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

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  • Arnab Bhattacharjee

Abstract

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.

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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 200807.

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Date of creation: 15 Jul 2008
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Handle: RePEc:san:wpecon:0807

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

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  1. 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.
  2. 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.
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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.

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