Year 2020,
Volume: 6 Issue: 2, 158 - 164, 31.12.2020
Aslıhan Şentürk Acar
,
Nihal Ata Tutkun
References
- Clark, T. G., Bradburn, M. J., Love S. B., and. Altman, D. G , “Survival analysis part I: basic concepts and first analyses,” Br. J. Cancer, vol. 89, no. 2, pp. 232–38, Jul. 2003.
- Babińska, M., Chudek, J., Elżbieta Chełmecka3, Janik, M., Klimek, K., and Owczarek, A., “Limitations of Cox Proportional Hazards Analysis in Mortality Prediction of Patients with Acute Coronary Syndrome", Studies in Logic, Grammar and Rhetoric , 2018.
- Nardi, A. and Schemper M., “Comparing Cox and parametric models in clinical studies,” Stat. Med., vol. 22, no. 23, pp. 3597–3610, Dec. 2003.
- Kleinbaum, D.G., Survival Analysis - A Self-Learning Text, Springer, 2010.
- Radespiel-Tröger, M., Rabenstein T., Schneider, H. T. and Lausena B., “Comparison of tree-based methods for prognostic stratification of survival data,”Artificial Intelligence in Medicine, 28(3), pp.323-341, 2003.
- Zhou, Y. and McArdle, J. J., “Rationale and Applications of Survival Tree and Survival Ensemble Methods,” Psychometrika, vol. 80, no. 3, pp. 811–833, Sep. 2015.
- Hu, C., and Steingrimsson, J. A., “Personalized Risk Prediction in Clinical Oncology Research: Applications and Practical Issues Using Survival Trees and Random Forests,” J. Biopharm. Stat., vol. 28, no. 2, pp. 333–349, Mar. 2018.
- Paraschiakos, F., “Machine learning for survival analysis on clinical data,” Master's thesis, 2016.
Wang, P., Li, Y. and Reddy C. K., “Machine Learning for Survival Analysis: A Survey", ACM Computing Surveys (CSUR), 51(6):1-36, 2019.
- Breiman, L., “Bagging predictors,” Mach. Learn., vol. 24, no. 2, pp. 123–140, 1996.
- Breiman, L., “Random forests,” Mach. Learn., vol. 45, no. 1, pp. 5–32, 2001.
- Schapire, R.E., “A brief introduction to boosting,” in Ijcai, vol. 99, pp. 1401–1406, 1999.
- Kuhn, M. and Johnson, K., Applied predictive modeling, vol. 26. Springer, 2013.
- Hothorn, T., Lausen, B., Benner, A. and Radespiel-Tröger, M. “Bagging survival trees,” Stat. Med., vol. 23, no. 1, pp. 77–91, Jan. 2004.
- Ishwaran, H., Kogalur, U. B., Blackstone, E. H. and Lauer, M. S. “Random survival forests,” Ann. Appl. Stat., vol. 2, no. 3, pp. 841–860, Sep. 2008.
- Hothorn, T., Bühlmann P., Dudoit, S., Molinaro A. and van der Laan M. J., “Survival ensembles,” Biostat. Oxf. Engl., vol. 7, no. 3, pp. 355–373, Jul. 2006.
- Graf, E., Schmoor, C., Sauerbrei, W. and Schumacher M., “Assessment and comparison of prognostic classification schemes for survival data,” Stat. Med., vol. 18, no. 17–18, pp. 2529–2545, 1999.
- Mogensen, U. B., Ishwaran, H. and Gerds, T. A., “Evaluating random forests for survival analysis using prediction error curves,” J. Stat. Softw., vol. 50, no. 11, p. 1, 2012.
- Friedman, J. H., “Greedy Function Approximation: A Gradient Boosting Machine,” Ann. Stat., vol. 29, no. 5, pp. 1189–1232, 2001.
- Bin, R. D., Sauerbrei, W. and Boulesteix, A. L., “Investigating the prediction ability of survival models based on both clinical and omics data: two case studies,” Stat. Med., vol. 33, no. 30, pp. 5310–5329, 2014.
- Bühlmann, P. and Hothorn, T., “Boosting algorithms: Regularization, prediction and model fitting,” Stat. Sci., pp. 477–505, 2007.
- Bühlmann, P., “Boosting for high-dimensional linear models,” Ann. Stat., vol. 34, no. 2, pp. 559–583, Apr. 2006.
- Graf, E., Schmoor, C., Sauerbrei, W. and Schumacher, M., “Assessment and comparison of prognostic classification schemes for survival data", Statistics in medicine, 18(17‐18), pp.2529-2545, 1999.
- Gerds, T. A. and Ozenne, B., “riskRegression: Risk Regression Models and Prediction Scores for Survival Analysis with Competing Risks.,” vol. R package version 2019.
- Gerds, T. A., Andersen, P. K. and Kattan, M. W., “Calibration plots for risk prediction models in the presence of competing risks,” Stat. Med., vol. 33, no. 18, pp. 3191–3203, 2014.
- Gerds, T. A. and Schumacher, M., “Consistent estimation of the expected Brier score in general survival models with right-censored event times,” Biom. J. Biom. Z., vol. 48, no. 6, pp. 1029–1040, Dec. 2006.
- Erdoğan, A., “Proportional Hazards Model,” Unpublished MSc thesis, Hacettepe University,Graduate School of Science and Engineering, Ankara, 1993.
- Hothorn, T., Hornik, K. and Zeileis, A., “Unbiased recursive partitioning: A conditional inference framework,” J. Comput. Graph. Stat., vol. 15, no. 3, pp. 651–674, 2006.
- LeBlanc M. and Crowley, J., “Survival trees by goodness of fit,” J. Am. Stat. Assoc., vol. 88, pp. 457–467, 1993.
- Hofner, B., Mayr, A., Robinzonov, N. and Schmid, M., “Model-based Boosting in R: A Hands-on Tutorial Using the R Package mboost,” Feb. 14, 2012.
- Biganzoli, E., Boracchi, P., Mariani, L. and Marubini, E., “Feed forward neural networks for the analysis of censored survival data: a partial logistic regression approach,” Statistics in medicine, May 30, 1998.
- Van Belle, V., Pelckmans, K., Van Huffel, S. and Suykens, J. A., “Support vector methods for survival analysis a comparison between ranking and regression approaches,” Artificial intelligence in medicine, Oct. 2011.
USE OF ENSEMBLE METHODS FOR SURVIVAL PREDICTION
Year 2020,
Volume: 6 Issue: 2, 158 - 164, 31.12.2020
Aslıhan Şentürk Acar
,
Nihal Ata Tutkun
Abstract
Cox regression model is used for modelling censored data to investigate the association between the survival time and covariates. It is important to assess the fit of Cox regression model since it has a key assumption called proportional hazards. Violation of this assumption induces an invalid model and changes the interpretation of the results. When the objective is the risk prediction, various machine learning methods can be good alternatives to Cox regression model due to their flexible structure. In this study, Turkish breast cancer data set is used to compare the predictive performance of Cox regression model and ensemble machine learning methods. Integrated Brier score is used to measure the predictive performance of candidate models. Based on case study results, machine learning methods are promising alternatives for survival prediction.
References
- Clark, T. G., Bradburn, M. J., Love S. B., and. Altman, D. G , “Survival analysis part I: basic concepts and first analyses,” Br. J. Cancer, vol. 89, no. 2, pp. 232–38, Jul. 2003.
- Babińska, M., Chudek, J., Elżbieta Chełmecka3, Janik, M., Klimek, K., and Owczarek, A., “Limitations of Cox Proportional Hazards Analysis in Mortality Prediction of Patients with Acute Coronary Syndrome", Studies in Logic, Grammar and Rhetoric , 2018.
- Nardi, A. and Schemper M., “Comparing Cox and parametric models in clinical studies,” Stat. Med., vol. 22, no. 23, pp. 3597–3610, Dec. 2003.
- Kleinbaum, D.G., Survival Analysis - A Self-Learning Text, Springer, 2010.
- Radespiel-Tröger, M., Rabenstein T., Schneider, H. T. and Lausena B., “Comparison of tree-based methods for prognostic stratification of survival data,”Artificial Intelligence in Medicine, 28(3), pp.323-341, 2003.
- Zhou, Y. and McArdle, J. J., “Rationale and Applications of Survival Tree and Survival Ensemble Methods,” Psychometrika, vol. 80, no. 3, pp. 811–833, Sep. 2015.
- Hu, C., and Steingrimsson, J. A., “Personalized Risk Prediction in Clinical Oncology Research: Applications and Practical Issues Using Survival Trees and Random Forests,” J. Biopharm. Stat., vol. 28, no. 2, pp. 333–349, Mar. 2018.
- Paraschiakos, F., “Machine learning for survival analysis on clinical data,” Master's thesis, 2016.
Wang, P., Li, Y. and Reddy C. K., “Machine Learning for Survival Analysis: A Survey", ACM Computing Surveys (CSUR), 51(6):1-36, 2019.
- Breiman, L., “Bagging predictors,” Mach. Learn., vol. 24, no. 2, pp. 123–140, 1996.
- Breiman, L., “Random forests,” Mach. Learn., vol. 45, no. 1, pp. 5–32, 2001.
- Schapire, R.E., “A brief introduction to boosting,” in Ijcai, vol. 99, pp. 1401–1406, 1999.
- Kuhn, M. and Johnson, K., Applied predictive modeling, vol. 26. Springer, 2013.
- Hothorn, T., Lausen, B., Benner, A. and Radespiel-Tröger, M. “Bagging survival trees,” Stat. Med., vol. 23, no. 1, pp. 77–91, Jan. 2004.
- Ishwaran, H., Kogalur, U. B., Blackstone, E. H. and Lauer, M. S. “Random survival forests,” Ann. Appl. Stat., vol. 2, no. 3, pp. 841–860, Sep. 2008.
- Hothorn, T., Bühlmann P., Dudoit, S., Molinaro A. and van der Laan M. J., “Survival ensembles,” Biostat. Oxf. Engl., vol. 7, no. 3, pp. 355–373, Jul. 2006.
- Graf, E., Schmoor, C., Sauerbrei, W. and Schumacher M., “Assessment and comparison of prognostic classification schemes for survival data,” Stat. Med., vol. 18, no. 17–18, pp. 2529–2545, 1999.
- Mogensen, U. B., Ishwaran, H. and Gerds, T. A., “Evaluating random forests for survival analysis using prediction error curves,” J. Stat. Softw., vol. 50, no. 11, p. 1, 2012.
- Friedman, J. H., “Greedy Function Approximation: A Gradient Boosting Machine,” Ann. Stat., vol. 29, no. 5, pp. 1189–1232, 2001.
- Bin, R. D., Sauerbrei, W. and Boulesteix, A. L., “Investigating the prediction ability of survival models based on both clinical and omics data: two case studies,” Stat. Med., vol. 33, no. 30, pp. 5310–5329, 2014.
- Bühlmann, P. and Hothorn, T., “Boosting algorithms: Regularization, prediction and model fitting,” Stat. Sci., pp. 477–505, 2007.
- Bühlmann, P., “Boosting for high-dimensional linear models,” Ann. Stat., vol. 34, no. 2, pp. 559–583, Apr. 2006.
- Graf, E., Schmoor, C., Sauerbrei, W. and Schumacher, M., “Assessment and comparison of prognostic classification schemes for survival data", Statistics in medicine, 18(17‐18), pp.2529-2545, 1999.
- Gerds, T. A. and Ozenne, B., “riskRegression: Risk Regression Models and Prediction Scores for Survival Analysis with Competing Risks.,” vol. R package version 2019.
- Gerds, T. A., Andersen, P. K. and Kattan, M. W., “Calibration plots for risk prediction models in the presence of competing risks,” Stat. Med., vol. 33, no. 18, pp. 3191–3203, 2014.
- Gerds, T. A. and Schumacher, M., “Consistent estimation of the expected Brier score in general survival models with right-censored event times,” Biom. J. Biom. Z., vol. 48, no. 6, pp. 1029–1040, Dec. 2006.
- Erdoğan, A., “Proportional Hazards Model,” Unpublished MSc thesis, Hacettepe University,Graduate School of Science and Engineering, Ankara, 1993.
- Hothorn, T., Hornik, K. and Zeileis, A., “Unbiased recursive partitioning: A conditional inference framework,” J. Comput. Graph. Stat., vol. 15, no. 3, pp. 651–674, 2006.
- LeBlanc M. and Crowley, J., “Survival trees by goodness of fit,” J. Am. Stat. Assoc., vol. 88, pp. 457–467, 1993.
- Hofner, B., Mayr, A., Robinzonov, N. and Schmid, M., “Model-based Boosting in R: A Hands-on Tutorial Using the R Package mboost,” Feb. 14, 2012.
- Biganzoli, E., Boracchi, P., Mariani, L. and Marubini, E., “Feed forward neural networks for the analysis of censored survival data: a partial logistic regression approach,” Statistics in medicine, May 30, 1998.
- Van Belle, V., Pelckmans, K., Van Huffel, S. and Suykens, J. A., “Support vector methods for survival analysis a comparison between ranking and regression approaches,” Artificial intelligence in medicine, Oct. 2011.