Abstract
Cox’s Proportional Hazards (CPH) model is quite likely the most popular modeling technique in survival analysis. While the CPH model is able to represent relationships between a collection of risks and their common effect, Bayesian networks have become an attractive alternative with far broader applications. Our paper focuses on a Bayesian network interpretation of the CPH model. We provide a method of encoding knowledge from existing CPH models in the process of knowledge engineering for Bayesian networks. We compare the accuracy of the resulting Bayesian network to the CPH model, Kaplan-Meier estimate, and Bayesian network learned from data using the EM algorithm. Bayesian networks constructed from CPH model lead to much higher accuracy than other approaches, especially when the number of data records is very small.
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References
Allison, P.D.: Survival Analysis Using SAS: A Practical Guide, 2nd edn. SAS Institute Inc., Cary (2010)
Kaplan, E.L., Meier, P.: Nonparametric estimation from incomplete observations. Journal of the American Statistical Association 53(282), 457–481 (1958)
Cox, D.R.: Regression models and life-tables. Journal of the Royal Statistical Society. Series B (Methodological) 34(2), 187–220 (1972)
Spruance, S.L., Reid, J.E., Grace, M., Samore, M.: Hazard ratio in clinical trials. Antimicrobial Agents and Chemotherapy 48(8), 2787–2892 (2004)
Levy, W.C., Mozaffarian, D., Linker, D.T., Sutradhar, S.C., Anker, S.D., Croppan, A.B., Anand, I., Maggionl, A., Burton, P., Sullivan, M.D., Pitt, B., Poole-Wilson, P.A., Mann, D.L., Packer, M.: The Seattle Heart Failure Model: Prediction of survival in heart failure. Circulation 113(11), 1424–1433 (2006)
Benza, R.L., Miller, D.P., Gomberg-Maitland, M., Frantz, R.P., Foreman, A.J., Coffey, C.S., Frost, A., Barst, R.J., Badesch, D.B., Elliott, C.G., Liou, T.G., McGoon, M.D.: Predicting survival in pulmonary arterial hypertension: Insights from the registry to evaluate early and long-term pulmonary arterial hypertension disease management (REVEAL). Circulation 122(2), 164–172 (2010)
Hanna, A.A., Lucas, P.J.: Prognostic models in medicine- AI and statistical approaches. Method Inform. Med. 40, 1–5 (2001)
Husmeier, D., Dybowski, R., Roberts, S.: Probabilistic modeling in bioinformatics and medical informatics. Springer (2005)
Klein, J.P., Moeschberger, M.L.: Survival Analysis: Censored and Truncated Data, 2nd edn. Springer-Verlag New York, Inc., New York (2003)
Christensen, E.: Multivariate survival analysis using Cox’s regression model. Hepatology 7, 1346–1358 (1987)
Casea, L.D., Kimmickb, G., Pasketta, E.D., Lohmana, K., Tucker, R.: Interpreting measures of treatment effect in cancer clinical trials. The Oncologist 7(3), 181–187 (2002)
Rossi, P.H., Berk, R.A., Lenihan, K.J.: Money, Work, and Crime - Experimental Evidence. Academic Press, Inc., San Diego (1980)
Fox, J.: An R and S-Plus Companion to Applied Regression. Sage Publication Inc., CA (2002)
Pearl, J.: Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann Publishers Inc., San Francisco (1988)
Gevaert, O., Smet, F.D., Timmerman, D., Moreau, Y., Moor, B.D.: Predicting the prognosis of breast cancer by integrating clinical and microarray data with bayesian networks. Bioinformatics 22(14), e184–e190 (2006)
van Gerven, M.A., Taal, B.G., Lucas, P.J.: Dynamic Bayesian networks as prognostic models for clinical patient management. Journal of Biomedical Informatics 41(4), 515–529 (2007)
Oniśko, A., Druzdzel, M.J., Wasyluk, H.: Learning Bayesian network parameters from small data sets: Application of Noisy-OR gates. In: Working Notes on the European Conference on Artificial Intelligence (ECAI) Workshop Bayesian and Causal Networks: From Inference to Data Mining (August 22, 2000)
Nodelman, U., Shelton, C.R., Koller, D.: Continuous Time Bayesian Networks. In: Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence, pp. 378–387. Morgan Kaufmann Publishers Inc. (2002)
Srinivas, S.: A generalization of the Noisy-Or model. In: Proceedings of the Ninth International Conference on Uncertainty in Artificial Intelligence, pp. 208–215. Morgan Kaufmann Publishers Inc. (1993)
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Kraisangka, J., Druzdzel, M.J. (2014). Discrete Bayesian Network Interpretation of the Cox’s Proportional Hazards Model. In: van der Gaag, L.C., Feelders, A.J. (eds) Probabilistic Graphical Models. PGM 2014. Lecture Notes in Computer Science(), vol 8754. Springer, Cham. https://doi.org/10.1007/978-3-319-11433-0_16
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DOI: https://doi.org/10.1007/978-3-319-11433-0_16
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11432-3
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