IDEAS home Printed from https://ideas.repec.org/p/cam/camdae/0337.html
   My bibliography  Save this paper

Estimation in Hazard Regression Models under Ordered Departures from Proportionality

Author

Listed:
  • Bhattacharjee, A.

Abstract

Notions of monotone ordering with respect to continuous covariates in duration data regression models have recently been discussed, and tests for the proportional hazards model against such alternatives have been developed (Bhattacharjee and Das, 2002). Such monotone/ ordered departures are common in applications, and provide useful additional information about the nature of covariate dependence. In this paper, we describe methods for estimating hazard regression models when such monotone departures are known to hold. In particular, it is shown how the histogram sieve estimators (Murphy and Sen, 1991) in this setup can be smoothed and order restricted estimation performed using biased bootstrap techniques like adaptive bandwidth kernel estimators (Brockmann et. al., 1993; Schucany, 1995) or data tilting (Hall and Huang, 2001). The performance of the methods is compared using simulated data, and their use is illustrated with applications from biomedicine and economic duration data.

Suggested Citation

  • 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.
  • Handle: RePEc:cam:camdae:0337
    Note: EM
    as

    Download full text from publisher

    File URL: http://www.econ.cam.ac.uk/research-files/repec/cam/pdf/cwpe0337.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. E. Mammen & C. Thomas‐Agnan, 1999. "Smoothing Splines and Shape Restrictions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 239-252, June.
    2. Hall, Peter & Turlach, Berwin A., 1999. "Reducing bias in curve estimation by use of weights," Computational Statistics & Data Analysis, Elsevier, vol. 30(1), pages 67-86, March.
    3. 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.
    4. Zongwu Cai & Yanqing Sun, 2003. "Local Linear Estimation for Time‐Dependent Coefficients in Cox's Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 93-111, March.
    5. 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.
    6. Farmen, Mark & Marron, J. S., 1999. "An assessment of finite sample performance of adaptive methods in density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 30(2), pages 143-168, April.
    7. Lee, Thomas C. M., 2003. "Smoothing parameter selection for smoothing splines: a simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 139-148, February.
    8. 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.
    9. Fischer, N. I. & Mammen, E. & Marron, J. S., 1994. "Testing for multimodality," Computational Statistics & Data Analysis, Elsevier, vol. 18(5), pages 499-512, December.
    10. Kathryn A. Prewitt, 2003. "Efficient Bandwidth Selection in Non‐parametric Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 75-92, March.
    11. Torben Martinussen & Thomas H. Scheike & Ib M. Skovgaard, 2002. "Efficient Estimation of Fixed and Time‐varying Covariate Effects in Multiplicative Intensity Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 57-74, March.
    12. A. Bhattacharjee & C. Higson & S. Holly & P. Kattuman, 2009. "Macroeconomic Instability and Business Exit: Determinants of Failures and Acquisitions of UK Firms," Economica, London School of Economics and Political Science, vol. 76(301), pages 108-131, February.
    13. P. Hall & B. Presnell, 1999. "Intentionally biased bootstrap methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 143-158.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bhattacharjee, Arnab, 2004. "A Simple Test for the Absence of Covariate Dependence in Hazard Regression Models," MPRA Paper 3937, University Library of Munich, Germany.
    2. 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.
    3. Bhattacharjee, A. & Higson, C. & Holly, S. & Kattuman, P., 2004. "Business Failure in UK and US Quoted Firms: Impact of Macroeconomic Instability and the Role of Legal Institutions," Cambridge Working Papers in Economics 0420, Faculty of Economics, University of Cambridge.
    4. A. Bhattacharjee & C. Higson & S. Holly & P. Kattuman, 2009. "Macroeconomic Instability and Business Exit: Determinants of Failures and Acquisitions of UK Firms," Economica, London School of Economics and Political Science, vol. 76(301), pages 108-131, February.
    5. Orbe, Jesus & Nunez-Anton, Vicente, 2006. "Alternative approaches to study lifetime data under different scenarios: from the PH to the modified semiparametric AFT model," Computational Statistics & Data Analysis, Elsevier, vol. 50(6), pages 1565-1582, March.
    6. Bhattacharjee, Arnab, 2009. "Testing for Proportional Hazards with Unrestricted Univariate Unobserved Heterogeneity," SIRE Discussion Papers 2009-22, Scottish Institute for Research in Economics (SIRE).
    7. 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).
    8. Arnab Bhattacharjee, 2008. "Partial Orders with Respect to Continuous Covariates and Tests for the Proportional Hazards Model," Discussion Paper Series, School of Economics and Finance 200807, School of Economics and Finance, University of St Andrews.
    9. Bhattacharjee, Arnab, 2009. "Testing for Proportional Hazards with Unrestricted Univariate Unobserved Heterogeneity," SIRE Discussion Papers 2009-22, Scottish Institute for Research in Economics (SIRE).
    10. Arnab Bhattacharjee, 2005. "Models of Firm Dynamics and the Hazard Rate of Exits: Reconciling Theory and Evidence using Hazard Regression Models," Econometrics 0503021, University Library of Munich, Germany.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Arnab Bhattacharjee, 2005. "Models of Firm Dynamics and the Hazard Rate of Exits: Reconciling Theory and Evidence using Hazard Regression Models," Econometrics 0503021, University Library of Munich, Germany.
    2. Yanqing Sun & Rajeshwari Sundaram & Yichuan Zhao, 2009. "Empirical Likelihood Inference for the Cox Model with Time‐dependent Coefficients via Local Partial Likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 444-462, September.
    3. Huazhen Lin & Zhe Fei & Yi Li, 2016. "A Semiparametrically Efficient Estimator of the Time-Varying Effects for Survival Data with Time-Dependent Treatment," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 649-663, September.
    4. Yanqing Sun & Seunggeun Hyun & Peter Gilbert, 2008. "Testing and Estimation of Time-Varying Cause-Specific Hazard Ratios with Covariate Adjustment," Biometrics, The International Biometric Society, vol. 64(4), pages 1070-1079, December.
    5. Guoqing Diao & Donglin Zeng & Song Yang, 2013. "Efficient Semiparametric Estimation of Short-Term and Long-Term Hazard Ratios with Right-Censored Data," Biometrics, The International Biometric Society, vol. 69(4), pages 840-849, December.
    6. Guoqing Diao & Anand N. Vidyashankar & Sarah Zohar & Sandrine Katsahian, 2021. "Competing Risks Model with Short-Term and Long-Term Covariate Effects for Cancer Studies," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(1), pages 142-159, April.
    7. Torben Martinussen & Odd O. Aalen & Thomas H. Scheike, 2008. "The Mizon–Richard Encompassing Test for the Cox and Aalen Additive Hazards Models," Biometrics, The International Biometric Society, vol. 64(1), pages 164-171, March.
    8. Bhattacharjee, Arnab, 2004. "A Simple Test for the Absence of Covariate Dependence in Hazard Regression Models," MPRA Paper 3937, University Library of Munich, Germany.
    9. Bhattacharjee, A., 2004. "A Simple Test for the Absence of Covariate Dependence in Duration Models," Cambridge Working Papers in Economics 0401, Faculty of Economics, University of Cambridge.
    10. Torben Martinussen & Christian Bressen Pipper, 2014. "Estimation of Causal Odds of Concordance using the Aalen Additive Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 141-151, March.
    11. Yassin Mazroui & Audrey Mauguen & Simone Mathoulin-Pélissier & Gaetan MacGrogan & Véronique Brouste & Virginie Rondeau, 2016. "Time-varying coefficients in a multivariate frailty model: Application to breast cancer recurrences of several types and death," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(2), pages 191-215, April.
    12. Qu, Lianqiang & Song, Xinyuan & Sun, Liuquan, 2018. "Identification of local sparsity and variable selection for varying coefficient additive hazards models," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 119-135.
    13. 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.
    14. Hazelton, Martin L. & Turlach, Berwin A., 2007. "Reweighted kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3057-3069, March.
    15. Anderl, Eva & Schumann, Jan Hendrik & Kunz, Werner, 2016. "Helping Firms Reduce Complexity in Multichannel Online Data: A New Taxonomy-Based Approach for Customer Journeys," Journal of Retailing, Elsevier, vol. 92(2), pages 185-203.
    16. Zahra Mansourvar & Torben Martinussen, 2017. "Estimation of average causal effect using the restricted mean residual lifetime as effect measure," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(3), pages 426-438, July.
    17. Zahra Mansourvar & Torben Martinussen, 0. "Estimation of average causal effect using the restricted mean residual lifetime as effect measure," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 0, pages 1-13.
    18. Hazelton, Martin L., 2007. "Bias reduction in kernel binary regression," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4393-4402, May.
    19. A. Bhattacharjee & C. Higson & S. Holly & P. Kattuman, 2009. "Macroeconomic Instability and Business Exit: Determinants of Failures and Acquisitions of UK Firms," Economica, London School of Economics and Political Science, vol. 76(301), pages 108-131, February.
    20. 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.

    More about this item

    Keywords

    Proportional hazards; Ordered restricted inference; Age-varying covariate effects; Biased bootstrap; Data tilting; Adaptive bandwidth selection; Histogram sieve estimator;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cam:camdae:0337. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://www.econ.cam.ac.uk/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Jake Dyer (email available below). General contact details of provider: https://www.econ.cam.ac.uk/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.