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Bounds in Competing Risks Models and the War on Cancer

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  • Bo E. Honore
  • Adriana Lleras Muney
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    Abstract

    In 1971 President Nixon declared war on cancer and increased the federal funds allocated to cancer research dramatically. Thirty years later, many have declared this war a failure. Overall cancer statistics confirm this view: age-adjusted mortality in 2000 was essentially unchanged from the early 1970s. At the same time, age-adjusted mortality rates from cardiovascular disease have fallen quite dramatically. Since the causes underlying cancer and cardiovascular disease are likely to be correlated, the decline in mortality rates from cardiovascular disease may be somewhat responsible for the rise in cancer mortality. It is natural to model mortality with more than one cause of death as a competing risks model. Such models are fundamentally unidentified, and it is therefore difficult to get a clear picture of the progress in cancer. This paper derives bounds for aspects of the underlying distributions under a number of different assumptions. Most importantly, we do not assume that the underlying risks are independent, and impose weak parametric assumptions in order to obtain identification. The theoretical contribution of the paper is to provide a framework to estimate competing risk models with interval data and discrete explanatory variables, both of which are common in empirical applications. We use our method to estimate changes in cancer and cardiovascular mortality since 1970. The estimated bounds for the effect of time on the duration until death for either cause are fairly tight and we find that trends in cancer show much larger improvements than previously estimated. For example, we find that time until death from cancer increased by about 10% for white males and 20% for white women.

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    File URL: http://www.nber.org/papers/w10963.pdf
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    Bibliographic Info

    Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 10963.

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    Date of creation: Dec 2004
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    Publication status: published as Honore, Bo E. and Adriana Lleras-Muney. "Bounds in Competing Risks Models and the War on Cancer." Econometrica 74, 6 (Novermber 2006): 1675-98.
    Handle: RePEc:nbr:nberwo:10963

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    1. Katz, Lawrence F & Meyer, Bruce D, 1990. "Unemployment Insurance, Recall Expectations, and Unemployment Outcomes," The Quarterly Journal of Economics, MIT Press, vol. 105(4), pages 973-1002, November.
    2. Bruce D. Meyer, 1988. "Unemployment Insurance And Unemployment Spells," NBER Working Papers 2546, National Bureau of Economic Research, Inc.
    3. Molinari, Francesca, 2005. "Partial Identification of Probability Distributions with Misclassified Data," Working Papers 05-10, Cornell University, Center for Analytic Economics.
    4. 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.
    5. Flinn, C. & Heckman, J., 1982. "New methods for analyzing structural models of labor force dynamics," Journal of Econometrics, Elsevier, vol. 18(1), pages 115-168, January.
    6. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 3-29, July.
    7. Bo E. Honoré & Elie Tamer, 2002. "Bounds on Parameters in Dynamic Discrete Choice Models," CAM Working Papers 2004-23, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics, revised Aug 2004.
    8. Deng, Yongheng & Quigley, John M. & Van Order, Robert, 1999. "Mortgage Terminations, Heterogeneity, and the Exercise of Mortgage Options," Berkeley Program on Housing and Urban Policy, Working Paper Series qt96r560pg, Berkeley Program on Housing and Urban Policy.
    9. Heckman, James J & Smith, Jeffrey, 1997. "Making the Most Out of Programme Evaluations and Social Experiments: Accounting for Heterogeneity in Programme Impacts," Review of Economic Studies, Wiley Blackwell, vol. 64(4), pages 487-535, October.
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    Cited by:
    1. Sokbae 'Simon' Lee & Ralf A. Wilke, 2005. "Reform of unemployment compensation in Germany: a nonparametric bounds analysis using register data," CeMMAP working papers CWP02/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Christian Bontemps & Thierry Magnac & Eric Maurin, 2012. "Set Identified Linear Models," Econometrica, Econometric Society, vol. 80(3), pages 1129-1155, 05.
    3. Molinari, Francesca, 2008. "Partial identification of probability distributions with misclassified data," Journal of Econometrics, Elsevier, vol. 144(1), pages 81-117, May.
    4. Sokbae Lee, 2006. "Identification of a competing risks model with unknown transformations of latent failure times," Biometrika, Biometrika Trust, vol. 93(4), pages 996-1002, December.
    5. Magnac, Thierry, 2014. "Identification partielle: méthodes et conséquences pour les applications empiriques," IDEI Working Papers 814, Institut d'Économie Industrielle (IDEI), Toulouse.
    6. Andrew Chesher, 2002. "Local identification in nonseparable models," CeMMAP working papers CWP05/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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