Bhattacharjee, Arnab
(2004):
*A Simple Test for the Absence of Covariate Dependence in Hazard Regression Models.*

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## Abstract

This paper extends commonly used tests for equality of hazard rates in a two-sample or k-sample setup to a situation where the covariate under study is continuous. In other words, we test the hypothesis that the conditional hazard rate is the same for all covariate values, against the omnibus alternative as well as more specific alternatives, when the covariate is continuous. The tests developed are particularly useful for detecting trend in the underlying conditional hazard rates or changepoint trend alternatives. Asymptotic distribution of the test statistics are established and small sample properties of the tests are studied. An application to the e¤ect of aggregate Q on corporate failure in the UK shows evidence of trend in the covariate e¤ect, whereas a Cox regression model failed to detect evidence of any covariate effect. Finally, we discuss an important extension to testing for proportionality of hazards in the presence of individual level frailty with arbitrary distribution.

Item Type: | MPRA Paper |
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Institution: | University of St Andrews |

Original Title: | A Simple Test for the Absence of Covariate Dependence in Hazard Regression Models |

Language: | English |

Keywords: | Covariate dependence; Continuous covariate; Two-sample tests; Trend tests; Proportional hazards; Frailty/ unobserved heterogeneity; Linear transformation model |

Subjects: | C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C41 - Duration Analysis ; Optimal Timing Strategies C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General |

Item ID: | 3937 |

Depositing User: | Arnab Bhattacharjee |

Date Deposited: | 09 Jul 2007 |

Last Modified: | 02 Oct 2019 16:43 |

References: | Andersen, P.K., Borgan, O., Gill, R.D. and Keiding, N. (1992). Statistical Models based on Counting Processes. Springer-Verlag, New York. Berman, S.M. (1992). Sojourns and Extremes of Stochastic Processes. Wadsworth and Brooks/ Cole, Pacific Grove, CA. Bhattacharjee, A. (2004). Estimation in hazard regression models under ordered departures from proportionality. Computational Statistics and Data Analysis 47, 517--536. Bhattacharjee, A. (2006). Testing Proportionality in Duration Models with Respect to Continuous Covariates. Mimeo. Bhattacharjee, A., Higson, C., Holly, S. and Kattuman, P. (2002). Macro economic instability and business exit: Determinants of failures and acquisitions of large UK firms. DAE Working Paper No. 0206, Department of Applied Economics, University of Cambridge. Breslow, N.E. (1970). A generalized Kruskal-Wallis test for comparing K samples subject to unequal patterns of censorship. Biometrika 57, 579--594. Brown, B.W., Jr., Hollander, M. and Korwar, R.M. (1974). Nonparametric tests of independence for censored data, with applications to heart transplant studies. In: Reliability and Biometry, Statistical Analysis of Lifelength (Eds.) Proschan, F. and Serfling, R.J., Society for Industrial and Applied Mathematics: Philadelphia, 327--354. Cox, D.R. (1972). Regression models and life tables (with discussion). Journal of the Royal Statistical Scociety, Series B 34, 187--220. Deshpande, J.V. and Sengupta, D. (1995). Testing for the hypothesis of proportional hazards in two populations. Biometrika 82, 251--261. Fleming, T.R. and Harrington, D.P. (1991). Counting processes and survival Analysis. John Wiley and Sons, New York. Gehan, E.A. (1965). A generalized Wilcoxon test for comparing arbitrarily singly censored samples. Biometrika 52, 203--223. Gill, R.D. and Schumacher, M. (1987). A simple test of the proportional hazards assumption. Biometrika 74, 289--300. Gu, M., Follmann, D. and Geller, N.L. (1999). Monitoring a general class of two-sample survival statistics with applications. Biometrika 86, 45--57. Harrington, D.P. and Fleming, T.R. (1982). A class of rank test procedures for censored survival data. Biometrika 69, 133--143. Horowitz, J. L. (1996). Semiparametric estimation of a regression model with an unknown transformation of the dependent variable. Econometrica 64, 103--107. Horowitz, J.L. (1999). Semiparametric estimation of a proportional hazard model with unobserved heterogeneity. Econometrica 67, 1001--1028. Horowitz, J.L. and Neumann, G.R. (1992). A generalised moments specification test of the proportional hazards model. Journal of the American Statistical Association 87, 234--240. Jespersen, N.C.B. (1986). Dichotomising a continuous covariate in the Cox regression model. Research Report 86/2, Statistical Research Unit, University of Copenhagen. Jones, M.P. and Crowley, J.J. (1989). A general class of nonparametric tests for survival analysis. Biometrics 45, 157--170. Jones, M.P. and Crowley, J.J. (1990). Asymptotic properties of a general class of nonparametric tests for survival analysis. Annals of Statistics 18, 1203--1220. Kortram, R.A., A.J. Lenstra, G. Ridder, and A.C.M. van Rooij (1995). Constructive identification of the mixed proportional hazards model. Statistica Neerlandica 49, 269--281. Lenstra, A.J. and van Rooij, A.C.M. (1998). Nonparametric estimation of the mixed proportional hazards model. Working paper, Free University, Amsterdam. Li, Y.-H., Klein, J.P. and Moeschberger, M.L. (1996). Effects of model misspecification in estimating covariate effects in survival analysis for small sample sizes. Computational Statistics and Data Analysis 22, 177--192. Lin, D.Y., Wei, L.J., Yang, I. and Ying, Z. (2000). Semiparametric regression for the mean and rate functions of recurrent events. Journal of the Royal Statistical Society Series B 62, 711--730. Lin, D.Y. and Ying, Z. (2001). Semiparametric and nonparametric regression analysis of longitudinal data (with discussion and a rejoinder). Journal of the American Statistical Association 96, 103--126. Liu, P.Y., Green, S., Wolf, M. and Crowley, J. (1993). Testing against ordered alternatives for censored survival data. Journal of the American Statistical Association 88, 421, 153--160. Liu, P.Y. and Tsai, W.Y. (1999). A modified logrank test for censored survival data under order restrictions. Statistics and Probability Letters 41, 57--63. Mantel, N. (1966). Evaluation of survival data and two new rank order statistics arising in its consideration. Cancer Chemotherapy. Report 50, 163--170. Mau, J. (1988). A generalization of a nonparametric test for stochastically ordered distributions to censored survival data. Journal of the Royal Statistical Society Series B 50, 403--412. Melino, A. and G.T. Sueyoshi (1990). A simple approach to the identifiability of the proportional hazards model. Economics Letters 33, 63--68. Murphy, S.A. and Sen, P.K. (1991). Time-dependent coefficients in a Cox-type regression model. Stochastic Processes and their Applications 39,153--180. Neumann, G.R. (1997). Search models and duration data. In: Handbook of Applied Econometrics Volume II: Microeconometrics (Eds.) Pesaran, M.H., Basil Blackwell: Oxford, Chapter 7, 300--351. O'Brien, P.C. (1978). A nonparametric test for association with censored data. Biometrics 34, 243--250. Peto, R. and Peto, J. (1972). Asymptotically efficient rank invariant test procedures (with discussion). Journal of the Royal Statistical Society Series A 135, 185--206. Prentice, R.L. (1978). Linear rank tests with right censored data. Biometrika 65, 167--179. Correction: 70, 304 (1983). Sengupta, D., Bhattacharjee, A., and Rajeev, B. (1998). Testing for the proportionality of hazards in two samples against the increasing cumulative hazard ratio alternative. Scandinavian Journal of Statistics 25, 637--647. Spiekerman, C.F. and Lin, D.Y. (1998). Marginal regression models for multivariate failure time data. Journal of the American Statistical Association 93, 1164--1175. Tarone, R.E. (1975). Tests for trend in life table analysis. Biometrika 62, 679--682. Tarone, R.E. and Ware, J.H. (1977). On distribution-free tests for equality of survival distributions. Biometrika 64, 156--160. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/3937 |