistic regres-sion in the prediction of no DGF (91 versus 70) while theneural network was more sensitive to the prediction of eyesfor DGF (56 versus 37) [17] Hussain et al (2011) proposedan intelligent tool for detecting breast cancer using supportvector machines (SVM) They compared the performanceof the proposed method with other classification methodsAccordingly SVM improved the diagnosis of the disease [18]

In recent years fuzzy intelligent methods especiallyfuzzy expert systems have been increasingly used to predictdifferent diseases It seems that employing this method alongwith the clinical tools for diagnosis of different diseases andconditions may drastically reduce diagnostic errors Fuzzyexpert technique is more accurate than machine learningtechniques

Adaptive neurofuzzy inference system (ANFIS) is a learn-ing based system based on the neural networks conceptsThe ANFIS network used in the present study is based onthe model proposed by Jang et al [19] This is a learnernetwork equivalent to Takagi-Sugeno fuzzy inference systemLearning in this network is continuous update of the networkparameters Factors of layers I and IV are of learner typethat respectively determinemembership functions and first-order estimated function The ANFIS training algorithm is ahybrid algorithm in which ordinary least squares algorithmis used to update coefficients of output functions (119891

119894) while

error back propagation algorithm is used to update funda-mental factors of the system [19 20]

If we canmodel and predict the renal functionworseningwe can effectively manage this disorder In this regard anappropriate parameter should be considered as the markerof disease worsening The GFR is the only reliable parameterof the renal function and progression of CKD [16] TheCockroft-Gault (C-G) MDRD and chronic kidney dis-ease epidemiology collaboration (CKD-EPI) equations are

the most common and validated equations to calculate GFR[21] For different age and racial groups these equations yielddifferent accuracy in estimating renal function [21] Accord-ing to the clinical measurements (independent physiologicalparameters) and clinical outcomes when GFR reaches lessthan 15 cckgmin173m2 renal replacement therapy (RRT)including dialysis or transplant is necessary for the patientsurvival If GFR variation is predicted in a CKD patient wecan appropriately predict the time to reach GFR thresholdvalue of 15 cckgmin173m2 In other words the time forrenal replacement therapy is predicted In this study speedof GFR decrease in CKD patients has been predicted basedon the follow-up of the CKDpatients during the study To ourknowledge there has not been any efficient method proposedfor predicting the timeframe of CKDworsening in individualcases [22] Furthermore fuzzy intelligent techniques havenot yet been used to predict renal function worseningThe present study proposes an ANFIS based model forpredicting the renal failure timeframe of CKD based on a10-year real clinical data The main objective is to provide apractical and reliablemethodwith acceptable accuracy to findunderpinning of a decision support system in health care andto support clinical decision making systems

2 Materials and Methods

21 Data Collection All the data of the present studywere theclinical records of a cohort study of newly diagnosed CKDpatients who were serially admitted to the Clinic of Nephrol-ogy Imam Khomeini Hospital (Tehran Iran) during Octo-ber 2002ndashOctober 2011 The inclusion criteria for CKD def-inition included small sized kidney in ultrasound images orGFR less than 60 cckgmin173m2 for more than 3 monthsThe datasets were built using the clinical and laboratory dataof different parameters All the procedures of the study wereapproved by the ethics committee of Tehran University ofMedical Sciences that completely coincide with the Decla-ration of Helsinki Ethical Principles for Medical ResearchInvolving Human Subjects The written consent form wasobtained from each patient to participate in the study

The patients were divided into two groups according tothe pattern of their adherence to follow-up schedule in theclinic A total of 465 CKD patients were enrolled in the studyThe test group consisted of 389 patients who continuously (atleast every six months) were visited in the clinic The controlgroup consisted of 76 patients who did not regularly followtheir visit schedule in the clinic but their visits had lasted atleast one year The details of demographic data and clinicalmeasurements of the patients are presented in Table 1

22 Input Selection The present study used ANFIS neuralnetworks to predict GFR values and compared the accuracyof the method At each visit patientrsquos demographic dataweight blood pressure blood sample test variables includingserum creatinine levels fasting plasma glucose levels lipidprofile calcium phosphorus hemoglobin and other param-eters were monitored The appropriate treatments for bloodpressure bone mineral metabolism indices and hemoglobin

Computational and Mathematical Methods in Medicine 3

Table 1 Baseline characteristics of the study population (119899 = 465)

Variable Mean plusmn standard deviationGFR (ccminm2) 348 plusmn 110Age (years) 613 plusmn 149BMI (kgM2) 265 plusmn 42Systolic blood pressure (CmHg) 140 plusmn 27Diastolic blood pressure (CmHg) 78 plusmn 13Hemoglobin (grdL) 126 plusmn 21Phosphorus (mgdL) 410 plusmn 08Uric acid (mgdL) 81 plusmn 19Cholesterol (mgdL) 1985 plusmn 589Triglyceride (mgdL) 2056 plusmn 1345

control were administered to each patient based on theclinical evaluations The GFR was calculated using MDRDequationThe end point of data collecting for each patient waseither GFR value less than 15 cckgmin173m2 start of RRTor patient death All quantitative variables were used as con-tinuous to have a better training of model According to thenephrologistsrsquo opinions and the kidney function ten variableswere initially selected as influencing parameters on the GFRvariations These variables included age sex weight under-lying diseases diastolic blood pressure (dbp) creatinine (Cr)calcium (Ca) phosphorus (P) uric acid and GFRThey wereconsidered as the inputs of the predicting model Some ofthese variables did not necessarily show strong correlationwith the output (GFR

(119905+119901)) On the other hand in ANFIS

model input number reduction increased the accuracy ofprediction and better training of model Therefore only themore significant inputs were selected according to the levelof their correlation with the output Pearson correlation coef-ficients test was used to determine the most significant inputvariables to be introduced in the ANFIS model The Pearsoncorrelation coefficients test was used because of the continu-ous nature of the variables Table 2 represents the correlationcoefficients between the inputs and output (GFR

(119905+119901)) at 6-

month interval Of the 10 inputs only four inputs underlyingdisease dbp weight and GFR

(119905)have an acceptable corre-

lation with the output (GFR(119905+119901)

) Therefore just these fourvariables were selected for future processing and modelingIn the next step the GFR values were predicted at 6- 12-and 18-month intervals usingANFIS networkmodelThe realdata recorded during a ten-year period were recorded at 6-month intervalsTherefore theGFRvalueswere predicted forthree sequential 6-month intervals at 6- 12- and 18-monthintervals The GFR

(119905+119901)with 119901 = 1 2 3 represents the GFR

values at 6- 12- and 18-month intervals that is if 119901 = 1 GFRprediction is performed for the subsequent 6-month interval

23 Building Training and Test Datasets Thefirst step to trainall neural networks and accurate modeling was to divide datainto training and test datasets Training data were used tooptimize the weights and other parameters in the modelThe test data were used to evaluate the quality of estimatesand forecasts In all further processing and modeling thetest dataset was not used for training models Test data

Table 2 The correlation coefficients between all inputs and targetoutput (GFR

119905+119901) for 6-month period dbp = diastolic blood pressure

Cr creatinine Ca calcium P phosphorus underlying disease(Diabetes) GFR glomerular filtration rate

Input Input number Correlation coefficientbetween input 119894 and output

Underlying disease(119905)

1 02505Sex(119905)

2 00706Age(119905)

3 minus01043dbp(119905)

4 07145Cr(119905)

5 00322Ca(119905)

6 minus02224P(119905)

7 minus01444Uric acid

(119905)8 01089

Weight(119905)

9 08120GFR(119905)

10 05196

realistically simulated the model in the case where there wasno information about the future

The test data were randomly selected so that all data hadan equal chance to participate in the selection process Thetest datasets are usually selected among 30 to 40 of theavailable data In this study 30 of the data were selected astest datasetThe remaining 70 were used as training datasetto estimate and train models

24 Fuzzification of Input Variables Genfis3 code in MAT-LAB was used to fuzzify input variables and to establishthe rule base Genfis3 uses fuzzy 119888-means (FCM) clusteringtechnique to fuzzify variablesThemembership functions areGaussian

25 Establishing a Fuzzy Rule Base for ANFIS It is easy toestablish a fuzzy rule base for ANFIS after fuzzifying variablesusing FCM clustering technique in Genfis3 The number offuzzy rules is equal to the number of membership functionsof input variables (11 functions) Thus 11 fuzzy rules havebeen created in the rule base and used to estimate GFRvalues Figures 1 and 2 respectively show the ANFIS networkstructure and schematic diagram of the predicting modelused in the present study

3 Results

A total of 465 CKD patients were evaluated in thestudy 277 of them were male Diabetes mellitus was theunderlying disease in 153 patients (33) The GFR valuesranged from 45 to 60 cckgmin173m2 in 154 patients(331) 30ndash45 cckgmin173m2 in 215 (462) and 15ndash30 cckgmin173m2 in 96 patients (207)

31 GFR Prediction with ANFIS According to the clinicaldataset recorded from patients fuzzy clustering of the foursignificant input variables is shown for the period of 6monthsin Figures 3ndash6 Inputs 1 2 3 and 4 were assigned to under-lying disease (as diabetes) diastolic blood pressure (dbp)


Inputs

Underlying Blood

ANFIS

GFR(t)

Phosphorus(t)

(t)

Calcium(t)

Creatinine(t)

(t)Age(t)

disease(t)

Sex(t)Weight(t)

GFR(t+p)

pressure

Uric acid

Figure 1 Schematic diagram of predicting model and input of variables

Input Inputmf Rule OutputOutputmf

Logical operationsAnd

Figure 2The ANFIS network structure used in the study to predictGFR values

weight and GFR respectively in the modeling and figuresFor each input 10 clusters were considered According to thetrial and error 10 clusters provide better results (with thelowest error)

32 Training ANFIS The rules in the rule base build afuzzy inference system After training it was converted toa fuzzy inference system called ANFIS ANFIS training wasperformed using MATLAB

Considering GFR modeling at one two or three futureperiods with the selected input variables including under-lying disease diastolic blood pressure weight and GFR

(119905)

values the number of observations for modeling was 674rows 30of the data 202 records for the test dataset and 472records were used as training dataset to train the ANFISThetrained ANFIS was used for estimating GFR at subsequent6 12 or 18 months Figures 7 and 8 respectively show theperformance of ANFIS model for training and test datasetsfor the 6-month period The GFR changes are well followedby ANFIS in test dataset (Figure 8)

In next step the GFR function was estimated for the6-month period according to the patientsrsquo records The

Input 1 (in1)

Deg

ree o

f mem

bers

hip

In1cluster1In1cluster2In1cluster3In1cluster4In1cluster5


0 01 02 03 04 05 06 07 08 09 1

0

02

04

06

08

1

Figure 3 The fuzzy functions selected for input 1 underlyingdisease (diabetes) for the 6-month period

results are presented as fitted surfaces for the output variableGFR(119905+1)

which is the value of GFR at 6-month interval(Figures 9ndash14) The fitted surfaces also show the relationshipbetween input variables and GFR

In next step themodel was used to predict theGFR valuesat sequential 12- and 18-month intervals (Figures 15ndash18) Theresults showed that ANFIS was able to predict GFR with anacceptable accuracy for the test dataThe assessments showedthat despite increasing the forecast period ANFIS was stillable to predict GFR with an acceptable accuracy (Figures 15ndash18)

For further assessments and comparisons of the model-ing the results were examined based on the error criteriaConsidering the variations of the results appropriate errorcriteria should be used to evaluate the accuracy and efficiencyof the predicting model Three criteria were selected toevaluate and compare the accuracy of the fuzzy model MeanSquare Error (MSE) Mean Absolute Error (MAE) and Nor-malizedMSE (NMSE) Of them the NMSE is preferred since


Input 2 (in2)

Deg

ree o

f mem

bers

hip

0

02

04

06

08

1

1 15 2 25 3 35 4 45 5 55



Figure 4 The fuzzy functions selected for input 2 diastolic bloodpressure (dbp) for the 6-month period

10 20 30 40 50 60Input 3 (in3)

Deg

ree o

f mem

bers

hip

0

02

04

06

08

1



Figure 5 The fuzzy functions selected for input 3 weight for the6-month period

10 20 30 40 50 60 70Input 4 (in4)

Deg

ree o

f mem

bers

hip

0

02

04

06

08

1



Figure 6 The fuzzy functions selected for input 4 GFR(119905) for the

6-month period

0 100 200 300 400 500 6000

20

40

60

80

100

120

Sample number

Training data

ANFIS outputReal output

GFR

(t+1)

(cc

min

)

Figure 7 Comparison of the ANFIS prediction and real GFR(119905+1)

values for the training dataset at 6-month interval

0 50 100 150 200 2500

10203040506070

Sample number

Testing data


GFR

(t+1)

(cc

min

)


values for the test dataset at 6-month interval

it provides the normalized error ranged from0 to 100 percentThe formulas for error criteria are expressed by (1) as follows

MSE =sum119873

119894=1(119910119894minus 119894)2

119873

MAE =sum119873

119894=1

1003816100381610038161003816119910119894 minus 119894

1003816100381610038161003816

119873

NMSE =sum119873

119894=1(119910119894minus 119894)2

sum119873

119894=1(119910119894)2times 100

(1)

Table 3 compares the ANFIS results at 6- 12- and 18-monthintervals for the training and test datasets based on the errorcriteria The comparisons show the high accuracy of ANFISmodel for predicting GFR values for all sequential 6- 12-and 18-month intervals in both training and test datasetsWith reference to the low error rate of test data the proposedANFIS could be generalized to predict GFR level in newpatients

As the number of input variables increases the modelingerror decreases As the ratio of observations to variablesincreases the reliability increases and thereby estimation


minus100minus50

050

100

Disease

555445

335225

115 0 01 0203 04

05 0607 08

09 1

Dbp

GFR

(t+1)

Figure 9 GFR(119905+1)

function and its relationship with the underlyingdisease and dbp variables for the 6-month period

1020

3040

5060

70

50

100

150

200

250

WeightDisease

002

0406

081

GFR

(t+1)

Figure 10 GFR(119905+1)

function and its relationship with the underly-ing disease and wt variables for the 6-month interval

1030

5070

90

0DiseaseGFR

minus1000

minus800

minus600

minus400

minus200

0

02 0103

05 04060708091

GFR

(t+1)

Figure 11 GFR(119905+1)

function and its relationshipwith the underlyingdisease and gfr variables for the 6-month period

2040

6080

100

12

34

5

Weight

minus500minus400minus300minus200minus100

0100

Dbp

GFR

(t+1)

Figure 12 GFR(119905+1)

function and its relationship with the dbp andwt variables for the 6-month period

2040

60

54

32

1

809070

5030

10

100

minus500

minus400

minus300

minus200

minus100

0

100

Dbp GFR

1525

3545

55

GFR

(t+1)

Figure 13 GFR(119905+1)

function and its relationship with the dbp andgfr variables for the 6-month period

20406080

100 20406080

100

minus500

minus400

minus300

minus200

minus100

0

100

WeightGFR

GFR

(t+1)

Figure 14 GFR(119905+1)

function and its relationship with the wt and gfrvariables for the 6-month period


0 100 200 300 400 5000

20

40

60

80

120

100

Sample number

Training data


GFR

(t+2)

(cc

min

)


for the training dataset for the 12-month period

0 50 100 150 200 2500

10

20

30

40

50

60

70

Sample number

Testing data


GFR

(t+2)

(cc

min

)


values for the test dataset for the 12-month period

Table 3 Comparison of error criteria for the trainingtest datasetsfor 6- 12- and 18-month periods MSE Mean Square Error MAEMean Absolute Error NMSE Normalized MSE

Training dataset ANFIS Test dataset ANFIS

6 monthsMSE 487053 586253MAE 49960 47654NMSE 37428 47676



error of themodel parameters decreasesThemodeler prefersfewer variables provided that the model error remains lowReviewing the relationships between the independent anddependent variables among 10 independent variables fourof themost important independent variables with the highestcorrelation with the dependent variable (GFR) were selected

0 50 100 150 200 250 300 350 4000

20

40

60

80

100

120

Sample number

Training data


GFR

(t+3)

(cc

min

)


values for the training dataset for the 18-month period

0 20 40 60 80 100 120 140 1600

20

40

60

80

Sample number

Testing data


GFR

(t+3)

(cc

min

)



The accuracy of models was enhanced through eliminatingother variables

The present study was conducted in specific clinicalsituations (predicting the CKD progression) by integratedfuzzy modeling This can be helpful in expediting medicalapplications However a question whether the numbers oftime periods or lags considered for prediction affectmodelingand error rate arises It is noteworthy that a modeler alwaysprefers to do forecasts for long periods provided that theforecast error is not very high Therefore the time delay (119901)should be selected so that is a tradeoff between time intervaland the modeling error The implementation of models andcomparisons confirm that ANFIS provides highly reliableresults for the all 6- 12- and 18-month periods Thereforethe ANFIS is considered as an acceptable model The mainreasons for preferring the ANFIS are as follows

(i) The model provides the ability to model fuzzy vari-ables In this regard the uncertainty can be appropri-ately modeled

(ii) Themodel is able to estimate and predict GFR so thatthe error rate has been reduced to 4 in some cases


(iii) In addition to GFR prediction the model producesa fuzzy database The database shows the complexrelationships between experimental inputs and GFRas simple linear models in different modeling envi-ronments The transparency of GFR membershipfunction in the ANFIS is the advantage of ANFIScompared to other models such as statistical modellike regression or neural network like multilayerperceptron neural network

4 Perspectives of Practical Implementation

The proposed model can be used as a core computationalcomponent in a perspective medical decision support system(MDSS) to help physicians in making appropriate decisionsabout the time of renal replacement therapy This systemcan take physiological parameters as input and predict theGFR values at future intervals Using appropriate thresholdvalue of GFR nephrologists can effectively manage the CKDpatients To build such MDSS it is necessary to complementthe predicting model through evaluating the other possibleinfluential parameters in kidney function

5 Discussion

The results of modeling and forecasting by ANFIS networksshow that the models have a reliable accuracy for all periodsof 6 12 and 18 months Therefore fuzzy model couldbe used to predict GFR with a high reliability The mainchallenge in modeling the renal failure progression is thehigh uncertainties of the human body as the environmentas well as high dynamicity of the disease Statistical andmachine learning based prediction models cannot effectivelyovercome these problems However the proposed modelcould significantly control these issues using neurofuzzyapproach Furthermore our model can accurately predictthe GFR values in long future period so that increasing theforecasting period to 12 and 18 months do not reduce theaccuracy of the predictionmodel (488NMAE)Thismodelcan be used in clinical practice

One of the main concerns of clinicians has been theefficacy of CKD patientsrsquo supervision and regular follow-up on decreasing the speed of disease progression andprevention of its inevitable complications Therefore theuse of efficient predicting model proposed in this study fordecision support system in the field of kidney diseases aswell as CKD management in a more quantitative mannermay be an important strategy for reducing its burden Usingthis model it is possible to monitor the impact of eachvariable routinely measured in CKD patients Rucci et alfound that patients with proteinuria and a baseline estimatedGFR (eGFR) of gt33mLmin173m2 had faster decline ofGFR (28mLmin173m2) than those with baseline eGFRof lt33mLmin173m2 and a baseline serum phosphorusof gt43mgdL in their retrospective study Among patientswithout proteinuria those younger than 67 years exhibiteda significantly faster progression which was even faster for

the subgroup with diabetes Among patients aged older than67 years females had more steady eGFR than men [12]

Our results in comparison with the results of Tian etal [23] on the survival time of hemodialysis patients aswell as other studies using machine learning based methodsare of high validity and reliability Furthermore choosingappropriate input variables is the most important feature ofthe model that can improve prediction accuracy One of thelimitations of this study may be the presence of intrinsicerrors in eGFR calculated with MDRD Recently Fan et alintroduced a new method for eGFR calculation based oncystatin C and concluded that it may be a better filtrationmarker than the equations based on serum creatinine valueparticularly in elderly patients [24] To validate our proposedmodel we can model the renal failure worsening frameworkusing different equations of eGFR

6 Conclusion

An ANFIS based model was developed for modeling therenal failure progression and predicting the renal failuretime The model could accurately (gt95) predict the GFRfor sequential 6- 12- and 18-month intervals The mainlimitation of this study from the clinical point of view wasthat urine protein was not among the variables evaluated forthe prediction of GFR in 6 to 18 months

Conflict of Interests

The authors of the present study have no conflict of interests

Acknowledgment

This study was financially supported by Ahvaz JundishapurUniversity of Medical Sciences (Grant no u-93185)

References

[1] M El Nahas R Barsoum G Eknoyan et al ldquoThe globalchallenge of chronic kidney diseaserdquo Kidney International vol68 no 6 pp 2918ndash2929 2005

[2] C O Alebiosu andO E Ayodele ldquoThe global burden of chronickidney disease and the way forwardrdquo Ethnicity and Disease vol15 no 3 pp 418ndash423 2005

[3] MMahdavi-Mazdeh ldquoWhy do we need chronic kidney diseasescreening and which way to gordquo Iranian Journal of KidneyDiseases vol 4 no 4 pp 275ndash281 2010

[4] H R Khalkhaali I Hajizadeh A Kazemnezhad and A GMoghadam ldquoPrediction of kidney failure in patients withchronic renal transplant dysfunctionrdquo Iranian Journal of Epi-demiology vol 6 no 2 pp 25ndash31 2010

[5] M J Lysaght ldquoMaintenance dialysis population dynamicscurrent trends and long-term implicationsrdquo Journal of theAmerican Society of Nephrology vol 13 no 1 pp S37ndashS40 2001

[6] A S Fauci Harrisonrsquos Principles of Internal Medicine vol 2McGraw-Hill Medical New York NY USA 2008

[7] MMahdavi-Mazdeh Z N Hatmi and S Shahpari-Niri ldquoDoesa medical management program for CKD patients postpone


renal replacement therapy and mortality A 5-year-cohortstudyrdquo BMC Nephrology vol 13 no 1 article 138 2012

[8] O S Indridason I Thorsteinsdottir and R Palsson ldquoAdvancesin detection evaluation and management of chronic kidneydiseaserdquo Laeligknabladid vol 93 no 3 pp 201ndash207 2007

[9] G T Obrador M Mahdavi-Mazdeh and A J CollinsldquoEstablishing the Global Kidney Disease Prevention Network(KDPN) a position statement from the National Kidney Foun-dationrdquo American Journal of Kidney Diseases vol 57 no 3 pp361ndash370 2011

[10] L A Stevens J Coresh T Greene and A S Levey ldquoAssessingkidney functionmdashmeasured and estimated glomerular filtra-tion raterdquo The New England Journal of Medicine vol 354 no23 pp 2473ndash2483 2006

[11] A S Levey K-U Eckardt Y Tsukamoto et al ldquoDefinition andclassification of chronic kidney disease a position statementfrom Kidney Disease Improving Global Outcomes (KDIGO)rdquoKidney International vol 67 no 6 pp 2089ndash2100 2005

[12] P Rucci M Mandreoli D Gibertoni et al ldquoA clinical stratifica-tion tool for chronic kidney disease progression rate based onclassification tree analysisrdquoNephrologyDialysis Transplantationvol 29 no 3 pp 603ndash610 2014

[13] E A Aguilar H Ashraf M Frontini M Ruiz T M Reske andC Cefalu ldquoAn analysis of chronic kidney disease risk factors ina Louisiana nursing home population a cross-sectional studyrdquoJournal of the Louisiana State Medical Society vol 165 no 5 pp260ndash263 265ndash267 2013

[14] C-M Lin M-C Yang S-J Hwang and J-M Sung ldquoProgres-sion of stages 3b-5 chronic kidney diseasemdashpreliminary resultsof TaiwanNational Pre-ESRDDiseaseManagement Program inSouthern Taiwanrdquo Journal of the FormosanMedical Associationvol 112 no 12 pp 773ndash782 2013

[15] A M El Nahas and A K Bello ldquoChronic kidney disease theglobal challengerdquo The Lancet vol 365 no 9456 pp 331ndash3402005

[16] F Gaspari S Ferrari N Stucchi et al ldquoPerformance of differentprediction equations for estimating renal function in kidneytransplantationrdquoAmerican Journal of Transplantation vol 4 no11 pp 1826ndash1835 2004

[17] M E Brier P C Ray and J B Klein ldquoPrediction of delayedrenal allograft function using an artificial neural networkrdquoNephrology Dialysis Transplantation vol 18 no 12 pp 2655ndash2659 2003

[18] M Hussain S K Wajid A Elzaart and M Berbar ldquoA com-parison of SVM kernel functions for breast cancer detectionrdquoin Proceedings of the 8th International Conference on ComputerGraphics Imaging and Visualization (CGIV rsquo11) pp 145ndash150IEEE Singapore August 2011

[19] R Jang C Sun and E MizutaniNeuro-Fuzzy and Soft Compu-tation Prentice Hall Upper Saddle River NJ USA 1997

[20] A Sengur ldquoAn expert system based on principal componentanalysis artificial immune system and fuzzy k-NN for diagnosisof valvular heart diseasesrdquo Computers in Biology and Medicinevol 38 no 3 pp 329ndash338 2008

[21] JMWillems TVlasveldW P J DenElzen et al ldquoPerformanceof Cockcroft-Gault MDRD and CKD-EPI in estimating preva-lence of renal function and predicting survival in the oldest oldrdquoBMC Geriatrics vol 13 no 1 article 113 2013

[22] A Yadollahpour ldquoApplications of expert systems in manage-ment of chronic kidney disease a review of predicting tech-niquesrdquo Oriental Journal of Computer Science and Technologyvol 7 no 2 pp 306ndash315 2014

[23] T M A U T U S O M Ma and S Computer Local andpersonalised modelling for renal medical decision support system[PhD thesis] Auckland University of Technology 2012

[24] L Fan A S Levey V Gudnason et al ldquoComparing GFRestimating equations using cystatin C and creatinine in elderlyindividualsrdquo Journal of the American Society of Nephrology vol26 no 8 pp 1982ndash1989 2015

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


MEDIATORSINFLAMMATION

of


Behavioural Neurology

EndocrinologyInternational Journal of



Disease Markers


BioMed Research International

OncologyJournal of



Oxidative Medicine and Cellular Longevity


PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of



Computational and Mathematical Methods in Medicine

OphthalmologyJournal of


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Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom


predict progression to ESRD in CKD stages [9 12] Howeverthey cannot quantitatively predict the variations of glomeru-lar filtration rate (GFR) in the patients Aguilar et al evaluatedthe effective factors associated with CKD on 103 patients withmean age of 708plusmn13 yearsThe CKD associated factors wereage gt65 years old male sex positive history of cardiovasculardisease anemia and obesity (BMI gt 30) Their findingsshowed that age and anemia were the strongest factors associ-ated with CKD in their population [13] There have been sev-eral studies on the GFR variations among different popula-tions of CKD patients [9 10 14ndash16] In this regard intelligentand machine learning methods have been increasingly usedin the context of health and disease forecasting Gaspari et al(2004) compared renal function derived from 12 predictionequations with GFR measurement by plasma iohexol clear-ance as reference method in a group of 81 renal transplantrecipients [16] They concluded that all models overestimaterenal function However Modification of Diet in RenalDisease (MDRD) and Walser formulas showed the best per-formance with the lowest bias and the highest precision [16]Brier et al (2003) compared artificial neural networks withtraditional logistical regression in the prediction of delayedgraft function (DGF) in kidney transplant patients Theycompared the results of neural network with logistic regres-sion method and founded more sensitivity of logistic regres-sion in the prediction of no DGF (91 versus 70) while theneural network was more sensitive to the prediction of eyesfor DGF (56 versus 37) [17] Hussain et al (2011) proposedan intelligent tool for detecting breast cancer using supportvector machines (SVM) They compared the performanceof the proposed method with other classification methodsAccordingly SVM improved the diagnosis of the disease [18]

In recent years fuzzy intelligent methods especiallyfuzzy expert systems have been increasingly used to predictdifferent diseases It seems that employing this method alongwith the clinical tools for diagnosis of different diseases andconditions may drastically reduce diagnostic errors Fuzzyexpert technique is more accurate than machine learningtechniques

Adaptive neurofuzzy inference system (ANFIS) is a learn-ing based system based on the neural networks conceptsThe ANFIS network used in the present study is based onthe model proposed by Jang et al [19] This is a learnernetwork equivalent to Takagi-Sugeno fuzzy inference systemLearning in this network is continuous update of the networkparameters Factors of layers I and IV are of learner typethat respectively determinemembership functions and first-order estimated function The ANFIS training algorithm is ahybrid algorithm in which ordinary least squares algorithmis used to update coefficients of output functions (119891

119894) while

error back propagation algorithm is used to update funda-mental factors of the system [19 20]

If we canmodel and predict the renal functionworseningwe can effectively manage this disorder In this regard anappropriate parameter should be considered as the markerof disease worsening The GFR is the only reliable parameterof the renal function and progression of CKD [16] TheCockroft-Gault (C-G) MDRD and chronic kidney dis-ease epidemiology collaboration (CKD-EPI) equations are

the most common and validated equations to calculate GFR[21] For different age and racial groups these equations yielddifferent accuracy in estimating renal function [21] Accord-ing to the clinical measurements (independent physiologicalparameters) and clinical outcomes when GFR reaches lessthan 15 cckgmin173m2 renal replacement therapy (RRT)including dialysis or transplant is necessary for the patientsurvival If GFR variation is predicted in a CKD patient wecan appropriately predict the time to reach GFR thresholdvalue of 15 cckgmin173m2 In other words the time forrenal replacement therapy is predicted In this study speedof GFR decrease in CKD patients has been predicted basedon the follow-up of the CKDpatients during the study To ourknowledge there has not been any efficient method proposedfor predicting the timeframe of CKDworsening in individualcases [22] Furthermore fuzzy intelligent techniques havenot yet been used to predict renal function worseningThe present study proposes an ANFIS based model forpredicting the renal failure timeframe of CKD based on a10-year real clinical data The main objective is to provide apractical and reliablemethodwith acceptable accuracy to findunderpinning of a decision support system in health care andto support clinical decision making systems

2 Materials and Methods

21 Data Collection All the data of the present studywere theclinical records of a cohort study of newly diagnosed CKDpatients who were serially admitted to the Clinic of Nephrol-ogy Imam Khomeini Hospital (Tehran Iran) during Octo-ber 2002ndashOctober 2011 The inclusion criteria for CKD def-inition included small sized kidney in ultrasound images orGFR less than 60 cckgmin173m2 for more than 3 monthsThe datasets were built using the clinical and laboratory dataof different parameters All the procedures of the study wereapproved by the ethics committee of Tehran University ofMedical Sciences that completely coincide with the Decla-ration of Helsinki Ethical Principles for Medical ResearchInvolving Human Subjects The written consent form wasobtained from each patient to participate in the study

The patients were divided into two groups according tothe pattern of their adherence to follow-up schedule in theclinic A total of 465 CKD patients were enrolled in the studyThe test group consisted of 389 patients who continuously (atleast every six months) were visited in the clinic The controlgroup consisted of 76 patients who did not regularly followtheir visit schedule in the clinic but their visits had lasted atleast one year The details of demographic data and clinicalmeasurements of the patients are presented in Table 1

22 Input Selection The present study used ANFIS neuralnetworks to predict GFR values and compared the accuracyof the method At each visit patientrsquos demographic dataweight blood pressure blood sample test variables includingserum creatinine levels fasting plasma glucose levels lipidprofile calcium phosphorus hemoglobin and other param-eters were monitored The appropriate treatments for bloodpressure bone mineral metabolism indices and hemoglobin







(119905+119901)) at 6-













1 02505Sex(119905)

2 00706Age(119905)

3 minus01043dbp(119905)

4 07145Cr(119905)

5 00322Ca(119905)

6 minus02224P(119905)


(119905)8 01089

Weight(119905)

9 08120GFR(119905)

10 05196





3 Results




Inputs

Underlying Blood

ANFIS

GFR(t)

Phosphorus(t)

(t)

Calcium(t)

Creatinine(t)

(t)Age(t)

disease(t)

Sex(t)Weight(t)

GFR(t+p)

pressure

Uric acid








(119905)



Input 1 (in1)

Deg

ree o

f mem

bers

hip



0 01 02 03 04 05 06 07 08 09 1

0

02

04

06

08

1







Input 2 (in2)

Deg

ree o

f mem

bers

hip

0

02

04

06

08

1

1 15 2 25 3 35 4 45 5 55




10 20 30 40 50 60Input 3 (in3)

Deg

ree o

f mem

bers

hip

0

02

04

06

08

1




10 20 30 40 50 60 70Input 4 (in4)

Deg

ree o

f mem

bers

hip

0

02

04

06

08

1




6-month period

0 100 200 300 400 500 6000

20

40

60

80

100

120

Sample number

Training data


GFR

(t+1)

(cc

min

)



0 50 100 150 200 2500

10203040506070

Sample number

Testing data


GFR

(t+1)

(cc

min

)




MSE =sum119873

119894=1(119910119894minus 119894)2

119873

MAE =sum119873

119894=1

1003816100381610038161003816119910119894 minus 119894

1003816100381610038161003816

119873

NMSE =sum119873

119894=1(119910119894minus 119894)2

sum119873

119894=1(119910119894)2times 100

(1)




minus100minus50

050

100

Disease

555445

335225

115 0 01 0203 04

05 0607 08

09 1

Dbp

GFR

(t+1)



1020

3040

5060

70

50

100

150

200

250

WeightDisease

002

0406

081

GFR

(t+1)

Figure 10 GFR(119905+1)


1030

5070

90

0DiseaseGFR

minus1000

minus800

minus600

minus400

minus200

0

02 0103

05 04060708091

GFR

(t+1)

Figure 11 GFR(119905+1)


2040

6080

100

12

34

5

Weight


0100

Dbp

GFR

(t+1)

Figure 12 GFR(119905+1)


2040

60

54

32

1

809070

5030

10

100

minus500

minus400

minus300

minus200

minus100

0

100

Dbp GFR

1525

3545

55

GFR

(t+1)

Figure 13 GFR(119905+1)


20406080

100 20406080

100

minus500

minus400

minus300

minus200

minus100

0

100

WeightGFR

GFR

(t+1)

Figure 14 GFR(119905+1)



0 100 200 300 400 5000

20

40

60

80

120

100

Sample number

Training data


GFR

(t+2)

(cc

min

)



0 50 100 150 200 2500

10

20

30

40

50

60

70

Sample number

Testing data


GFR

(t+2)

(cc

min

)









0 50 100 150 200 250 300 350 4000

20

40

60

80

100

120

Sample number

Training data


GFR

(t+3)

(cc

min

)



0 20 40 60 80 100 120 140 1600

20

40

60

80

Sample number

Testing data


GFR

(t+3)

(cc

min

)











5 Discussion





6 Conclusion




Acknowledgment


References
































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of






















(119905+119901)) at 6-













1 02505Sex(119905)

2 00706Age(119905)

3 minus01043dbp(119905)

4 07145Cr(119905)

5 00322Ca(119905)

6 minus02224P(119905)


(119905)8 01089

Weight(119905)

9 08120GFR(119905)

10 05196





3 Results




Inputs

Underlying Blood

ANFIS

GFR(t)

Phosphorus(t)

(t)

Calcium(t)

Creatinine(t)

(t)Age(t)

disease(t)

Sex(t)Weight(t)

GFR(t+p)

pressure

Uric acid








(119905)



Input 1 (in1)

Deg

ree o

f mem

bers

hip



0 01 02 03 04 05 06 07 08 09 1

0

02

04

06

08

1







Input 2 (in2)

Deg

ree o

f mem

bers

hip

0

02

04

06

08

1

1 15 2 25 3 35 4 45 5 55




10 20 30 40 50 60Input 3 (in3)

Deg

ree o

f mem

bers

hip

0

02

04

06

08

1




10 20 30 40 50 60 70Input 4 (in4)

Deg

ree o

f mem

bers

hip

0

02

04

06

08

1




6-month period

0 100 200 300 400 500 6000

20

40

60

80

100

120

Sample number

Training data


GFR

(t+1)

(cc

min

)



0 50 100 150 200 2500

10203040506070

Sample number

Testing data


GFR

(t+1)

(cc

min

)




MSE =sum119873

119894=1(119910119894minus 119894)2

119873

MAE =sum119873

119894=1

1003816100381610038161003816119910119894 minus 119894

1003816100381610038161003816

119873

NMSE =sum119873

119894=1(119910119894minus 119894)2

sum119873

119894=1(119910119894)2times 100

(1)




minus100minus50

050

100

Disease

555445

335225

115 0 01 0203 04

05 0607 08

09 1

Dbp

GFR

(t+1)



1020

3040

5060

70

50

100

150

200

250

WeightDisease

002

0406

081

GFR

(t+1)

Figure 10 GFR(119905+1)


1030

5070

90

0DiseaseGFR

minus1000

minus800

minus600

minus400

minus200

0

02 0103

05 04060708091

GFR

(t+1)

Figure 11 GFR(119905+1)


2040

6080

100

12

34

5

Weight


0100

Dbp

GFR

(t+1)

Figure 12 GFR(119905+1)


2040

60

54

32

1

809070

5030

10

100

minus500

minus400

minus300

minus200

minus100

0

100

Dbp GFR

1525

3545

55

GFR

(t+1)

Figure 13 GFR(119905+1)


20406080

100 20406080

100

minus500

minus400

minus300

minus200

minus100

0

100

WeightGFR

GFR

(t+1)

Figure 14 GFR(119905+1)



0 100 200 300 400 5000

20

40

60

80

120

100

Sample number

Training data


GFR

(t+2)

(cc

min

)



0 50 100 150 200 2500

10

20

30

40

50

60

70

Sample number

Testing data


GFR

(t+2)

(cc

min

)









0 50 100 150 200 250 300 350 4000

20

40

60

80

100

120

Sample number

Training data


GFR

(t+3)

(cc

min

)



0 20 40 60 80 100 120 140 1600

20

40

60

80

Sample number

Testing data


GFR

(t+3)

(cc

min

)











5 Discussion





6 Conclusion




Acknowledgment


References
































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















Inputs

Underlying Blood

ANFIS

GFR(t)

Phosphorus(t)

(t)

Calcium(t)

Creatinine(t)

(t)Age(t)

disease(t)

Sex(t)Weight(t)

GFR(t+p)

pressure

Uric acid








(119905)



Input 1 (in1)

Deg

ree o

f mem

bers

hip



0 01 02 03 04 05 06 07 08 09 1

0

02

04

06

08

1







Input 2 (in2)

Deg

ree o

f mem

bers

hip

0

02

04

06

08

1

1 15 2 25 3 35 4 45 5 55




10 20 30 40 50 60Input 3 (in3)

Deg

ree o

f mem

bers

hip

0

02

04

06

08

1




10 20 30 40 50 60 70Input 4 (in4)

Deg

ree o

f mem

bers

hip

0

02

04

06

08

1




6-month period

0 100 200 300 400 500 6000

20

40

60

80

100

120

Sample number

Training data


GFR

(t+1)

(cc

min

)



0 50 100 150 200 2500

10203040506070

Sample number

Testing data


GFR

(t+1)

(cc

min

)




MSE =sum119873

119894=1(119910119894minus 119894)2

119873

MAE =sum119873

119894=1

1003816100381610038161003816119910119894 minus 119894

1003816100381610038161003816

119873

NMSE =sum119873

119894=1(119910119894minus 119894)2

sum119873

119894=1(119910119894)2times 100

(1)




minus100minus50

050

100

Disease

555445

335225

115 0 01 0203 04

05 0607 08

09 1

Dbp

GFR

(t+1)



1020

3040

5060

70

50

100

150

200

250

WeightDisease

002

0406

081

GFR

(t+1)

Figure 10 GFR(119905+1)


1030

5070

90

0DiseaseGFR

minus1000

minus800

minus600

minus400

minus200

0

02 0103

05 04060708091

GFR

(t+1)

Figure 11 GFR(119905+1)


2040

6080

100

12

34

5

Weight


0100

Dbp

GFR

(t+1)

Figure 12 GFR(119905+1)


2040

60

54

32

1

809070

5030

10

100

minus500

minus400

minus300

minus200

minus100

0

100

Dbp GFR

1525

3545

55

GFR

(t+1)

Figure 13 GFR(119905+1)


20406080

100 20406080

100

minus500

minus400

minus300

minus200

minus100

0

100

WeightGFR

GFR

(t+1)

Figure 14 GFR(119905+1)



0 100 200 300 400 5000

20

40

60

80

120

100

Sample number

Training data


GFR

(t+2)

(cc

min

)



0 50 100 150 200 2500

10

20

30

40

50

60

70

Sample number

Testing data


GFR

(t+2)

(cc

min

)









0 50 100 150 200 250 300 350 4000

20

40

60

80

100

120

Sample number

Training data


GFR

(t+3)

(cc

min

)



0 20 40 60 80 100 120 140 1600

20

40

60

80

Sample number

Testing data


GFR

(t+3)

(cc

min

)











5 Discussion





6 Conclusion




Acknowledgment


References
































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















Input 2 (in2)

Deg

ree o

f mem

bers

hip

0

02

04

06

08

1

1 15 2 25 3 35 4 45 5 55




10 20 30 40 50 60Input 3 (in3)

Deg

ree o

f mem

bers

hip

0

02

04

06

08

1




10 20 30 40 50 60 70Input 4 (in4)

Deg

ree o

f mem

bers

hip

0

02

04

06

08

1




6-month period

0 100 200 300 400 500 6000

20

40

60

80

100

120

Sample number

Training data


GFR

(t+1)

(cc

min

)



0 50 100 150 200 2500

10203040506070

Sample number

Testing data


GFR

(t+1)

(cc

min

)




MSE =sum119873

119894=1(119910119894minus 119894)2

119873

MAE =sum119873

119894=1

1003816100381610038161003816119910119894 minus 119894

1003816100381610038161003816

119873

NMSE =sum119873

119894=1(119910119894minus 119894)2

sum119873

119894=1(119910119894)2times 100

(1)




minus100minus50

050

100

Disease

555445

335225

115 0 01 0203 04

05 0607 08

09 1

Dbp

GFR

(t+1)



1020

3040

5060

70

50

100

150

200

250

WeightDisease

002

0406

081

GFR

(t+1)

Figure 10 GFR(119905+1)


1030

5070

90

0DiseaseGFR

minus1000

minus800

minus600

minus400

minus200

0

02 0103

05 04060708091

GFR

(t+1)

Figure 11 GFR(119905+1)


2040

6080

100

12

34

5

Weight


0100

Dbp

GFR

(t+1)

Figure 12 GFR(119905+1)


2040

60

54

32

1

809070

5030

10

100

minus500

minus400

minus300

minus200

minus100

0

100

Dbp GFR

1525

3545

55

GFR

(t+1)

Figure 13 GFR(119905+1)


20406080

100 20406080

100

minus500

minus400

minus300

minus200

minus100

0

100

WeightGFR

GFR

(t+1)

Figure 14 GFR(119905+1)



0 100 200 300 400 5000

20

40

60

80

120

100

Sample number

Training data


GFR

(t+2)

(cc

min

)



0 50 100 150 200 2500

10

20

30

40

50

60

70

Sample number

Testing data


GFR

(t+2)

(cc

min

)









0 50 100 150 200 250 300 350 4000

20

40

60

80

100

120

Sample number

Training data


GFR

(t+3)

(cc

min

)



0 20 40 60 80 100 120 140 1600

20

40

60

80

Sample number

Testing data


GFR

(t+3)

(cc

min

)











5 Discussion





6 Conclusion




Acknowledgment


References
































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















minus100minus50

050

100

Disease

555445

335225

115 0 01 0203 04

05 0607 08

09 1

Dbp

GFR

(t+1)



1020

3040

5060

70

50

100

150

200

250

WeightDisease

002

0406

081

GFR

(t+1)

Figure 10 GFR(119905+1)


1030

5070

90

0DiseaseGFR

minus1000

minus800

minus600

minus400

minus200

0

02 0103

05 04060708091

GFR

(t+1)

Figure 11 GFR(119905+1)


2040

6080

100

12

34

5

Weight


0100

Dbp

GFR

(t+1)

Figure 12 GFR(119905+1)


2040

60

54

32

1

809070

5030

10

100

minus500

minus400

minus300

minus200

minus100

0

100

Dbp GFR

1525

3545

55

GFR

(t+1)

Figure 13 GFR(119905+1)


20406080

100 20406080

100

minus500

minus400

minus300

minus200

minus100

0

100

WeightGFR

GFR

(t+1)

Figure 14 GFR(119905+1)



0 100 200 300 400 5000

20

40

60

80

120

100

Sample number

Training data


GFR

(t+2)

(cc

min

)



0 50 100 150 200 2500

10

20

30

40

50

60

70

Sample number

Testing data


GFR

(t+2)

(cc

min

)









0 50 100 150 200 250 300 350 4000

20

40

60

80

100

120

Sample number

Training data


GFR

(t+3)

(cc

min

)



0 20 40 60 80 100 120 140 1600

20

40

60

80

Sample number

Testing data


GFR

(t+3)

(cc

min

)











5 Discussion





6 Conclusion




Acknowledgment


References
































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















0 100 200 300 400 5000

20

40

60

80

120

100

Sample number

Training data


GFR

(t+2)

(cc

min

)



0 50 100 150 200 2500

10

20

30

40

50

60

70

Sample number

Testing data


GFR

(t+2)

(cc

min

)









0 50 100 150 200 250 300 350 4000

20

40

60

80

100

120

Sample number

Training data


GFR

(t+3)

(cc

min

)



0 20 40 60 80 100 120 140 1600

20

40

60

80

Sample number

Testing data


GFR

(t+3)

(cc

min

)











5 Discussion





6 Conclusion




Acknowledgment


References
































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of




















5 Discussion





6 Conclusion




Acknowledgment


References
































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of








































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of





















of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of
















Documents

Research Article Predicting Renal Failure Progression in