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

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  • Bhattacharjee, Arnab

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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  • Bhattacharjee, Arnab, 2004. "A Simple Test for the Absence of Covariate Dependence in Hazard Regression Models," MPRA Paper 3937, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:3937
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    File URL: https://mpra.ub.uni-muenchen.de/3937/1/MPRA_paper_3937.pdf
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    References listed on IDEAS

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    1. 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.
    2. Joel L. Horowitz, 1999. "Semiparametric Estimation of a Proportional Hazard Model with Unobserved Heterogeneity," Econometrica, Econometric Society, vol. 67(5), pages 1001-1028, September.
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    4. 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.
    5. Gorgens, Tue & Horowitz, Joel L., 1999. "Semiparametric estimation of a censored regression model with an unknown transformation of the dependent variable," Journal of Econometrics, Elsevier, vol. 90(2), pages 155-191, June.
    6. 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.
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    9. 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.
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    11. R. A. Kortram & A. C. M. van Rooij & A. J. Lenstra & G. Ridder, 1995. "Constructive identification of the mixed proportional hazards model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 49(3), pages 269-281, November.
    12. 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.
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    Cited by:

    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.

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    More about this item

    Keywords

    Covariate dependence; Continuous covariate; Two-sample tests; Trend tests; Proportional hazards; Frailty/ unobserved heterogeneity; Linear transformation model;
    All these keywords.

    JEL classification:

    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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