Predictive Accuracy and Covariates Selection Performance of Time-To-Event Data: A Comparison Study of Cox Proportional Hazard and Random Survival Forest Models
DOI:
https://doi.org/10.14738/tecs.123.17112Keywords:
Predictive accuracy, Random survival forest, Covariates significance, Cox proportional hazard model, Survival analysis, time-to-eventAbstract
Background: The Cox proportional hazard (Cox PH) model is the most common and widely used method for analyzing time-to-event data. This approach, however, has been criticized for predicting patient outcomes since it assumes that the outcome is a linear combination of covariates and a constant hazard ratio over time, which is invalid in many cases and may not always be fulfilled, and thus Random Survival Forest (RSF) for time-to-event data has been proposed as an alternative to Cox PH. By considering non-linearity and interrelated covariates, the RSF is recognized as a way to correct bias in Cox proportional hazard models. Methods: The Cox PH model was compared to the Random Survival Forest by a relaxed proportional hazard (PH) assumption in this retrospective cohort study, which included 189 patients who underwent a new algorithmic treatment of an advanced human immunodeficiency virus clinical trial proposed by the World Health Organization from January to December 2018 at Kibong'oto infectious diseases hospital. Results: The study results show that the Random Survival Forest outperforms the Cox PH model in time-to-event data analysis by integrating covariates that do not meet proportional hazard assumptions based on predictive error curves, concordance indices, Brier scores, and integrated Brier scores as predictive indicators. Despite the fact that the PH assumption was relaxed for all covariates in the dataset, the Cox PH model selected only a few, and all deselected covariates were highly significant in the RSF, implying that the Cox PH model was inbuilt with the proportional hazard assumption. Conclusions: As a result, only covariates that satisfied the PH inbuilt assumption were chosen, regardless of whether the assumption was tested or not, rendering it ineffective when compared to a random survival forest. Therefore, having a dataset free from non-linearity and interrelated variables is impossible in the real world; hence, the RSF model outperforms the Cox PH model in predictive accuracy and covariate selection performance.
References
Wang W, Liu W. Integration of gene interaction information into a reweighted random survival forest approach for accurate survival prediction and survival biomarker discovery. Sci Rep 2018; 8: 1–14.
Freeman SC, Cooper NJ, Sutton AJ, et al. Challenges of modelling approaches for network meta-analysis of time-to-event outcomes in the presence of non-proportional hazards to aid decision making: Application to a melanoma network. Stat Methods Med Res 2022; 31: 839–861.
Sun T, Wei Y, Chen W, et al. Genome-wide association study-based deep learning for survival prediction. Stat Med 2020; 39: 4605–4620.
Huang Z, Zhang H, Boss J, et al. Complete hazard ranking to analyze right-censored data: An ALS survival study. PLoS Comput Biol 2017; 13: 1–21.
Tilman N. Prediction models for survival data with machine learning: an application to soft tissue sarcoma cohort statistical science for the life and behavioural science. Universiteit Leiden, 2020.
Liu Y, Zhou S, Wei H, et al. A comparative study of forest methods for time-to-event data: variable selection and predictive performance. BMC Med Res Methodol 2021; 21: 193.
Babińska M, Chudek J, Chełmecka E, et al. Limitations of Cox proportional hazards analysis in mortality prediction of patients with acute coronary syndrome. Stud Logic, Gramm Rhetor 2015; 43: 33–48.
Austin PC. Statistical power to detect violation of the proportional hazards assumption when using the Cox regression model. J Stat Comput Simul 2018; 88: 533–552.
Xue Y, Schifano ED. Diagnostics for the Cox model. Commun Stat Appl Methods 2017; 24: 583–604.
Waititu HW, Koske JKA, Onyango NO. Analysis of Balanced Random Survival Forest Using Different Splitting Rules : Application on Child Mortality. 2021; 11: 37–49.
Bellera CA, MacGrogan G, Debled M, et al. Variables with time-varying effects and the Cox model: Some statistical concepts illustrated with a prognostic factor study in breast cancer. BMC Med Res Methodol 2010; 10: 20.
Wang H, Zhou L. Random survival forest with space extensions for censored data. Artif Intell Med 2017; 79: 52–61.
Du M, Haag DG, Lynch JW, et al. Comparison of the tree-based machine learning algorithms to cox regression in predicting the survival of oral and pharyngeal cancers: Analyses based on seer database. Cancers (Basel) 2020; 12: 1–16.
Miao F, Cai YP, Zhang YX, et al. Predictive modeling of hospital mortality for patients with heart failure by using an improved random survival forest. IEEE Access 2018; 6: 7244–7253.
Dietrich S. Investigation of the machine learning method Random Survival Forest as an exploratory analysis tool for the identification of variables associated with disease risks in complex survival data . Technischen Universität Berlin, 2016.
Kim DW, Lee S, Kwon S, et al. Deep learning-based survival prediction of oral cancer patients. Sci Rep 2019; 9: 1–10.
Nasejje JB, Mwambi H, Dheda K, et al. A comparison of the conditional inference survival forest model to random survival forests based on a simulation study as well as on two applications with time-to-event data. BMC Med Res Methodol 2017; 17: 115.
Nasejje JB, Mwambi H. Application of random survival forests in understanding the determinants of underfive child mortality in Uganda in the presence of covariates that satisfy the proportional and nonproportional hazards assumption. BMC Res Notes 2017; 10: 1–18.
Abeysekera W, Sooriyarachchi M. Use of Schoenfeld’s global test to test the proportional hazards assumption in the Cox proportional hazards model: an application to a clinical study. J Natl Sci Found Sri Lanka 2009; 37: 41.
Binder DA. Fitting Cox’s proportional hazards models from survey data. Biometrika 1992; 79: 139–147.
Yosefian I, Mosa Farkhani E, Baneshi MR. Application of Random Forest Survival Models to Increase Generalizability of Decision Trees: A Case Study in Acute Myocardial Infarction. Comput Math Methods Med 2015; 2015: 1–6.
Lipson R. Predicting Ovarian Cancer Survival Times: Performance of Parametric Methods and Random Survival Forests. Simon Frasel University, http://summit.sfu.ca/item/13829 (2014).
Rono CM. Feature selection methods and Resampling techniques in Survival data: Determination of risk factors of under-five child mortality Research. University of Nairobi, 2021.
Dietrich S, Floegel A, Troll M, et al. Random Survival Forest in practice: a method for modelling complex metabolomics data in time to event analysis. Int J Epidemiol 2016; 45: 1406–1420.
Haider H, Hoehn B, Davis S, et al. Effective ways to build and evaluate individual survival distributions. J Mach Learn Res 2020; 21: 1–63.
Ishwaran H, Kogalur UB, Blackstone EH, et al. Random survival forests. Ann Appl Stat 2008; 2: 841–860.
Wanyonyi KS. Comparison of Random Survival Forests Split rules in selecting the determinants of under-five mortality in Kenya using 2014 DHS data. University of Nairobi, https://math.umn.edu/sites/math.umn.edu/files/math.umn_.edu-newsletter_2009_0.pdf (2019).
Weathers B, Cutler R. Comparision of Survival Curves Between Cox Proportional Hazards, Random Forests, and Conditional Inference Forests in Survival Analysis. Utah State Univ Thesis; 2, https://digitalcommons.usu.edu/gradreports/927 (2017).
Saha S, Ryu D, Ebrahimi N. Variable Selection with Random Survival Forest and Bayesian Additive Regression Tree for Survival Data. 2019; 48824: 1–27.
Wubie BA. Clustering Survival Data using Random Forest and Persistent Master of Science. University of Alberta, 2016.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Ramkumar T Balan, Oscar Leonard. K
This work is licensed under a Creative Commons Attribution 4.0 International License.
