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Proportionally Difficult: Testing for Nonproportional Hazards in Cox Models

Published online by Cambridge University Press:  04 January 2017

Luke Keele
Luke Keele*
Affiliation:
Department of Political Science, 2140 Derby Hall, 150 North Oval Mall, Ohio State University, Columbus, OH 43210
*
e-mail: keele.4@polisci.osu.edu (corresponding author)
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Abstract

The Cox proportional hazards model is widely used to model durations in the social sciences. Although this model allows analysts to forgo choices about the form of the hazard, it demands careful attention to the proportional hazards assumption. To this end, a standard diagnostic method has been developed to test this assumption. I argue that the standard test for nonproportional hazards has been misunderstood in current practice. This test detects a variety of specification errors, and these specification errors must be corrected before one can correctly diagnose nonproportionality. In particular, unmodeled nonlinearity can appear as a violation of the proportional hazard assumption for the Cox model. Using both simulation and empirical examples, I demonstrate how an analyst might be led astray by incorrectly applying the nonproportionality test.

Type
Research Article
Information
Political Analysis , Volume 18 , Issue 2 , Spring 2010 , pp. 189 - 205
Copyright
Copyright © The Author 2010. Published by Oxford University Press on behalf of the Society for Political Methodology 

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Footnotes

Author's note: For helpful comments, I thank Jan Box-Steffensmeier, Mark Kayser, Irfan Nooruddin, and the anonymous reviewers. I also thank Hein Goemans for sharing his data.

References

Anderson, Garnet L., and Fleming, Thomas R. 1995. Model misspecification in proportional hazards regression. Biometrika 82: 527–41.CrossRefGoogle Scholar
Beck, Nathaniel, and Jackman, Simon. 1998. Beyond linearity by default: Generalized additive models. American Journal of Political Science 42: 596–627.Google Scholar
Beck, Nathaniel, Katz, Jonathan N., and Tucker, Richard. 1998. Taking time seriously: Time-series-cross-section analysis with a binary dependent variable. American Journal of Political Science 42: 1260–88.Google Scholar
Bowman, Adrian W., and Azzalini, Adelchi. 1997. Applied, smoothing techniques for data analysis. Oxford, UK: Oxford University Press.CrossRefGoogle Scholar
Box-Steffensmeier, Janet M., and Jones, Bradford S. 2004. Event history modeling: A guide for social scientists. New York: Cambridge University Press.CrossRefGoogle Scholar
Box-Steffensmeier, Janet M., and Zorn, Christopher J. W. 2001. Duration models and proportional hazards in political science. American Journal of Political Science 45: 972–88.Google Scholar
Box-Steffensmeier, Janet M., and Zorn, Christopher J. W. 2002. Duration models for repeated events. Journal of Politics 64: 1069–94.CrossRefGoogle Scholar
Carpenter, Daniel P. 2002. Groups, the media, agency waiting costs, and FDA drug approval. American Journal of Political Science 46: 490–505.Google Scholar
Chiozza, Giacomo, and Goemans, H. E. 2004. International conflict and the tenure of leaders: Is war still ex post inefficient? American Journal of Political Science 48: 604–19.Google Scholar
Cox, D. R. 1972. Regression models and life tables. Journal of the Royal Statistical Society, Serial B 34: 187–220.Google Scholar
Gordon, Sanford. 2002. Stochastic dependence in competing risks. American Journal of Political Science 46: 200–17.Google Scholar
Grambsch, Patricia M., and Therneau, Terry M. 1994. Proportional hazards tests and diagnostics based on weighted residuals. Biometrika 81: 515–26.CrossRefGoogle Scholar
Harrell, F. E. 1986. The PHGLM procedure. SUGI supplemental library user's guide, ed. Hastings, Robert P. Cary, NC: SAS Institute.Google Scholar
Harrell, Frank E. 2001. Regression modeling strategies: With applications to linear models, logistic regression, and survival analysis. New York: Springer.Google Scholar
Hastie, T. J., and Tibshirani, R. J. 1990. Generalized additive models. London: Chapman and Hall.Google Scholar
Hosmer, David W., and Lemeshow, Stanely. 1999. Applied survival analysis regression modeling of time to event data. New York: Wiley and Sons.Google Scholar
Keele, Luke. 2008. Semiparametric regression for the social sciences. Chichester, UK: Wiley and Sons.Google Scholar
Lagakos, S. W., and Schoenfeld, D. A. 1984. Properties of proportional-hazards score tests under misspecified regression models. Biometrics 40: 1037–48.CrossRefGoogle ScholarPubMed
LeBlanc, Michael, and Crowley, John. 1999. Adaptive regression splines in the Cox model. Biometrics 55: 204–13.Google Scholar
Loader, Clive. 1999. Local regression and likelihood. New York: Springer.Google Scholar
Oneal, John R., and Russett, Bruce. 1997. The classical liberals were right: Democracy, interdependence, and conflict, 1950–1985. International Studies Quarterly 41: 267–94.Google Scholar
Reed, William. 2000. A unified statistical model of conflict and escalation. American Journal of Political Science 44: 84–93.Google Scholar
Reid, Nancy. 1994. A conversation with Sir David Cox. Statistical Science 9: 439–55.Google Scholar
Ruppert, David, Wand, M. P., and Carroll, R. J. 2003. Semiparametric regression. New York: Cambridge University Press.Google Scholar
Struthers, C. A., and Kalbfleisch, J. D. 1986. Misspecified proportional hazards models. Biometrika 73: 363–9.Google Scholar
Therneau, Terry M., and Grambsch, Patricia M. 2000. Modeling survival data: Extending the Cox model. New York: Springer-Verlag.Google Scholar
Therneau, T. M., Grambsch, P. M., and Fleming, T. R. 1990. Martingale based residuals for survival models. Biometrika 77: 147–60.CrossRefGoogle Scholar
Wood, Simon. 2006. Generalized additive models: An introduction with R. Boca Raton, FL: Chapman & Hall/CRC.Google Scholar