{"title":"Decision Tree for Competing Risks Survival Probability in Breast Cancer Study","authors":"N. A. Ibrahim, A. Kudus, I. Daud, M. R. Abu Bakar","volume":14,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":70,"pagesEnd":75,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/12319","abstract":"Competing risks survival data that comprises of more\r\nthan one type of event has been used in many applications, and one\r\nof these is in clinical study (e.g. in breast cancer study). The\r\ndecision tree method can be extended to competing risks survival\r\ndata by modifying the split function so as to accommodate two or\r\nmore risks which might be dependent on each other. Recently,\r\nresearchers have constructed some decision trees for recurrent\r\nsurvival time data using frailty and marginal modelling. We further\r\nextended the method for the case of competing risks. In this paper,\r\nwe developed the decision tree method for competing risks survival\r\ntime data based on proportional hazards for subdistribution of\r\ncompeting risks. In particular, we grow a tree by using deviance\r\nstatistic. The application of breast cancer data is presented. Finally,\r\nto investigate the performance of the proposed method, simulation\r\nstudies on identification of true group of observations were executed.","references":"[1] L. Breiman, J. Friedman, R. Olshen and C. Stone, \"Classification and\r\nregression trees\", New York: Chapman and Hall, 1984.\r\n[2] J. R. Quinlan, \"C4.5: Program for Machine Learning\", 1992, California:\r\nMorgan Kaufmann.\r\n[3] L. Gordon, and R. Olshen, \"Tree-structured survival analysis\", 1985,\r\nCancer Treatment Reports 69, pp. 1065-1069.\r\n[4] M. R. Segal, \"Regression trees for censored data\", 1988, Biometrics 44,\r\npp. 35-47.\r\n[5] R. Davis and J. Anderson, \"Exponential survival trees\", 1989, Statistics\r\nin Medicine 8, pp. 947-962.\r\n[6] M. LeBlanc, and J. Crowley, \"Relative risk trees for censored survival\r\ndata\", 1992, Biometrics 48, pp. 411-425.\r\n[7] M. LeBlanc, and J. Crowley, \"Survival trees by goodness of split\", 1993,\r\nJournal of the American Statistical Association 88, pp. 457-467.\r\n[8] M. R. Segal, \"Extending the elements of tree-structured regression\",\r\nStatist. Methods Med. Res. 4, pp. 219-236.\r\n[9] X. Huang, S. Chen, and S. Soong, \"Piecewise exponential survival trees\r\nwith time-dependent covariates\", 1998, Biometrics 54, pp. 1420-1433.\r\n[10] M. R. Segal, \"Tree-structured method for longitudinal data\", 1992,\r\nJournal of the American Statistical Association 87, pp. 407-418.\r\n[11] H. P. Zhang, \"Classification tree for multiple binary responses\", 1998,\r\nJournal of the American Statistical Association 93, pp. 180-193.\r\n[12] X. G. Su and J.J. Fan, \"Multivariate survival trees: a maximum\r\nlikelihood approach based on frailty models\", Biometrics 60, pp. 93-99.\r\n[13] F. Gao, A. K. Manatunga, and S. Chen, \"Identification of prognostic\r\nfactors with multivariate survival data\", 2004, Computational Statistics\r\nand Data Analysis 45, pp. 813-824.\r\n[14] A. W. Fyles, D. R. McCready, L. A Manchul., M. E. Trudeau, P.\r\nMerante, M. Pintilie, L. M. Weir, and I. A. Olivotto, \"Tamoxifen with\r\nor without breast irradiation in women 50 years of age or older with\r\nearly breast cancer\", 2004, New England Journal of Medicine 351, pp.\r\n963-970.\r\n[15] J. P. Fine and R. J. Gray , \"A proportional hazards model for the\r\nsubdistribution of a competing risk\", 1999, Journal of the American\r\nStatistical Association 94, pp. 496-509.\r\n[16] D. Collett, \"Modelling survival data in medical research\", London:\r\nChapman and Hall, 1994.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 14, 2008"}