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Bayesian Analysis of Hazard Regression Models under Order Restrictions on Covariate Effects and Ageing

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  • Arnab Bhattacharjee
  • Madhuchhanda Bhattacharjee

Abstract

We propose Bayesian inference in hazard regression models where the baseline hazard is unknown, covariate effects are possibly agevarying (non-proportional), and there is multiplicative frailty with arbitrary distribution. Our framework incorporates a wide variety of order restrictions on covariate dependence and duration dependence (ageing). We propose estimation and evaluation of age-varying covariate e¤ects when covariate dependence is monotone rather than proportional. In particular, we consider situations where the lifetime conditional on a higher value of the covariate ages faster or slower than that conditional on a lower value; this kind of situation is common in applications. In addition, there may be restrictions on the nature of ageing. For example, relevant theory may suggest that the baseline hazard function decreases with age. The proposed framework enables evaluation of order restrictions in the nature of both covariate and duration dependence as well as estimation of hazard regression models under such restrictions. The usefulness of the proposed Bayesian model and inference methods are illustrated with an application to corporate bankruptcies in the UK.

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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 0707.

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Date of creation: Sep 2007
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Handle: RePEc:san:wpecon:0707

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Postal: School of Economics and Finance, University of St. Andrews, Fife KY16 9AL
Phone: 01334 462420
Fax: 01334 462444
Web page: http://www.st-andrews.ac.uk/economics/
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Keywords: Bayesian nonparametrics; Nonproportional hazards; Frailty; Age-varying covariate e¤ects; Ageing.;

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  1. Michele Campolieti, 2001. "Bayesian semiparametric estimation of discrete duration models: an application of the dirichlet process prior," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(1), pages 1-22.
  2. 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.
  3. 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.
  4. Arnab Bhattacharjee, 2007. "A Simple Test for the Absence of Covariate Dependence in Hazard Regression Models," Discussion Paper Series, Department of Economics 0708, Department of Economics, University of St. Andrews.
  5. Alan Gelfand & Athanasios Kottas, 2001. "Nonparametric Bayesian Modeling for Stochastic Order," Annals of the Institute of Statistical Mathematics, Springer, vol. 53(4), pages 865-876, December.
  6. Luis E. Nieto-Barajas, 2002. "Markov Beta and Gamma Processes for Modelling Hazard Rates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 29(3), pages 413-424.
  7. P Ingram & David Metcalf & Jonathan Wadsworth, 1992. "Do Strikes Pay?," CEP Discussion Papers dp0092, Centre for Economic Performance, LSE.
  8. 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.
  9. Narendranathan, W & Stewart, Mark B, 1993. "How Does the Benefit Effect Vary as Unemployment Spells Lengthen?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 361-81, Oct.-Dec..
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