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Identifiability and estimation of the sign of a covariate effect in the competing risks model

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  • Simon M.S. Lo
  • Ralf A. Wilke

Abstract

It is well known that the competing risks model is identified if the dependence structure between risks (the copula function) is known or assumed. Special cases include independence of risks or independent censoring. If the copula function is not specified, parameters of interest are only set identified. As these sets are often wide in applications, it is difficult to obtain informative results. In this paper we strike a balance between imposing too much and too little structure. By establishing a general link between observable changes in subdistributions (cumulative incidence curves) and the sign of changes in marginal distributions (the causal treatment effect) we are able to show the identifiability of the latter if the copula function is independent of the varying covariate. This has two important implications: First, it is possible to obtain informative results even if the copula function is mainly unspecified or unknown. Second, the sign of the covariate effect tends to be invariant with respect to the chosen dependence structure. Our method is computationally very simple and our simulations suggest that it identifies and consistently estimates the sign of the treatment effect for large sets of duration times. An application to unemployment duration data illustrates the usefulness of our method for empirical research.

Suggested Citation

  • Simon M.S. Lo & Ralf A. Wilke, 2011. "Identifiability and estimation of the sign of a covariate effect in the competing risks model," Discussion Papers 11/03, University of Nottingham, School of Economics.
    • Handle: RePEc:not:notecp:11/03
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    File URL: https://www.nottingham.ac.uk/economics/documents/discussion-papers/11-03.pdf
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    1. Bo E. Honoré & Adriana Lleras-Muney, 2006. "Bounds in Competing Risks Models and the War on Cancer," Econometrica, Econometric Society, vol. 74(6), pages 1675-1698, November.
    2. Simon M. S. Lo & Ralf A. Wilke, 2010. "A copula model for dependent competing risks," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(2), pages 359-376, March.
    3. Peng, Limin & Fine, Jason P., 2009. "Competing Risks Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1440-1453.
    4. Rivest, Louis-Paul & Wells, Martin T., 2001. "A Martingale Approach to the Copula-Graphic Estimator for the Survival Function under Dependent Censoring," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 138-155, October.
    5. Jaap H. Abbring & Gerard J. Van Den Berg, 2003. "The identifiability of the mixed proportional hazards competing risks model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 701-710, August.
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    Cited by:

    1. Lo Simon M.S. & Wilke Ralf A., 2014. "A Regression Model for the Copula-Graphic Estimator," Journal of Econometric Methods, De Gruyter, vol. 3(1), pages 21-46, January.
    2. Lo Simon M.S. & Wilke Ralf A., 2014. "A Regression Model for the Copula-Graphic Estimator," Journal of Econometric Methods, De Gruyter, vol. 3(1), pages 21-46, January.

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