Abstract
Models for predicting the risk of cardiovascular (CV) events based on individual patient characteristics are important tools for managing patient care. Most current and commonly used risk prediction models have been built from carefully selected epidemiological cohorts. However, the homogeneity and limited size of such cohorts restrict the predictive power and generalizability of these risk models to other populations. Electronic health data (EHD) from large health care systems provide access to data on large, heterogeneous, and contemporaneous patient populations. The unique features and challenges of EHD, including missing risk factor information, non-linear relationships between risk factors and CV event outcomes, and differing effects from different patient subgroups, demand novel machine learning approaches to risk model development. In this paper, we present a machine learning approach based on Bayesian networks trained on EHD to predict the probability of having a CV event within 5 years. In such data, event status may be unknown for some individuals, as the event time is right-censored due to disenrollment and incomplete follow-up. Since many traditional data mining methods are not well-suited for such data, we describe how to modify both modeling and assessment techniques to account for censored observation times. We show that our approach can lead to better predictive performance than the Cox proportional hazards model (i.e., a regression-based approach commonly used for censored, time-to-event data) or a Bayesian network with ad hoc approaches to right-censoring. Our techniques are motivated by and illustrated on data from a large US Midwestern health care system.
Similar content being viewed by others
References
Agaku IT, King BA, Dube SR (2011) Vital signs: current cigarette smoking among adults aged 18 years-united states, 2005–2010. MMWR Morb Mortal Wkly Rep 60(35):1207
Andreassen S, Riekehr C, Kristensen B, Schonheyder H, Leibovici L (1999) Using probabilistic and decision-theoretic methods in treatment and prognosis modeling. Artif Intell Med 15(2):121–134
Assmann G, Cullen P, Schulte H (2002) Simple scoring scheme for calculating the risk of acute coronary events based on the 10-year follow-up of the prospective cardiovascular Munster (PROCAM) study. Circulation 105(7):900–900
Bang H, Tsiatis AA (2000) Estimating medical costs with censored data. Biometrika 87(2):329–343
Bang H, Tsiatis AA (2002) Median regression with censored cost data. Biometrics 58(3):643–649
Bilmes JA (1998) A gentle tutorial of the em algorithm and its application to parameter estimation for gaussian mixture and hidden markov models. Technical report. University of California, Berkeley
Blanco R, Inza M, Merino M, Quiroga J, Larranaga P (2005) Feature selection in Bayesian classifiers for the prognosis of survival of cirrhotic patients treated with TIPS. J Biomed Inform 38(5):376–388
Buckley J, James I (1979) Linear-regression with censored data. Biometrika 66(3):429–436
Clarke PM, Gray AM, Briggs A, Farmer AJ, Fenn P, Stevens RJ, Matthews DR, Stratton IM, Holman RR (2004) A model to estimate the lifetime health outcomes of patients with type 2 diabetes: the United Kingdom Prospective Diabetes Study (UKPDS) outcomes model. Diabetologia 47(10):1747–1759
Collins GS, Altman DG (2009) An independent external validation and evaluation of QRISK cardiovascular risk prediction: a prospective open cohort study. Br Med J 339:b2584
Colombet I, Ruelland A, Chatellier G, Gueyffier F, Degoulet P, Jaulent MC (2000) Models to predict cardiovascular risk: comparison of CART, multilayer perceptron and logistic regression. In: Proceedings of the AMIA symposium, American Medical Informatics Association, pp 156–160
Conroy RM, Pyorala K, Fitzgerald AP, Sans S, Menotti A, DeBacker G, DeBacquer D, Ducimetiere P, Jousilahti P, Keil U, Njolstad I, Oganov RG, Thomsen T, Tunstall-Pedoe H, Tverdal A, Wedel H, Whincup P, Wilhelmsen L, Graham IM (2003) Estimation of ten-year risk of fatal cardiovascular disease in Europe: the SCORE project. Eur Heart J 24(11):987–1003
Cook NR, Ridker PM (2009) The use and magnitude of reclassification measures for individual predictors of global cardiovascular risk. Ann Intern Med 150(11):795–802
Cooney MT, Dudina AL, Graham IM (2009) Value and limitations of existing scores for the assessment of cardiovascular risk a review for clinicians. J Am Coll Cardiol 54(14):1209–1227
Cooney MT, Dudina A, D’Agostino R, Graham IM (2010) Cardiovascular risk-estimation systems in primary prevention: do they differ? Do they make a difference? Can we see the future? Circulation 122(3):300–310
Cox DR (1972) Regression models and life-tables. J R Stat Soc A Met 34(2):187–220
D’Agostino RB, Vasan RS, Pencina MJ, Wolf PA, Cobain M, Massaro JM, Kannel WB (2008) General cardiovascular risk profile for use in primary care: the Framingham Heart Study. Circulation 118(4):E86–E86
Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc B Met 39(1):1–38
Fraley C, Raftery AE, Murphy TB, Scrucca L (2012) MCLUST version 4 for R: normal mixture modeling for model-based clustering, classification, and density estimation. Technical report, University of Washington, Department of Statistics
Go AS, Mozaffarian D, Roger VL, Benjamin EJ, Berry JD, Blaha MJ, Dai S, Ford ES, Fox CS, Franco S, Fullerton HJ, Gillespie C, Hailpern SM, Heit JA, Howard VJ, Huffman MD, Judd SE, Kissela BM, Kittner SJ, Lackland DT, Lichtman JH, Lisabeth LD, Mackey RH, Magid DJ, Marcus GM, Marelli A, Matchar DB, McGuire DK, III MER, Moy CS, Mussolino ME, Neumar RW, Nichol G, Pandey DK, Paynter NP, Reeves MJ, Sorlie PD, Stein J, Towfighi A, Turan TN, Virani SS, Wong ND, Woo D, Turner MB (2014) Heart disease and stroke statistics 2014 update: a report from the American Heart Association. Circulation 129(3):E28–E292
Greenwood M et al (1926) A report on the natural duration of cancer. Rep Public Health Med Subj Minist Health 33:1–26
Harrell FE (2001) Regression modeling strategies. Springer, New York
Hippisley-Cox J, Coupland C, Vinogradova Y, Robson J, May M, Brindle P (2007) Derivation and validation of QRISK, a new cardiovascular disease risk score for the United Kingdom: prospective open cohort study. Br Med J 335(7611):136–141
Hippisley-Cox J, Coupland C, Vinogradova Y, Robson J, Brindle P (2008a) Performance of the qrisk cardiovascular risk prediction algorithm in an independent UK sample of patients from general practice: a validation study. Heart 94(1):34–39
Hippisley-Cox J, Coupland C, Vinogradova Y, Robson J, Minhas R, Sheikh A, Brindle P (2008b) Predicting cardiovascular risk in England and Wales: prospective derivation and validation of QRISK2. Br Med J 336(7659):1475–1489
Hosmer DW, Lemeshow S (1980) Goodness of fit tests for the multiple logistic regression-model. Commun Stat Theory Methods 9(10):1043–1069
Ishwaran H, Kogalur UB, Blackstone EH, Lauer MS (2008) Random survival forests. Ann Appl Stat 2:841–860
Jackson CH, Thompson SG, Sharples LD (2009) Accounting for uncertainty in health economic decision models by using model averaging. J R Stat Soc Ser A Stat Soc 172:383–404
Kalbfleisch JD, Prentice RL (2002) The statistical analysis of failure time data. Wiley, Hoboken, NJ
Kattan MW (2003) Comparison of Cox regression with other methods for determining prediction models and nomograms. J Urol 170(6):S6–S9
Kattan MW, Hess KR, Beck JR (1998) Experiments to determine whether recursive partitioning (CART) or an artificial neural network overcomes theoretical limitations of Cox proportional hazards regression. Comput Biomed Res 31(5):363–373
Kazmierska J, Malicki J (2008) Application of the naive Bayesian classifier to optimize treatment decisions. Radiother Oncol 86(2):211–216
Lamon-Fava S, Wilson PW, Schaefer EJ (1996) Impact of body mass index on coronary heart disease risk factors in men and women the framingham offspring study. Arterioscler Thromb Vasc Biol 16(12):1509–1515
Lappenschaar M, Hommersom A, Lucas PJF, Lagro J, Visscher S (2013) Multilevel Bayesian networks for the analysis of hierarchical health care data. Artif Intell Med 57(3):171–183
Larranaga P, Sierra B, Gallego MJ, Michelena MJ, Picaza JM (1997) Learning Bayesian networks by genetic algorithms: a case study in the prediction of survival in malignant skin melanoma. Artif Intell Med 1211:261–272
Law MR, Wald NJ, Rudnicka A (2003) Quantifying effect of statins on low density lipoprotein cholesterol, ischaemic heart disease, and stroke: systematic review and meta-analysis. BMJ 326(7404):1423
Lemeshow S, Hosmer DW (1982) A review of goodness of fit statistics for use in the development of logistic-regression models. Am J Epidemiol 115(1):92–106
Lipsky AM, Lewis RJ (2005) Placing the Bayesian network approach to patient diagnosis in perspective. Ann Emerg Med 45(3):291–294
Lloyd-Jones DM (2010) Cardiovascular risk prediction basic concepts, current status, and future directions. Circulation 121(15):1768–1777
Lucas PJF, Boot H, Taal BG (1998) Computer-based decision support in the management of primary gastric non-Hodgkin lymphoma. Methods Inf Med 37(3):206–219
Lucas PJF, deBruijn NC, Schurink K, Hoepelman A (2000) A probabilistic and decision-theoretic approach to the management of infectious disease at the ICU. Artif Intell Med 19(3):251–279
Lucas PJF, van der Gaag L, Abu-Hanna A (2004) Bayesian networks in biomedicine and health-care. Artif Intell Med 30(3):201–214
Matheny M, McPheeters ML, Glasser A, Mercaldo N, Weaver RB, Jerome RN, Walden R, McKoy JN, Pritchett J, Tsai C (2011) Systematic review of cardiovascular disease risk assessment tools. Technical report, Agency for Healthcare Research and Quality (US)
Murphy KP (1998) Inference and learning in hybrid Bayesian networks. Technical report, University of California, Berkeley, Computer Science Division
Pencina MJ, D’Agostino RB Sr, D’Agostino RB Jr, Vasan RS (2008) Evaluating the added predictive ability of a new marker: from area under the ROC curve to reclassification and beyond. Stat Med 27(2):157–172
Pencina MJ, D’Agostino RB Sr, Steyerberg EW (2011) Extensions of net reclassification improvement calculations to measure usefulness of new biomarkers. Stat Med 30(1):11–21
Pepe MS (2011) Problems with risk reclassification methods for evaluating prediction models. Am J Epidemiol 173(11):1327–35
Ridker PM, Buring JE, Rifai N, Cook NR (2007) Development and validation of improved algorithms for the assessment of global cardiovascular risk in women: The Reynolds risk score. J Am Med Assoc 297(13):1433–1433
Ridker PM, Paynter NP, Rifai N, Gaziano M, Cook NR (2008) C-reactive protein and parental history improve global cardiovascular risk prediction: the Reynolds risk score for men. Circulation 118(18):S1145–S1145
Robins JM, Finkelstein DM (2000) Correcting for noncompliance and dependent censoring in an AIDS clinical trial with inverse probability of censoring weighted (IPCW) log-rank tests. Biometrics 56(3):779–788
Rockwood MR, Howlett SE (2011) Blood pressure in relation to age and frailty. Can Geriatr J 14(1):2–7
Rotnitzky AG, Robins JM (2004) Inverse probability weighted estimation in survival analysis. In: Armitage P, Colton T (eds) The encyclopedia of biostatistics, 2nd edn. Wiley, Hoboken, NJ
Sarkar S, Koehler J (2013) A dynamic risk score to identify increased risk for heart failure decompensation. IEEE Trans Biomed Eng 60(1):147–150
Sesen MB, Nicholson AE, Banares-Alcantara R, Kadir T, Brady M (2013) Bayesian networks for clinical decision support in lung cancer care. PLOS One 8(12):e82,349
Sierra B, Larranaga P (1998) Predicting survival in malignant skill melanoma using Bayesian networks automatically induced by genetic algorithms: An empirical comparison between different approaches. Artif Intell Med 14(1–2):215–230
Smith WP, Doctor J, Meyer J, Kalet IJ, Phillips MH (2009) A decision aid for intensity-modulated radiation-therapy plan selection in prostate cancer based on a prognostic Bayesian network and a Markov model. Artif Intell Med 46(2):119–130
Song X, Mitnitski A, Cox J, Rockwood K (2004) Comparison of machine learning techniques with classical statistical models in predicting health outcomes. Medinfo 11(1):736–40
Stajduhar I, Dalbelo-Basic B (2010) Learning Bayesian networks from survival data using weighting censored instances. J Biomed Inform 43(4):613–622
Stajduhar I, Dalbelo-Basic B (2012) Uncensoring censored data for machine learning: a likelihood-based approach. Expert Syst Appl 39(8):7226–7234
Stajduhar I, Dalbelo-Basic B, Bogunovic N (2009) Impact of censoring on learning Bayesian networks in survival modelling. Artif Intell Med 47(3):199–217
Stamler J, Stamler R, Neaton JD (1993) Blood pressure, systolic and diastolic, and cardiovascular risks: US population data. Arch Intern Med 153(5):598
Stuart R, Peter N (2003) Artificial intelligence: a modern approach, vol 2. Prentice Hall, Upper Saddle River, NJ
Therneau TM, Grambsch PM, Fleming TR (1990) Martingale-based residuals for survival models. Biometrika 77(1):147–160
Tian J, He R, Ram L (2010) Bayesian model averaging using the k-best Bayesian network structures. In: Proceedings of the twenty-sixth conference annual conference on uncertainty in artificial intelligence (UAI-10). AUAI Press, Corvallis, Oregon, pp 589–597
Tsiatis AA (2006) Semiparametric theory and missing data. Springer, New York
Velikova M, van Scheltinga JT, Lucas PJF, Spaanderman M (2014) Exploiting causal functional relationships in bayesian network modelling for personalised healthcare. Int J Approx Reason 55(1):59–73
Verduijn M, Peek N, Rosseel PMJ, de Jonge E, de Mol BAJM (2007) Prognostic Bayesian networks I: rationale, learning procedure, and clinical use. J Biomed Inform 40(6):609–618
Vila-Frances J, Sanchis J, Soria-Olivas E, Serrano AJ, Martinez-Sober M, Bonanad C, Ventura S (2013) Expert system for predicting unstable angina based on Bayesian networks. Expert Syst Appl 40(12):5004–5010
Woodward M, Brindle P, Tunstall-Pedoe H (2007) Adding social deprivation and family history to cardiovascular risk assessment: the ASSIGN score from the Scottish Heart Health Extended Cohort (SHHEC). Heart 93(2):172–176
Yet B, Bastani K, Raharjo H, Lifvergren S, Marsh W, Bergman B (2013) Decision support system for Warfarin therapy management using Bayesian networks. Decis Support Syst 55(2):488–498
Zupan B, Demsar J, Kattan MW, Beck JR, Bratko I (1999) Machine learning for survival analysis: a case study on recurrence of prostate cancer. Artif Intell Med 1620:346–355
Acknowledgments
This work was partially supported by NHLBI Grant R01HL102144-01 and AHRQ Grant R21HS017622-01.
Author information
Authors and Affiliations
Corresponding author
Additional information
Responsible editors: Fei Wang, Gregor Stiglic, Ian Davidson and Zoran Obradovic.
Rights and permissions
About this article
Cite this article
Bandyopadhyay, S., Wolfson, J., Vock, D.M. et al. Data mining for censored time-to-event data: a Bayesian network model for predicting cardiovascular risk from electronic health record data. Data Min Knowl Disc 29, 1033–1069 (2015). https://doi.org/10.1007/s10618-014-0386-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10618-014-0386-6