Your SlideShare is downloading. ×
0
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
P.M.Pardalos - On Big Data Application
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

P.M.Pardalos - On Big Data Application

518

Published on

Published in: Technology, Economy & Finance
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
518
On Slideshare
0
From Embeds
0
Number of Embeds
3
Actions
Shares
0
Downloads
9
Comments
0
Likes
0
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. Big DataCase StudyProposed ModelResults and ConclusionsOn Big Data ApplicationsP. M. Pardalos1, 21Center for Applied OptimizationDepartment of Industrial and Systems EngineeringUniversity of Florida2Laboratory of Algorithms and Technologies for Networks Analysis (LATNA)National Research University Higher School of EconomicsItForum, 2013P. M. Pardalos, On Big Data Applications
  • 2. Big DataCase StudyProposed ModelResults and ConclusionsP. M. Pardalos, On Big Data Applications
  • 3. Big DataCase StudyProposed ModelResults and ConclusionsHow big will the data be tomorrow?Cisco: Global ’Net Traffic to Surpass 1 Zettabyte in 2016http://cacm.acm.org/news/150041-cisco-global-net-traffic-to-surpass-1-zettabyte-in-2016/fulltextP. M. Pardalos, On Big Data Applications
  • 4. Big DataCase StudyProposed ModelResults and ConclusionsWhat is BigData?The proliferation of massive datasets brings with it a seriesof special computational challenges.This data avalanche arises in a wide range of scientific andcommercial applications.With advances in computer and information technologies,many of these challenges are beginning to be addressed.P. M. Pardalos, On Big Data Applications
  • 5. Big DataCase StudyProposed ModelResults and ConclusionsHandBook of Massive DatasetsHandbook of Massive Data Sets,co-editors: J. Abello, P.M. Pardalos,and M. Resende, Kluwer AcademicPublishers, (2002).P. M. Pardalos, On Big Data Applications
  • 6. Big DataCase StudyProposed ModelResults and ConclusionsData Mining: the practice of searching through largeamounts of computerized data to find useful patterns ortrends.Optimization: An act, process, or methodology of makingsomething (as a design, system, or decision) as fullyperfect, functional, or effective as possible; specifically :the mathematical procedures (as finding the maximum of afunction) involved in this.P. M. Pardalos, On Big Data Applications
  • 7. Big DataCase StudyProposed ModelResults and ConclusionsHard drive CostP. M. Pardalos, On Big Data Applications
  • 8. Big DataCase StudyProposed ModelResults and ConclusionsHard drive CapacityP. M. Pardalos, On Big Data Applications
  • 9. Big DataCase StudyProposed ModelResults and ConclusionsProcessing powerP. M. Pardalos, On Big Data Applications
  • 10. Big DataCase StudyProposed ModelResults and ConclusionsSome Examples of Massive DatasetsInternet DataWeather DataTelecommunications DataMedical DataDemographics DataFinancial DataP. M. Pardalos, On Big Data Applications
  • 11. Big DataCase StudyProposed ModelResults and ConclusionsHandling Massive DatasetsNew computing technologies are needed to handle massivedatasetsInput-Output Parallel SystemsExternal Memory AlgorithmsQuantum ComputingP. M. Pardalos, On Big Data Applications
  • 12. Big DataCase StudyProposed ModelResults and ConclusionsStudy ObjectiveAn example in biomedicineAcute Kidney Injury (AKI) is one of common complicationsin post-operative patients.The in-hospital mortality rate for patients with AKI may beas high as 60%.An elevated serum creatinine (sCr) level in blood iscommonly recognized as an indicator of AKI.The degree to which patterns of sCr change areassociated with in-hospital mortality is unknown.P. M. Pardalos, On Big Data Applications
  • 13. Big DataCase StudyProposed ModelResults and ConclusionsStudy ObjectiveStudy OutlineObjectives:To develop a comprehensive model for assessing themortality risk in post-operative patientsTo establish a quantitative relationship between sCr patternand mortality riskResults:A probabilistic model was designed to assess mortality riskin post-operative patientsThe model provided high discriminative capacity andaccuracy (ROC = 0.92)A quantitative association between sCr time series andmortality risk was establishedSimple and informative sCr risk factors were derivedP. M. Pardalos, On Big Data Applications
  • 14. Big DataCase StudyProposed ModelResults and ConclusionsStudy ObjectiveData SetWe performed a retrospective study involving patientsadmitted to Shands Hospital (Gainesville, FL) from 2000through 2010.For each patient who underwent a surgery detailed clinicaland outcome data were collected.The analysis included 60,074 patients who underwentin-patient surgery at Shands Hospital during a 10-yearsperiod.P. M. Pardalos, On Big Data Applications
  • 15. Big DataCase StudyProposed ModelResults and ConclusionsProbabilistic score for mortality riskRisk Factors EstimationCreatinine time series analysisLogistic FunctionProbabilistic score 1P(C = 1|X = x) = 1 + exp w0 +mi=1wigi(xi)−1; (1)C ∈ {0, 1} is an outcome;X = (X1, . . . , Xm) - the risk factors;gi - nonlinear function associated with the ith factorw0 = ln P(C = 1)/P(C = 0) is the a priori log odds ratio.{wi}, i > 0 - weights indicating importance of the risk factors1S. Saria, A. Rajani,J. Gould,D. Koller,A. Penn, Integration of EarlyPhysiological Responses Predicts Later Illness Severity in Preterm Infants,Sci Transl Med, 2010P. M. Pardalos, On Big Data Applications
  • 16. Big DataCase StudyProposed ModelResults and ConclusionsProbabilistic score for mortality riskRisk Factors EstimationCreatinine time series analysisNonlinear Risk Factors EstimationFrom the probabilistic score equation we can derivew0 +mi=1wi · gi(xi) = logP(X = x|C = 0)P(X = x|C = 1)+ logP(C = 0)P(C = 1)Under assumption of risk factors independence:w0 +mi=1wi · gi(xi) =mi=1logP(Xi = xi|C = 0)P(Xi = xi|C = 1)+ logP(C = 0)P(C = 1).For continuous factors P(Xi = xi|C) impliesP(Xi ∈ [xi − ε, xi + ε]|C) where ε is sufficiently smallP. M. Pardalos, On Big Data Applications
  • 17. Big DataCase StudyProposed ModelResults and ConclusionsProbabilistic score for mortality riskRisk Factors EstimationCreatinine time series analysisModel Parametersmaxwk∈{0,1} j: Cj =kln P(Cj= k|Xi = xji , . . . , Xi = xjm);j denotes patients in the data set;Cj ∈ {0, 1} - outcome for the jth patient;xji - value of ith risk factor for the jth patient.We solved this problem approximately with interior pointmethod implemented in MATLABP. M. Pardalos, On Big Data Applications
  • 18. Big DataCase StudyProposed ModelResults and ConclusionsProbabilistic score for mortality riskRisk Factors EstimationCreatinine time series analysisNonlinear risk functionsWe getgi(xi) = lnP(Xi = xi|C = 0)P(Xi = xi|C = 1);w0 = lnP(C = 1)P(C = 0);wi = 1, i = 1, . . . , m.The probabilities P(Xi = xi|C), i = 1, . . . , m were learnedfrom the data using maximum likelihood principle.P. M. Pardalos, On Big Data Applications
  • 19. Big DataCase StudyProposed ModelResults and ConclusionsProbabilistic score for mortality riskRisk Factors EstimationCreatinine time series analysisDiscrete risk factors estimationFor discrete valued factorsgi(x) = ln#{j : Cj = 1, xji = x}#{j : Cj = 1}#{j : Cj = 0}#{j : Cj = 1, xji = x}.P. M. Pardalos, On Big Data Applications
  • 20. Big DataCase StudyProposed ModelResults and ConclusionsProbabilistic score for mortality riskRisk Factors EstimationCreatinine time series analysisContinuous Risk Factors EstimationFor continuous factors we definedgi(x) = lnf0i (x)f1i (x),fki (x) = ϕ∗(x − h∗, θ∗),{ϕ∗, h∗, θ∗} = arg maxϕ∈Φ,θ,hLki (ϕ, θ, h),Lki (ϕ, θ, h) =j:Cj =klnϕ(xji − h, θ)Fϕ(l2i , θ) − Fϕ(l1i , θ).P. M. Pardalos, On Big Data Applications
  • 21. Big DataCase StudyProposed ModelResults and ConclusionsProbabilistic score for mortality riskRisk Factors EstimationCreatinine time series analysisContinuous Risk Factors Estimation1 2 3 4 5 6 7050100150200maxCr/minCr valueHistogramofvalues,C=1Observed valuesLearned Inverse Gaussian distribution1 2 3 4 5 6 700.511.52x 104maxCr/minCr valueHistogramofvalues,C=0Observed valuesLearned Loglogistic distribution1 2 3 4 5 6 7050100150200recentCr/minCr valueHistogramofvalues,C=1Histogram of observed valuesLearned Lognormal distribution1 2 3 4 5 6 70123x 104recentCr/minCr valueHistogramofvalues,C=0Histogram of observed valuesLearned LogLogistic distributionP. M. Pardalos, On Big Data Applications
  • 22. Big DataCase StudyProposed ModelResults and ConclusionsProbabilistic score for mortality riskRisk Factors EstimationCreatinine time series analysisAge Risk Factor20 40 60 80 1000204060AgeDistributionofvalues,C=120 40 60 80 1000100020003000AgeDistributionofvalues,C=0P. M. Pardalos, On Big Data Applications
  • 23. Big DataCase StudyProposed ModelResults and ConclusionsProbabilistic score for mortality riskRisk Factors EstimationCreatinine time series analysisWhich creatinine (Cr) characteristics are ”good”?Absolute Cr value is not very informative(maximal Cr value)/(minimal Cr value) works goodRecent Cr value is importantP. M. Pardalos, On Big Data Applications
  • 24. Big DataCase StudyProposed ModelResults and ConclusionsProbabilistic score for mortality riskRisk Factors EstimationCreatinine time series analysisCr plots in patients with elevated Cr levelP. M. Pardalos, On Big Data Applications
  • 25. Big DataCase StudyProposed ModelResults and ConclusionsProbabilistic score for mortality riskRisk Factors EstimationCreatinine time series analysisOur SpeculationsThe risk is defined by a function R(RC, OD),RC stands for recent conditionOD stands for overall damage suffered during AKIOne should look for features describing these two factorsP. M. Pardalos, On Big Data Applications
  • 26. Big DataCase StudyProposed ModelResults and ConclusionsResulting nonlinear risk functionsP. M. Pardalos, On Big Data Applications
  • 27. Big DataCase StudyProposed ModelResults and ConclusionsClassification accuracy evaluation70/30 cross-validation analysis has been performedRandom split into 70% training subset and 30% testingsubsetThe average over 100 runs results are reportedP. M. Pardalos, On Big Data Applications
  • 28. Big DataCase StudyProposed ModelResults and ConclusionsLearned risk factors weights0.2 0.4 0.6 0.8 1procedureadmission_typedoctormorbidityagemaxCr/minCrrecentCr/minCrOddsratio20 30 40 50 60 70 80 90024Age1 1.5 2 2.5 30510recentCr/minCr value1 1.5 2 2.5 3012maxCr/minCr valueP. M. Pardalos, On Big Data Applications
  • 29. Big DataCase StudyProposed ModelResults and ConclusionsThe odds ratio based on Cr factors1.5 2 2.5 31.522.53maxCr/minCr valuerecentCr/minCrvalue2468101214P. M. Pardalos, On Big Data Applications
  • 30. Big DataCase StudyProposed ModelResults and ConclusionsThe Resulting ROC Curves0 0.2 0.4 0.6 0.8 100.10.20.30.40.50.60.70.80.91False positive rate (1 − specificity)Truepositiverate(sensitivity)Both Cr factors, AUC = 0.85maxCr/minCr, AUC = 0.84recentCr/minCr, 0.760 0.2 0.4 0.6 0.8 100.10.20.30.40.50.60.70.80.91False positive rate (1 − specificity)Truepositiverate(sensitivity)Preop. + both Cr factors, AUC = 0.92Preop. + maxCr/minCr, AUC = 0.91Preop. + recentCr/minCr, AUC = 0.91Preop. only, AUC = 0.83P. M. Pardalos, On Big Data Applications
  • 31. Big DataCase StudyProposed ModelResults and ConclusionsCr time series patternsadmission discharge1234Odds ratios: No recoverytimesCr/minCr1.79 (1.7,1.85)6.46 (6.04,6.91)21.39 (19.42,23.5)admission discharge1234Odds ratios: Partial recoverytimesCr/minCr0.79 (0.75,0.83)2.34 (2.26,2.49)8.3 (7.85,9.04)admission discharge1234Odds ratios: Full recoverytimesCr/minCr0.48 (0.44,0.53)0.63 (0.57,0.73)0.81 (0.71,0.99)admission discharge1234Odds ratios: Reference patternstimesCr/minCr1 (0.88,1.22)1.121 (0.93,1.12)1.241 (0.96,1.03) 1.320.22 (0.17,0.25)P. M. Pardalos, On Big Data Applications
  • 32. Big DataCase StudyProposed ModelResults and ConclusionsModel Calibration20 40 60 80 10000.10.20.30.40.50.60.7PercentileMortalityriskProbabilistic model score compared to mortality risks derived from the dataP. M. Pardalos, On Big Data Applications
  • 33. Big DataCase StudyProposed ModelResults and ConclusionsRisk factors included Prob. model AUC (95% CI)Preop. 0.835 (0.817-0.854)Hosmer-Lemeshow statistics s = 95.06; p = 0.57Preop. + maxCr/minCr 0.900 (0.888-0.911)Hosmer-Lemeshow statistics s = 84.33; p = 0.84Preop. + recentCr/minCr 0.910 (0.897-0.923)Hosmer-Lemeshow statistics s = 72.19; p = 0.98Preop. + both sCr factors 0.917 (0.906-0.929)Hosmer-Lemeshow statistics s = 68.94; p = 0.99maxCr/minCr only 0.834 (0.816-0.852)Hosmer-Lemeshow statistics s = 1,818; p = 0recentCr/minCr only 0.791 (0.764-0.818)Hosmer-Lemeshow statistics s = 112.88; p = 0.14both sCr factors 0.855 (0.837-0.873)Hosmer-Lemeshow statistics s = 137.31; p = 0.01P. M. Pardalos, On Big Data Applications
  • 34. Big DataCase StudyProposed ModelResults and ConclusionsConclusionsRelatively high classification accuracy was obtained usingprobabilistic modelCreatinine time series do provide complimentaryinformation on patient’s risk of deathPresumably AKI effect on risk of death depends on twofactors:Kidney recent conditionOverall kidney damage suffered since surgeryP. M. Pardalos, On Big Data Applications
  • 35. Big DataCase StudyProposed ModelResults and ConclusionsThe EndThank you!P. M. Pardalos, On Big Data Applications

×