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

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  • Arnab Bhattacharjee

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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Bibliographic Info

Paper provided by Department of Economics, University of St. Andrews in its series Discussion Paper Series, Department of Economics with number 200708.

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Date of creation: 15 Sep 2007
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Handle: RePEc:san:wpecon:0708

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Keywords: Covariate dependence; Continuous covariate; Two-sample tests; Trend tests; Proportional hazards; Frailty; Linear transformation mode;

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  1. 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.
  2. 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.
  3. 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.
  4. Bhattacharjee, A., 2003. "Estimation in Hazard Regression Models under Ordered Departures from Proportionality," Cambridge Working Papers in Economics 0337, Faculty of Economics, University of Cambridge.
  5. A. Bhattacharjee & Higson, C. & Holly, S. & Kattuman, P., 2002. "Macro Economic Instability and Business Exit: Determinants of Failures and Acquisitions of Large UK Firms," Cambridge Working Papers in Economics 0206, Faculty of Economics, University of Cambridge.
  6. 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.
  7. 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.
  8. Liu, P. Y. & Wei Yann Tsai, 1999. "A modified logrank test for censored survival data under order restrictions," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 57-63, January.
  9. 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.
  10. Joel L. Horowitz, 1999. "Semiparametric Estimation of a Proportional Hazard Model with Unobserved Heterogeneity," Econometrica, Econometric Society, vol. 67(5), pages 1001-1028, September.
  11. 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.
  12. Murphy, S. A. & Sen, P. K., 1991. "Time-dependent coefficients in a Cox-type regression model," Stochastic Processes and their Applications, Elsevier, vol. 39(1), pages 153-180, October.
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Cited by:
  1. Arnab Bhattacharjee & Madhuchhanda Bhattacharjee, 2007. "Bayesian Analysis of Hazard Regression Models under Order Restrictions on Covariate Effects and Ageing," Discussion Paper Series, Department of Economics 200707, Department of Economics, University of St. Andrews.

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