Decision Tree for Competing Risks Survival Probability in Breast Cancer Study

Authors: N. A. Ibrahim, A. Kudus, I. Daud, M. R. Abu Bakar

Abstract:

Competing risks survival data that comprises of more than one type of event has been used in many applications, and one of these is in clinical study (e.g. in breast cancer study). The decision tree method can be extended to competing risks survival data by modifying the split function so as to accommodate two or more risks which might be dependent on each other. Recently, researchers have constructed some decision trees for recurrent survival time data using frailty and marginal modelling. We further extended the method for the case of competing risks. In this paper, we developed the decision tree method for competing risks survival time data based on proportional hazards for subdistribution of competing risks. In particular, we grow a tree by using deviance statistic. The application of breast cancer data is presented. Finally, to investigate the performance of the proposed method, simulation studies on identification of true group of observations were executed.

Keywords: Competing risks, Decision tree, Simulation, Subdistribution Proportional Hazard.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1078975

References:

[1] L. Breiman, J. Friedman, R. Olshen and C. Stone, "Classification and regression trees", New York: Chapman and Hall, 1984.
[2] J. R. Quinlan, "C4.5: Program for Machine Learning", 1992, California: Morgan Kaufmann.
[3] L. Gordon, and R. Olshen, "Tree-structured survival analysis", 1985, Cancer Treatment Reports 69, pp. 1065-1069.
[4] M. R. Segal, "Regression trees for censored data", 1988, Biometrics 44, pp. 35-47.
[5] R. Davis and J. Anderson, "Exponential survival trees", 1989, Statistics in Medicine 8, pp. 947-962.
[6] M. LeBlanc, and J. Crowley, "Relative risk trees for censored survival data", 1992, Biometrics 48, pp. 411-425.
[7] M. LeBlanc, and J. Crowley, "Survival trees by goodness of split", 1993, Journal of the American Statistical Association 88, pp. 457-467.
[8] M. R. Segal, "Extending the elements of tree-structured regression", Statist. Methods Med. Res. 4, pp. 219-236.
[9] X. Huang, S. Chen, and S. Soong, "Piecewise exponential survival trees with time-dependent covariates", 1998, Biometrics 54, pp. 1420-1433.
[10] M. R. Segal, "Tree-structured method for longitudinal data", 1992, Journal of the American Statistical Association 87, pp. 407-418.
[11] H. P. Zhang, "Classification tree for multiple binary responses", 1998, Journal of the American Statistical Association 93, pp. 180-193.
[12] X. G. Su and J.J. Fan, "Multivariate survival trees: a maximum likelihood approach based on frailty models", Biometrics 60, pp. 93-99.
[13] F. Gao, A. K. Manatunga, and S. Chen, "Identification of prognostic factors with multivariate survival data", 2004, Computational Statistics and Data Analysis 45, pp. 813-824.
[14] A. W. Fyles, D. R. McCready, L. A Manchul., M. E. Trudeau, P. Merante, M. Pintilie, L. M. Weir, and I. A. Olivotto, "Tamoxifen with or without breast irradiation in women 50 years of age or older with early breast cancer", 2004, New England Journal of Medicine 351, pp. 963-970.
[15] J. P. Fine and R. J. Gray , "A proportional hazards model for the subdistribution of a competing risk", 1999, Journal of the American Statistical Association 94, pp. 496-509.
[16] D. Collett, "Modelling survival data in medical research", London: Chapman and Hall, 1994.