Decision tree for modeling survival data with competing risks

Abstract This work considers decision tree for modeling survival data with competing risks. A Survival Classification and Regression Tree (SCART) technique is proposed for analysing survival data by modifying classification and regression tree (CART) algorithm to handle censored data for both regression and classification problems. Different performance measures for regression and classification tree are proposed. Model validation is done by two different cross-validation methods. Two real life data sets are analyzed for illustration. It is found that the proposed method improve upon the existing classical method for analysis of survival data with competing risks.

[1]  J. Lawless Statistical Models and Methods for Lifetime Data , 2002 .

[2]  M S Pepe,et al.  Kaplan-Meier, marginal or conditional probability curves in summarizing competing risks failure time data? , 1993, Statistics in medicine.

[3]  Magni Martens,et al.  Multivariate Analysis of Quality : An Introduction , 2001 .

[4]  Gang Li,et al.  Joint Inference for Competing Risks Survival Data , 2016, Journal of the American Statistical Association.

[5]  T. Lumley,et al.  Time‐Dependent ROC Curves for Censored Survival Data and a Diagnostic Marker , 2000, Biometrics.

[6]  G. Brier VERIFICATION OF FORECASTS EXPRESSED IN TERMS OF PROBABILITY , 1950 .

[7]  Zhigang Chen,et al.  Decision based on big data research for non-small cell lung cancer in medical artificial system in developing country , 2018, Comput. Methods Programs Biomed..

[8]  Michael W. Kattan,et al.  An empirical approach to model selection through validation for censored survival data , 2011, J. Biomed. Informatics.

[9]  M. Crowder Multivariate Survival Analysis and Competing Risks , 2012 .

[10]  Wei Xu,et al.  Recursive Partitioning Method on Competing Risk Outcomes , 2016, Cancer informatics.

[11]  D. Kundu,et al.  Analysis of hybrid censored competing risks data , 2014 .

[12]  M. Crowder Classical Competing Risks , 2001 .

[13]  D. Kundu,et al.  Bayesian analysis of progressively censored competing risks data , 2011 .

[14]  Abdul Kudus,et al.  Decision Tree for Competing Risks Survival Probability in Breast Cancer Study , 2008 .

[15]  Malgorzata Kretowska Piecewise-linear criterion functions in oblique survival tree induction , 2017, Artif. Intell. Medicine.

[16]  Mihaela van der Schaar,et al.  Tree-based Bayesian Mixture Model for Competing Risks , 2018, AISTATS.

[17]  R. Dennis Cook,et al.  Cross-Validation of Regression Models , 1984 .

[18]  Thomas A Gerds,et al.  Absolute risk regression for competing risks: interpretation, link functions, and prediction , 2012, Statistics in medicine.

[19]  John W. Tukey,et al.  Data Analysis and Regression: A Second Course in Statistics , 1977 .

[20]  Feng Gao,et al.  Developing Multivariate Survival Trees with a Proportional Hazards Structure , 2021, Journal of Data Science.

[21]  Thomas A Gerds,et al.  Estimating a time‐dependent concordance index for survival prediction models with covariate dependent censoring , 2013, Statistics in medicine.

[22]  Changhee Lee,et al.  DeepHit: A Deep Learning Approach to Survival Analysis With Competing Risks , 2018, AAAI.

[23]  Wei-Yin Loh,et al.  Classification and regression trees , 2011, WIREs Data Mining Knowl. Discov..

[24]  Mahboob Rahman,et al.  Statistical Methods for Cohort Studies of CKD: Survival Analysis in the Setting of Competing Risks. , 2017, Clinical journal of the American Society of Nephrology : CJASN.

[25]  D. Cox Regression Models and Life-Tables , 1972 .

[26]  D. Harrington,et al.  Counting Processes and Survival Analysis , 1991 .

[27]  Philip S Rosenberg,et al.  Competing Risks Analysis of Correlated Failure Time Data , 2008, Biometrics.

[28]  Zhongheng Zhang,et al.  Overview of model validation for survival regression model with competing risks using melanoma study data. , 2018, Annals of translational medicine.

[29]  S. Keleş,et al.  Residual‐based tree‐structured survival analysis , 2002, Statistics in medicine.

[30]  Denis Larocque,et al.  Survival forests for data with dependent censoring , 2019, Statistical methods in medical research.

[31]  R. Olshen,et al.  Tree-structured survival analysis. , 1985, Cancer treatment reports.

[32]  E Graf,et al.  Assessment and comparison of prognostic classification schemes for survival data. , 1999, Statistics in medicine.

[33]  R. Tibshirani,et al.  Improvements on Cross-Validation: The 632+ Bootstrap Method , 1997 .

[34]  Harald Binder,et al.  A general, prediction error‐based criterion for selecting model complexity for high‐dimensional survival models , 2010, Statistics in medicine.

[35]  John P. Klein,et al.  Two-sample tests of the equality of two cumulative incidence functions , 2007, Comput. Stat. Data Anal..

[36]  Wentao Bao Survival analysis in the presence of competing risks. , 2017, Annals of translational medicine.

[37]  Tianxi Cai,et al.  Evaluating Prediction Rules for t-Year Survivors With Censored Regression Models , 2007 .

[38]  F. Oliva,et al.  Application of competing risks analysis improved prognostic assessment of patients with decompensated chronic heart failure and reduced left ventricular ejection fraction. , 2018, Journal of clinical epidemiology.

[39]  Harald Binder,et al.  Bioinformatics Applications Note Parallelized Prediction Error Estimation for Evaluation of High-dimensional Models , 2022 .

[40]  P. Heagerty,et al.  Survival Model Predictive Accuracy and ROC Curves , 2005, Biometrics.

[41]  Mihaela van der Schaar,et al.  Multitask Boosting for Survival Analysis with Competing Risks , 2018, NeurIPS.

[42]  Ariel Linden,et al.  Modeling time-to-event (survival) data using classification tree analysis. , 2017, Journal of evaluation in clinical practice.

[43]  Thomas A Gerds,et al.  Efron‐Type Measures of Prediction Error for Survival Analysis , 2007, Biometrics.

[44]  Ataur Rahman,et al.  Applicability of Monte Carlo cross validation technique for model development and validation using generalised least squares regression , 2013 .

[45]  Yi-Zeng Liang,et al.  Monte Carlo cross‐validation for selecting a model and estimating the prediction error in multivariate calibration , 2004 .

[46]  Robert Gray,et al.  A Proportional Hazards Model for the Subdistribution of a Competing Risk , 1999 .

[47]  Mark R. Segal,et al.  Regression Trees for Censored Data , 1988 .

[48]  M. Schumacher,et al.  Consistent Estimation of the Expected Brier Score in General Survival Models with Right‐Censored Event Times , 2006, Biometrical journal. Biometrische Zeitschrift.

[49]  Kurt Ulm,et al.  Applying competing risks regression models: an overview , 2013, Lifetime data analysis.

[50]  M. Enriquez-Sarano,et al.  Competing risks need to be considered in survival analysis models for cardiovascular outcomes , 2017, The Journal of thoracic and cardiovascular surgery.

[51]  Nigel Sim,et al.  Statistical Confidence for Variable Selection in QSAR Models via Monte Carlo Cross-Validation , 2008, J. Chem. Inf. Model..

[52]  K. Hornik,et al.  Unbiased Recursive Partitioning: A Conditional Inference Framework , 2006 .

[53]  Purushottam W. Laud,et al.  Nonparametric survival analysis using Bayesian Additive Regression Trees (BART) , 2016, Statistics in medicine.

[54]  Tianxi Cai,et al.  The Performance of Risk Prediction Models , 2008, Biometrical journal. Biometrische Zeitschrift.

[55]  F. Oliva,et al.  Long-term prognostic implications of the ADHF/NT-proBNP risk score in patients admitted with advanced heart failure. , 2016, The Journal of heart and lung transplantation : the official publication of the International Society for Heart Transplantation.

[56]  Harald Binder,et al.  The benefit of data-based model complexity selection via prediction error curves in time-to-event data , 2011, Comput. Stat..

[57]  Melania Pintilie,et al.  Competing Risks: A Practical Perspective , 2006 .

[58]  Seungbong Han,et al.  Multiple imputation for competing risks survival data via pseudo-observations , 2018 .

[59]  Hemant Ishwaran,et al.  Random Survival Forests , 2008, Wiley StatsRef: Statistics Reference Online.

[60]  M. LeBlanc,et al.  Survival Trees by Goodness of Split , 1993 .

[61]  Wenbin Lu,et al.  ANALYSIS OF COMPETING RISKS DATA WITH MISSING CAUSE OF FAILURE UNDER ADDITIVE HAZARDS MODEL , 2008 .

[62]  Hemant Ishwaran,et al.  Random survival forests for competing risks. , 2014, Biostatistics.