Skip to main content

Discrete Bayesian Network Interpretation of the Cox’s Proportional Hazards Model

  • Conference paper
Probabilistic Graphical Models (PGM 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8754))

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allison, P.D.: Survival Analysis Using SAS: A Practical Guide, 2nd edn. SAS Institute Inc., Cary (2010)

    Google Scholar 

  2. Kaplan, E.L., Meier, P.: Nonparametric estimation from incomplete observations. Journal of the American Statistical Association 53(282), 457–481 (1958)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cox, D.R.: Regression models and life-tables. Journal of the Royal Statistical Society. Series B (Methodological) 34(2), 187–220 (1972)

    MathSciNet  MATH  Google Scholar 

  4. Spruance, S.L., Reid, J.E., Grace, M., Samore, M.: Hazard ratio in clinical trials. Antimicrobial Agents and Chemotherapy 48(8), 2787–2892 (2004)

    Article  Google Scholar 

  5. 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)

    Article  Google Scholar 

  6. 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)

    Article  Google Scholar 

  7. Hanna, A.A., Lucas, P.J.: Prognostic models in medicine- AI and statistical approaches. Method Inform. Med. 40, 1–5 (2001)

    Google Scholar 

  8. Husmeier, D., Dybowski, R., Roberts, S.: Probabilistic modeling in bioinformatics and medical informatics. Springer (2005)

    Google Scholar 

  9. Klein, J.P., Moeschberger, M.L.: Survival Analysis: Censored and Truncated Data, 2nd edn. Springer-Verlag New York, Inc., New York (2003)

    Google Scholar 

  10. Christensen, E.: Multivariate survival analysis using Cox’s regression model. Hepatology 7, 1346–1358 (1987)

    Article  Google Scholar 

  11. 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)

    Article  Google Scholar 

  12. Rossi, P.H., Berk, R.A., Lenihan, K.J.: Money, Work, and Crime - Experimental Evidence. Academic Press, Inc., San Diego (1980)

    Google Scholar 

  13. Fox, J.: An R and S-Plus Companion to Applied Regression. Sage Publication Inc., CA (2002)

    Google Scholar 

  14. Pearl, J.: Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann Publishers Inc., San Francisco (1988)

    Google Scholar 

  15. 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)

    Google Scholar 

  16. 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)

    Article  Google Scholar 

  17. 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)

    Google Scholar 

  18. 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)

    Google Scholar 

  19. 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)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

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

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-11433-0_16

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11432-3

  • Online ISBN: 978-3-319-11433-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics