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Econometrica
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# Bounds in Competing Risks Models and the War on Cancer

## Authors

- ### Bo E. Honoré,

  1. 1 Dept. of Economics, Princeton University, Princeton, NJ 08544-1021, U.S.A. honore@princeton.edu http://www.princeton.edu/~honore, 2Dept. of Economics and Woodrow Wilson School of Public and International Affairs, Princeton University, Princeton, NJ 08544-1013, U.S.A. alleras@princeton.edu http://www.princeton.edu/~alleras
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- ### and 1 Adriana Lleras-Muney 2

  1. 1 Dept. of Economics, Princeton University, Princeton, NJ 08544-1021, U.S.A. honore@princeton.edu http://www.princeton.edu/~honore, 2Dept. of Economics and Woodrow Wilson School of Public and International Affairs, Princeton University, Princeton, NJ 08544-1013, U.S.A. alleras@princeton.edu http://www.princeton.edu/~alleras
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- First published: 1 November 2006 Full publication history
- DOI: 10.1111/j.1468-0262.2006.00722.x View/save citation
- Cited by (CrossRef): 36 articles Check for updates
  - Citing literature

- This is a shorter version of Honoré and Lleras-Muney (2005). More detail and additional information can also be found in the supplement to this paper, Honoré and Llears-Muney (2006), (hereafter referred to as HL). We thank Jaap Abbring, Josh Angrist, Eric J. Feuer, Marco Manacorda, Costas Meghir, Hilary Sarneski-Hayes, researchers at the National Cancer Institute, and seminar participants at CAM at the University of Copenhagen, London School of Economics, MIT, NBER Summer Institute, Princeton University, University College London, and the Harvard–MIT–Boston University Health seminar, and two anonymous referees for their suggestions. This research was supported by the National Institute on Aging, Grant K12-AG00983 to the NBER (Lleras-Muney) and by the NSF Grant SES-0417895 to Princeton University, The Gregory C. Chow Econometric Research Program at Princeton University, and the Danish National Research Foundation, through CAM at the University of Copenhagen (Honoré).

## Abstract

In 1971, President Nixon declared war on cancer. Thirty years later, many declared this war a failure: the age-adjusted mortality rate from cancer in 2000 was essentially the same as in the early 1970s. Meanwhile the age-adjusted mortality rate from cardiovascular disease fell dramatically. Since the causes that underlie cancer and cardiovascular disease are likely dependent, the decline in mortality rates from cardiovascular disease may partially explain the lack of progress in cancer mortality. Because competing risks models (used to model mortality from multiple causes) are fundamentally unidentified, it is difficult to estimate cancer trends. We derive bounds for aspects of the underlying distributions without assuming that the underlying risks are independent. We then estimate changes in cancer and cardiovascular mortality since 1970. The bounds for the change in duration until death for either cause are fairly tight and suggest much larger improvements in cancer than previously estimated.

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