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A Simple Test for the Absence of Covariate Dependence in Hazard Regression Models

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Bhattacharjee, Arnab

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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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 3937.

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Date of creation: 2004
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Handle: RePEc:pra:mprapa:3937

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

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Find related papers by JEL classification:
C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing

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  1. Bhattacharjee, Arnab, 2004. "Estimation in hazard regression models under ordered departures from proportionality," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 517-536, October. [Downloadable!] (restricted)
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  2. D. Y. Lin & L. J. Wei & I. Yang & Z. Ying, 2000. "Semiparametric regression for the mean and rate functions of recurrent events," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 711-730. [Downloadable!] (restricted)
  3. Tue Gorgens & Joel L. Horowitz, 1996. "Semiparametric Estimation of a Censored Regression Model with an Unknown Transformation of the Dependent Variable," Econometrics 9603001, EconWPA. [Downloadable!]
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  4. Melino, Angelo & Sueyoshi, Glenn T., 1990. "A simple approach to the identifiability of the proportional hazards model," Economics Letters, Elsevier, vol. 33(1), pages 63-68, May. [Downloadable!] (restricted)
  5. Bhattacharjee, A. & Samarjit Das, 2002. "Testing Proportionality in Duration Models with Respect to Continuous Covariates," Cambridge Working Papers in Economics 0220, Faculty of Economics, University of Cambridge. [Downloadable!]
  6. Lin D Y & Ying Z, 2001. "Semiparametric and Nonparametric Regression Analysis of Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 103-126, March. [Downloadable!] (restricted)
  7. Bhattacharje,e A. & C.Higson & S.Holly & P.Kattuman, 2002. "Macro Economic Instability and Business Exit: Determinants of Failures and Acquisitions of Large UK Firms," Royal Economic Society Annual Conference 2002 27, Royal Economic Society. [Downloadable!]
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  8. Joel L. Horowitz, 1999. "Semiparametric Estimation of a Proportional Hazard Model with Unobserved Heterogeneity," Econometrica, Econometric Society, vol. 67(5), pages 1001-1028, September.
  9. Li, Yi-Hwei & Klein, John P. & Moeschberger, M. L., 1996. "Effects of model misspecification in estimating covariate effects in survival analysis for small sample sizes," Computational Statistics & Data Analysis, Elsevier, vol. 22(2), pages 177-192, July. [Downloadable!] (restricted)
  10. Horowitz, Joel L, 1996. "Semiparametric Estimation of a Regression Model with an Unknown Transformation of the Dependent Variable," Econometrica, Econometric Society, vol. 64(1), pages 103-37, January. [Downloadable!] (restricted)
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  1. Bhattacharjee, Arnab & Bhattacharjee, Madhuchhanda, 2007. "Bayesian Analysis of Hazard Regression Models under Order Restrictions on Covariate Effects and Ageing," MPRA Paper 3938, University Library of Munich, Germany. [Downloadable!]
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