The aim of this paper is to propose a new survival tree method for discrete-time survival data with time-varying covariates. This method can accommodate simultaneously time-varying covariates and time-varying effects. The method is then used for bankruptcy analysis of US firms that conducted an Initial Public Offerings between 1990 and 1999 using accounting and financial ratios.
Altman EI (1968) Financial ratios: discriminant analysis and the prediction of corporate bankruptcy. Journal of Finance, 23, 589–609.
2.
Bacchetti P and Segal M (1995) Survival trees with time-dependent covariates: application to estimating changes in the incubation period of AIDS. Lifetime Data Analysis, 1, 35–47.
3.
Beaver W (1966) Financial ratios as predictors of failure. Journal of Accounting Research, 5, 71–111.
4.
Bellovary JL, Giacomino DE and Akers MD (2007) A review of bankruptcy prediction studies: 1930 to present. Journal of Financial Education, 33, 1–42.
5.
Bou-Hamad I, Larocque D, Ben-Ameur H, Masse L, et al. (2009). Discrete-time survival trees. Canadian Journal of Statistics, 37, 17–32.
6.
Breiman L (1996) Bagging predictors. Machine Learning, 24, 123–40.
7.
Breiman L (2001) Random forests. Machine Learning, 45, 5–32.
8.
Breiman L, Friedman J, Olshen R and Stone C (1984) Classification and regression trees. Belmont, California: Wadsworth International Group.
9.
Ciampi A, Thiffault J, Nakache J-P and Asselain B (1986) Stratification by stepwise regression, correspondance analysis and recursive partition: a comparison of three methods of analysis for survival data with covariates. Computational Statistics & Data Analysis, 4, 185–204.
10.
Davis RB and Anderson JR (1989) Exponential survival trees. Statistics in Medicine, 8, 947–61.
11.
De Leonardis D and Rocci R (2008) Assessing the default risk by means of a discrete-time survival analysis approach. Applied Stochastic Models in Business and Industry, 24, 291–306.
12.
Doornik JA (2002) Object-oriented matrix programming using ox, 3rd edition. London: Timberlake Consultants Press and Oxford. Available at www.doornik.com.
13.
Fan J, Su X-G, Levine RA, Nunn MA et al. (2006) Trees for correlated survival data by goodness of split, with applications to tooth prognosis. Journal ofthe American Statistical Association, 101, 959–67.
14.
Fanning K and Cogger KO (1994) A comparative analysis of artificial neural networks using financial distress prediction. Intelligent Systems in Accounting, Finance and Management, 3, 241–52.
15.
Freeman E (2007) PresenceAbsence: an R package for presence-absence model evaluation.Ogden,UT: USDA Forest Service.
16.
Frydman H, Altman EI and Kao D (1985) Introducing recursive partitioning for financial classification: the case of financial distress. Journal of Finance, 40, 269–91.
17.
Gao F, Manatunga AK and Chen S (2004) Identification of prognostic factors with multivariate survival data. Computational Statistics & Data Analysis, 45, 813–24.
18.
Gordon L and Olshen RA (1985) Tree-structured survival analysis. Cancer Treatment Reports, 69, 1065–69.
19.
Hamza M and Larocque D (2005) An empirical comparison of ensemble methods based on classification trees. Journal of Statistical Computation and Simulation, 75, 629–43.
20.
Hastie T, Tibshirani R and Friedman J (2009) The elements ofstatistical learning: data mining, inference, and prediction, 2nd edition. New York: Springer.
21.
Hothorn T, Bühlmann P, Dudoit S, Molinaro AM et al. (2006). Survival ensembles. Biostatistics, 7, 355–73.
22.
Hothorn T, Lausen B, Benner A and Radespiel-Tröger M (2004) Bagging survival trees. Statistics in Medicine, 23, 77–91.
23.
Huang X, Chen S and Soong S (1998) Piecewise exponential survival trees with time-dependent covariates. Biometrics, 54, 1420–33.
24.
Ishwaran H, Kogalur UB, Blackstone EH and Lauer MS (2008) Random survival forests. The Annals of Applied Statistics, 2, 841–60.
25.
Jin H, Lu Y, Stone K and Black DM (2004) Alternative tree-structured survival analysis based on variance of survival time. Medical Decision Making, 24, 670–80.
26.
LeBlanc M and Crowley J (1992) Relative risk trees for censored survival data. Biometrics, 48, 411–25.
27.
LeBlanc M and Crowley J (1993) Survival trees by goodness of split. Journal of the American Statistical Association, 88, 457–67.
28.
Liaw A and Wiener M (2002) Classification and regression by randomForest. RNews, 2, 18–22.
29.
Meyer PA and Pifer H (1970) Prediction of bank failures. Journal of Finance, 25, 853–68.
30.
Molinaro AM, Dudoit S and van der Laan, MJ (2004) Tree-based multivariate regression and density estimation with right-censored data. Journal of Multivariate Analysis, 90, 154–77.
31.
Morgan J and Sonquist J (1963) Problems in the analysis of survey data and a proposal. Journal of the American Statistical Association, 58, 415–34.
32.
Nam CW, Kim TS, Park NJ and Lee HK (2008) Bankruptcy prediction using a discrete-time duration model incorporating temporal and macroeconomic dependencies. Journal of Forecasting, 27, 493–506.
33.
Ohlson JA (1980) Financial ratios and the probabilistic prediction of bankruptcy. Journal of Accounting Research, 18, 109–31.
34.
R Development Core Team (2009) R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Available at http://www.R-project.org.
35.
Ross SA, Westerfield RW, Jordan BD and Roberts GS (2002) Fundamentals of corporate finance. Fourth Canadian Edition. Toronto: McGraw-Hill Ryerson.
36.
Segal MR (1988) Regression trees for censored data. Biometrics, 44, 35–48.
37.
Segal MR (1992) Tree-structured methods for longitudinal data. Journal ofthe American Statistical Association, 87, 407–18.
38.
Shumway T (2001) Forecasting bankruptcy more accurately: a simple hazard model. Journal of Business, 74, 101–24.
39.
Singer JD and Willett JB (1993) It’s about time: using discrete-time survival analysis to study duration and the timing of events. Journal of Educational Statistics, 18, 155–95.
40.
Su X and Fan J (2004) Multivariate survival trees: a maximum likelihood approach based on frailty models. Biometrics, 60, 93–99.
41.
Su X and Tsai C-L (2005) Tree-augmented Cox proportional hazards models. Biostatistics, 6, 486–99.
42.
Therneau TM and Atkinson B (2009) R port by Brian Ripley. rpart: Recursive Partitioning. R package version 3.1–45. Available at http://CRAN.R-project.org/package=rpart.
43.
Wood SN (2008) Fast stable direct fitting and smoothness selection for generalized additive models. Journal of the Royal Statistical Society B, 70, 495–518.
44.
Xu R and Adak S (2002) Survival analysis with time-varying regression effects using a tree-based approach. Biometrics, 58, 305–15.
45.
Zmijewski M (1984) Methodological issues related to the estimation of financial distress prediction models. Journal of Accounting Research, 22, 59–82.
