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Partial Orders with Respect to Continuous Covariates and Tests for the Proportional Hazards Model


  • Arnab Bhattacharjee


Several omnibus tests of the proportional hazards assumption have been proposed in the literature. In the two-sample case, tests have also been developed against ordered alternatives like monotone hazard ratio and monotone ratio of cumulative hazards. Here we propose a natural extension of these partial orders to the case of continuous covariates. The work is motivated by applications in biomedicine and economics where covariate e¤ects often decay over lifetime. We develop tests for the proportional hazards assumption against ordered alternatives and propose a graphical method to identify the nature of departures from proportionality. The proposed tests do not make restrictive assumptions on the underlying regression model, and are applicable in the presence of multiple covariates and frailty. Small sample performance and applications to real data highlight the usefulness of the framework and methodology.

Suggested Citation

  • Arnab Bhattacharjee, 2008. "Partial Orders with Respect to Continuous Covariates and Tests for the Proportional Hazards Model," Discussion Paper Series, Department of Economics 200807, Department of Economics, University of St. Andrews.
  • Handle: RePEc:san:wpecon:0807

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    References listed on IDEAS

    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.
    2. Arnab Bhattacharjee & Chris Higson & Sean Holly & Paul Kattuman, 2007. "Macroeconomic Conditions and Business Exit: Determinants of Failures and Acquisitions of UK Firms," CDMA Working Paper Series 200713, Centre for Dynamic Macroeconomic Analysis.
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    Cited by:

    1. Arnab Bhattacharjee, 2009. "Testing for Proportional Hazards with Unrestricted Univariate Unobserved Heterogeneity," Discussion Paper Series, Department of Economics 200904, Department of Economics, University of St. Andrews.
    2. Bhattacharjee, Arnab & Hany, Jie, 2010. "Financial Distress in Chinese Industry: Microeconomic, Macroeconomic and Institutional Infuences," SIRE Discussion Papers 2010-53, Scottish Institute for Research in Economics (SIRE).
    3. Bhattacharjee, Arnab & Han, Jie, 2014. "Financial distress of Chinese firms: Microeconomic, macroeconomic and institutional influences," China Economic Review, Elsevier, vol. 30(C), pages 244-262.

    More about this item


    Two-sample tests; Increasing hazard ratio; Continuous covariate; Proportional hazards; Frailty; Partial orders; Time varying coe¢cients.;

    JEL classification:

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

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