A review of survival trees

Statistics Surveys

Volumn 5, Issue , 2011, Pages 44-71

  Bou Hamad, Imad ^a   Larocque, Denis ^b   Ben Ameur, Hatem ^b  

^a AMERICAN UNIVERSITY OF BEIRUT   (Lebanon)

^b HEC MONTRÉAL   (Canada)

Author keywords

Bagging; CART; Discrete time; Ensemble methods; Right censored data; Survival forest; Survival trees; Time varying covariate; Time varying effect

Indexed keywords

EID: 84857308440     PISSN: None     EISSN: 19357516     Source Type: Journal    
DOI: 10.1214/09-SS047     Document Type: Article

References (74)

1. Ahn, H. and Loh, W.-Y. (1994). Tree-Structured Proportional Hazards Regression Modeling. Biometrics 50, 471-485.
2. Bacchetti, P. and Segal, M. (1995). Survival Trees with Time-Dependent Covariates: Application to Estimating Changes in the Incubation Period of AIDS. Lifetime Data Analysis 1, 35-47.
3. Benner, A. (2002). Application of "Aggregated Classifiers" in Survival Time Studies. COMPSTAT 2002 - Proceedings in Computational Statistics: 15th Symposium Held in Berlin, Germany, 2002 MR1973489
4. Bou-Hamad, I., Larocque, D., Ben-Ameur, H., Mâsse, L., Vitaro, F. and Tremblay, R. (2009). Discrete-Time Survival Trees. Canadian Journal of Statistics 37, 17-32.MR2509459
5. Bou-Hamad, I., Larocque, D. and Ben-Ameur, H. (2011). Discrete-Time Survival Trees and Forests with Time-Varying Covariates: Application to Bankruptcy Data. To appear in Statistical Modeling.
6. Breiman, L., Friedman, J., Olshen, R. and Stone, C. (1984). Classification and Regression Trees. Wadsworth International Group, Belmont, California. MR0726392
7. Breiman, L. (1996). Bagging Predictors. Machine Learning 24, 123-140.
8. Breiman, L. (2001). Random Forests. Machine Learning 45, 5-32.
9. Cho, H. and Hong, S-M. (2008). Median Regression Tree for Analysis of Censored Survival Data. Systems, Man and Cybernetics, Part A, IEEE Transactions on 38, 715-726.
10. Ciampi, A., Bush, R. S., Gospodarowicz, M. and Till, J. E. (1981). An Approach to Classifying Prognostic Factors Related to Survival Experience for Non-Hodgkin's Lymphoma Patients: Based on a Series of 982 Patients: 1967-1975. Cancer 47, 621-627.
11. Ciampi, A., Thiffault, J., Nakache, J.-P. and Asselain, B. (1986). Stratification by Stepwise Regression, Correspondance Analysis and Recursive Partition: A Comparison of Three Methods of Analysis for Survival Data with Covariates. Computational Statistics & Data Analysis 4, 185-204.
12. Ciampi, A., Chang, C. H., Hogg, S. and McKinney, S. (1987). Recursive Partition: A Versatile Method for Exploratory Data Analysis in Biostatistics. Biostatistics 23-50
13. Ciampi, A., Hogg, S. A., McKinney, S. and Thiffault, J. (1988). RECPAM: A Computer Program for Recursive Partition and Amalgamation for Censored Survival Data and Other Situations Frequently Occurring in Biostatistics. I. Methods and Program Features. Computer Methods and Programs in Biomedicine 26, 239-256.
14. Ciampi, A., Hogg, S. A., McKinney, S. and Thiffault, J. (1989). RECPAM: A Computer Program for Recursive Partition and Amalgamation for Censored Survival Data and Other Situations Frequently Occurring in Biostatistics. II. Applications to Data on Small Cell Carcinoma of the Lung (SCCL). Computer Methods and Programs in Biomedicine 30, 283-296.
15. Ciampi, A., Negassa, A. and Lou, Z. (1995). Tree-Structured Prediction for Censored Survival Data and the Cox Model. Journal of Clinical Epidemiology 48, 675-689.
16. Ciampi, A., Thiffault, J. and Sagman, U. (1989). RECPAM: A Computer Program for Recursive Partition and Amalgamation for Censored Survival Data and Other Situations Frequently Occurring in Biostatistics. II. Applications to Data on Small Cell Carcinoma of the Lung (SCCL). Computer Methods and Programs in Biomedicine 30, 283-296.
17. Dannegger, F. (2000). Tree Stability Diagnostics and Some Remedies for Instability. Statistics in Medicine 19, 475-491.
18. Davis, R. B. and Anderson, J. R. (1989). Exponential Survival Trees. Statistics in Medicine 8, 947-961.
19. Ding, Y. and Simonoff, J. S. (2010). An Investigation of Missing Data Methods for Classification Trees Applied to Binary Response Data. Journal of Machine Learning Research, 11, 131-170.MR2591624
20. Eckel, K. T., Pfahlberg, A., Gefeller, O. and Hothorn, T. (2008). Flexible Modeling of Malignant Melanoma Survival. Methods of Information in Medicine 47, 47-55.
21. Fan, J., Nunn, M. E. and Su, X. (2009). Multivariate Exponential Survival Trees and Their Application to Tooth Prognosis. Computational Statistics and Data Analysis 53, 1110-1121. MR2657075
22. Fan, J., Su, X.-G., Levine, R., Nunn, M. and Leblanc, M. (2006). Trees for Censored Survival Data by Goodness of Split, with Application to Tooth Prognosis. Journal of American Statistical Association 101, 959-967.MR2324107
23. Fleming, T. R. and Harrington, D. P. (1991). Counting Processes and Survival Analysis. Wiley, New Jersey.MR1100924
24. Gao, F., Manatunga, A. K. and Chen, S. (2004). Identification of Prognostic Factors with Multivariate Survival Data. Computational Statistics & Data Analysis 45, 813-824. MR2054888
25. Gao, F., Manatunga, A. K. and Chen, S. (2006). Developing Multivariate Survival Trees with a Proportonal Hazards Structure. Journal of Data Science 4, 343-356.
26. Gordon, L. and Olshen, R. A. (1985). Tree-structured Survival Analysis. Cancer Treatment Reports 69, 1065-1069.
27. Graf, E., Schmoor, C., Sauerbrei, W. and Schumacher, M. (1999). Assessment and Comparisons of Prognostic Classification Schemes for Survival Data. Statistics in Medicine 18, 2529-2545.
28. Hammer, P. L. and Bonates, T. O. (2006). Logical Analysis of Data-An Overview: From Combinatorial Optimization to Medical Applications. Annals of Operations Research 148, 203-225.
29. Harrell, F., Califf, R., Pryor, D., Lee, K. and Rosati, R. (1982). Evaluating the Yield of Medical Tests. Journal of the American Medical Association 247, 2543-2546.
30. Hothorn, T., Lausen, B., Benner, A. and Radespiel-Tr̈oger, M. (2004). Bagging Survival Trees. Statistics in Medicine 23, 77-91.
31. Hothorn, T., Bühlmann, P., Dudoit, S., Molinaro, A. M. and van der Laan, M. J. (2006). Survival Ensembles. Biostatistics 7, 355-373.
32. Huang, X., Chen, S. and Soong, S. (1998). Piecewise Exponential Survival Trees with Time-Dependent Covariates. Biometrics, 54, 1420-1433.
33. Ishwaran, H., Blackstone, E. H., Pothier, C. E. and Lauer, M. S. (2004). Relative Risk Forests for Exercise Heart Rate Recovery as a Predictor of Mortality. Journal of the American Statistical Association 99, 591-600.MR2086385
34. Ishwaran, H., Kogalur, U. B., Blackstone, E. H. and Lauer, M. S. (2008). Random Survival Forests. Annals of Applied Statistics 2, 841-860. MR2516796
35. Ishwaran, H. and Kogalur, U. B. (2010a). Consistency of Random Survival Forests. Statistics and Probability Letters 80, 1056-1064.MR2651045
36. Ishwaran, H. and Kogalur, U. B. (2010b). Random Survival Forests, R package version 3.6.3.
37. Ishwaran, H., Kogalur, U. B., Gorodeski, E. Z., Minn, A. J. and Lauer, M. S. (2010). High Dimensional Variable Selection for Survival Data. Journal of the American Statistical Association 105, 205-217.
38. Jin, H., Lu, Y., Stone, K. and Black, D. M. (2004). Alternative Tree-Structured Survival Analysis Based on Variance of Survival Time. Medical Decision Making 24, 670-680.
39. Keles, S. and Segal, M. R. (2002). Residual-Based Tree-Structured Survival Analysis. Statistics in Medicine 21, 313-326.
40. Kretowska, M. (2004). Dipolar Regression Trees in Survival Analysis. Biocybernetics and Biomedical Engineering 24, 25-33.
41. Kretowska, M. (2006). Random Forests of Dipolar Trees for Survival Prediction. Artificial Intelligence and Soft Computing - ICAISC 2006, Proceedings. Lecture Notes In Computer Science 4029, 909-918.
42. Kretowska, M. (2010). The influence of Censoring for the Performance of Survival Tree Ensemble. Artificial Intelligence and Soft Computing, Pt II - ICAISC 2010, Proceedings. Lecture Notes in Artificial Intelligence 6114, 524-531.
43. Kronek, L. P., and Reddy, A. (2008). Logical Analysis of Survival Data: Prognostic Survival Models by Detecting High-Degree Interactions in Right-Censored Data. Bioinformatics 24, 248-253.
44. Lausen, B., Hothorn, T., Bretz, F. and Schumacher, M. (2004). Assessment of Optimal Selected Prognostic Factors. Biometrical Journal 46, 364-374. MR2079857
45. LeBlanc, M. and Crowley, J. (1992). Relative Risk Trees for Censored Survival Data. Biometrics 48, 411-425.
46. LeBlanc, M. and Crowley, J. (1993). Survival Trees by Goodness of Split. Journal of the American Statistical Association 88, 457-467. MR1224370
47. LeBlanc, M. and Crowley, J. (1995). A Review of Tree-Based Prognostic Models. Journal of Cancer Treatment and Research 75, 113-124.
48. Loh, W-Y. (1991). Survival Modeling Through Recursive Stratification. Computational Statistics and Data Analysis 12, 295-313.
49. Marubini, E., Morabito, A. and Valsecchi, M. G. (1983). Prognostic Factors and Risk Groups: Some Results Given by Using an Algorithm Suitable for Censored Survival Data. Statistics in Medicine 2, 295-303.
50. Molinaro, A. M., Dudoit, S. and van der Laan, M. J. (2004). Tree-based Multivariate Regression and Density Estimation with Right-censored Data. Journal of Multivariate Analysis 90, 154-177.MR2064940
51. Morgan, J. and Sonquist, J. (1963). Problems in the Analysis of Survey Data and a Proposal. Journal of the American Statistical Association 58, 415-434.
52. Negassa, A., Ciampi, A., Abrahamowicz, M., Shapiro, S. and Boivin, J.-F. (2000). Tree-Structured Prognostic Classification for Censored Survival Data: Validation of Computationally Inexpensive Model Selection Criteria. Journal of Statistical Computation and Simulation 67, 289-318.MR1815167
53. Negassa, A., Ciampi, A., Abrahamowicz, M., Shapiro, S. and Boivin, J.-F. (2005) Tree-Structured Subgroup Analysis for Censored Survival Data: Validation of Computationally Inexpensive Model Selection Criteria. Statistics and Computing 15, 231-239.MR2147555
54. Peters, A. and Hothorn, T. (2009). Ipred: Improved Predictors. R package version 0.8-8. http://CRAN.R-project.org/package=ipred.
55. R Development Core Team (2010). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org.
56. Radespiel-Tröger, M., Rabenstein, T., Schneider, H. T. and Lausen, B. (2003). Comparison of Tree-based Methods for Prognostic Stratification of Survival Data. Artificial Intelligence in Medicine 28, 323-341.
57. Radespiel-Tröger, M., Gefeller, O., Rabenstein, T. and Hothorn, T. (2006). Association Between Split Selection Instability and Predictive Error in Survival Trees. Methods of Information in Medicine 45, 548-556.
58. Ridgeway, G. (1999). The State of Boosting. Computing Science and Statistics. 31, 172-181.
59. Rokach, L. (2008). Taxonomy for Characterizing Ensemble Methods in Classification Tasks: A Review and Annotated Bibliography. Computational Statistics and Data Analysis 53, 4046-4072.MR2744304
60. Schlittgen, R. (1999). Regression Trees for Survival Data - an Approach to Select Discontinuous Split Points by Rank Statistics. Biometrical Journal 41, 943-954.MR1747521
61. Segal, M. R. (1988). Regression Trees for Censored Data. Biometrics 44, 35-48.
62. Segal, M. R. (1992). Tree-Structured Methods for Longitudinal Data. Journal of the American Statistical Association 87, 407-418.
63. Siroky, D.S. (2009). Navigating Random Forests and Related Advances in Algorithmic Modeling. Statistics Surveys 3, 147-163.MR2556872
64. Su, X. and Fan, J. (2004).Multivariate Survival Trees: A Maximum Likelihood Approach Based on Frailty Models. Biometrics 60, 93-99.MR2043623
65. Su, X. and Tsai, C.-L. (2005). Tree-augmented Cox Proportional Hazards Models. Biostatistics 6, 486-499.
66. Therneau, T., Grambsch, P. and Fleming, T. (1990). Martingale-Based Residuals for Survival Models. Biometrika 77, 147-160.MR1049416
67. Therneau, T. M. and Atkinson, B. (2010). R port by Brian Ripley. rpart: Recursive Partitioning. R package version 3.1-46. http://CRAN.Rproject.org/package=rpart.
68. Tsai, C., Chen, D.-T., Chen, J., Balch, C. M., Thompson, J. and Soong, S.-J. (2007). An Integrated Tree-Based Classification Approach to Prognostic Grouping with Application to Localized Melanoma Patients. Journal of Biopharmaceutical Statistics 17, 445-460. MR2370755
69. Verikas, A., Gelzinis, A. and Bacauskiene, M. (2011). Mining Data With Random Forests: A Survey and Results of New Tests. Pattern Recognition 44, 330-349.
70. Wallace, M. L., Anderson, S. J. and Mazumdar, S. (2010). A Stochastic Multiple Imputation Algorithm for Missing Covariate Data in Tree-Structured Survival Analysis. Statistics in Medicine 29, 3004-3016.
71. Xu, R. and Adak, S. (2001). Survival Analysis with Time-Varying Relative Risks: A Tree-Based Approach. Methods of information in medicine 40, 141-147.
72. Xu, R. and Adak, S. (2002). Survival Analysis with Time-Varying Regression Effects Using a Tree-Based Approach. Biometrics 58, 305-315.MR1908170
73. Yin, Y. and Anderson, J. (2002). Nonparametric Tree-Structured Modeling for Interval-Censored Survival Data. Joint Statistical Meeting, August 2002. 6 pages. MR2703473
74. Zhang, H.P. (1995). Splitting Criteria in Survival Trees. In Statistical Modeling: Proceedings of the 10th International Workshop on Statistical Modeling, 305-314, Springer.