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Consistency of random survival forests

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  • Ishwaran, Hemant
  • Kogalur, Udaya B.

Abstract

We prove uniform consistency of Random Survival Forests (RSF), a newly introduced forest ensemble learner for analysis of right-censored survival data. Consistency is proven under general splitting rules, bootstrapping, and random selection of variables--that is, under true implementation of the methodology. Under this setting we show that the forest ensemble survival function converges uniformly to the true population survival function. To prove this result we make one key assumption regarding the feature space: we assume that all variables are factors. Doing so ensures that the feature space has finite cardinality and enables us to exploit counting process theory and the uniform consistency of the Kaplan-Meier survival function.

Suggested Citation

  • Ishwaran, Hemant & Kogalur, Udaya B., 2010. "Consistency of random survival forests," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1056-1064, July.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:13-14:p:1056-1064
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    References listed on IDEAS

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    1. Lin, Yi & Jeon, Yongho, 2006. "Random Forests and Adaptive Nearest Neighbors," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 578-590, June.
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    1. Hoora Moradian & Denis Larocque & François Bellavance, 2017. "$$L_1$$ L 1 splitting rules in survival forests," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(4), pages 671-691, October.
    2. Yifei Sun & Sy Han Chiou & Mei‐Cheng Wang, 2020. "ROC‐guided survival trees and ensembles," Biometrics, The International Biometric Society, vol. 76(4), pages 1177-1189, December.
    3. Susan Athey & Julie Tibshirani & Stefan Wager, 2016. "Generalized Random Forests," Papers 1610.01271, arXiv.org, revised Apr 2018.
    4. Scornet, Erwan, 2016. "On the asymptotics of random forests," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 72-83.
    5. Wenju Mo & Yuqin Ding & Shuai Zhao & Dehong Zou & Xiaowen Ding, 2020. "Identification of a 6-gene signature for the survival prediction of breast cancer patients based on integrated multi-omics data analysis," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-18, November.
    6. Gérard Biau & Erwan Scornet, 2016. "A random forest guided tour," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 197-227, June.
    7. Claudia Bühnemann & Simon Li & Haiyue Yu & Harriet Branford White & Karl L Schäfer & Antonio Llombart-Bosch & Isidro Machado & Piero Picci & Pancras C W Hogendoorn & Nicholas A Athanasou & J Alison No, 2014. "Quantification of the Heterogeneity of Prognostic Cellular Biomarkers in Ewing Sarcoma Using Automated Image and Random Survival Forest Analysis," PLOS ONE, Public Library of Science, vol. 9(9), pages 1-14, September.

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