Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-23T15:11:11.175Z Has data issue: false hasContentIssue false
  • English
  • Français

Beyond the Hazard Ratio: Generating Expected Durations from the Cox Proportional Hazards Model

Published online by Cambridge University Press:  27 November 2017

Jonathan Kropko  and
Jeffrey J. Harden
Get access Rights & Permissions [Opens in a new window]

Abstract

The Cox proportional hazards model is a commonly used method for duration analysis in political science. Typical quantities of interest used to communicate results come from the hazard function (for example, hazard ratios or percentage changes in the hazard rate). These quantities are substantively vague, difficult for many audiences to understand and incongruent with researchers’ substantive focus on duration. We propose methods for computing expected durations and marginal changes in duration for a specified change in a covariate from the Cox model. These duration-based quantities closely match researchers’ theoretical interests and are easily understood by most readers. We demonstrate the substantive improvements in interpretation of Cox model results afforded by the methods with reanalyses of articles from three subfields of political science.

Keywords

duration modelsCox proportional hazards modelquantities of interestexpected durations
Type
Articles
Information
British Journal of Political Science , Volume 50 , Issue 1 , January 2020 , pp. 303 - 320
Copyright
© Cambridge University Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

Department of Politics, University of Virginia (email: jkropko@virginia.edu); Department of Political Science, University of Notre Dame, (email: jeff.harden@nd.edu). Previous versions of this article benefited from presentation at the 2014 Annual Meeting of the Society for Political Methodology, Athens, GA. We would also like to thank Justin Kirkland, Bruce Desmarais, Meg Shannon, Fred Boehmke, Anand Sokhey, the editor and three anonymous reviewers for helpful comments. Data replication sets and code are available in Harvard Dataverse at: https://dx.doi.org/10.7910/DVN/ELT9VD and online appendices at https://doi.org/doi: 10.1017/S000712341700045X.

References

Beck, Nathaniel, and Jackman, Simon. 1998. Beyond Linearity by Default: Generalized Additive Models. American Journal of Political Science 42 (2):596–627.Google Scholar
Bender, Ralf, Augustin, Thomas, and Blettner, Maria. 2005. Generating Survival Times to Simulate Cox Proportional Hazards Models. Statistics in Medicine 24 (11):1713–1723.Google Scholar
Binder, Sarah A., and Maltzman, Forrest. 2002. Senatorial Delay in Confirming Federal Judges, 1947–98. American Journal of Political Science 46 (1):190–199.Google Scholar
Box-Steffensmeier, Janet M. 1996. A Dynamic Analysis of the Role of War Chests in Campaign Strategy. American Journal of Political Science 40 (2):352–371.Google Scholar
Box-Steffensmeier, Janet M., and Jones, Bradford S.. 2004. Event History Modeling: A Guide for Social Scientists. New York: Cambridge University Press.Google Scholar
Box-Steffensmeier, Janet M., Arnold, Laura W., and Zorn, Christopher J. W.. 1997. The Strategic Timing of Position Taking in Congress: A Study of the North American Free Trade Agreement. American Political Science Review 91 (2):324–338.Google Scholar
Collett, David. 2003. Modelling Survival Data in Medical Research, 2nd edition. Boca Raton, FL: Chapman & Hall/CRC.Google Scholar
Cox, Christopher, Chu, Haitao, Schneider, Michael F., and Munoz, Alvaro. 2007. Parametric Survival Analysis and Taxonomy of Hazard Functions for the Generalized Gamma Distribution. Statistics in Medicine 26 (23):4352–4374.Google Scholar
Cox, David R. 1972. Regression Models and Life-Tables. Journal of the Royal Statistical Society . Series B (Methodological) 34 (2):187–220.Google Scholar
Cox, David R. 1975. Partial Likelihood. Biometrika 62 (2):269–276.Google Scholar
Cox, David R., and Oakes, David. 1984. Analysis of Survival Data. Monographs on Statistics and Applied Probability. Boca Raton, FL: Chapman & Hall/CRC.Google Scholar
Diermeier, Daniel, and van Roozendaal, Peter. 1998. The Duration of Cabinet Formation Processes in Western Multi-Party Democracies. British Journal of Political Science 28 (4):609–626.Google Scholar
Fortna, Virginia Page. 2004. Does Peacekeeping Keep Peace? International Intervention and the Duration of Peace After Civil War. International Studies Quarterly 48 (2):269–292.Google Scholar
Hanmer, Michael J., and Kalkan, Kerem Ozan. 2013. Behind the Curve: Clarifying the Best Approach to Calculating Predicted Probabilities and Marginal Effects from Limited Dependent Variable Models. American Journal of Political Science 57 (1):263–277.Google Scholar
Harden, Jeffrey J. 2011. A Bootstrap Method for Conducting Statistical Inference with Clustered Data. State Politics and Policy Quarterly 11 (2):223–246.Google Scholar
Hernan, Miguel A. 2010. The Hazards of Hazard Ratios. Epidemiology 21 (1):13–15.Google Scholar
Kalbfleisch, John D., and Prentice, Ross L.. 2002. The Statistical Analysis of Failure Time Data. Hoboken, NJ: Wiley-Interscience.Google Scholar
Katz, Jonathan N., and Sala, Brian R.. 1996. Careerism, Committee Assignments, and the Electoral Connection. American Political Science Review 90 (1):21–33.Google Scholar
King, Gary, Tomz, Michael, and Wittenberg, Jason. 2000. Making the Most of Statistical Analyses: Improving Interpretation and Presentation. American Journal of Political Science 44 (2):341–355.Google Scholar
Kropko, Jonathan; Harden, Jeffrey J 2017. “Replication Data for: Beyond the Hazard Ratio: Generating Expected Durations from the Cox Proportional Hazards Model”, doi:10.7910/DVN/ELT9VD, Harvard Dataverse, V1, UNF:6:GaAP2KOYxqS0AjITdz96nw==.Google Scholar
Krustev, Valentin L. 2006. Interdependence and the Duration of Militarized Conflict. Journal of Peace Research 43 (3):243–260.Google Scholar
Lupia, Arthur, and Aldrich, John H.. 2015. How Political Science Can Better Communicate its Value: 12 Recommendations from the APSA Task Force. PS: Political Science and Politics 48 (S1):1–19.Google Scholar
Martin, Lanny W., and Vanberg, Georg. 2003. Wasting Time? The Impact of Ideology and Size on Delay in Coalition Formation. British Journal of Political Science 33 (2):323–344.Google Scholar
Mattes, Michaela, and Savun, Burcu. 2010. Information, Agreement Design, and the Durability of Civil War Settlements. American Journal of Political Science 54 (2):511–524.Google Scholar
Meernik, James, and Brown, Chelsea. 2007. The Short Path and the Long Road: Explaining the Duration of U.S. Military Operations. Journal of Peace Research 44 (1):65–80.Google Scholar
Royston, Patrick, and Parmar, Mahesh K. B.. 2002. Flexible Parametric Proportional-Hazards and Proportional-Odds Models for Censored Survival Data, with Application to Prognostic Modelling and Estimation of Treatment Effects. Statistics in Medicine 21 (15):2175–2197.Google Scholar
Shipan, Charles R., and Shannon, Megan L.. 2003. Delaying Justice(s): A Duration Analysis of Supreme Court Confirmation. American Journal of Political Science 47 (4):654–668.Google Scholar
Uno, Hajime, Brian Claggett, Lu Tian, Eisuke Inoue, Paul Gallo, Toshio Miyata, Deborah Schrag, Masahiro Takeuchi, Yoshiaki Uyama, Lihui Zhao, Hicham Skali, Scott Solomon, Susanna Jacobus, Michael Hughes, Milton Packer, and Lee-Jen Wei. 2014. Moving Beyond the Hazard Ratio in Quantifying the Between-Group Difference in Survival Analysis. Journal of Clinical Oncology 32 (22):2380–2385.Google Scholar
Wood, Simon N. 2006. Generalized Additive Models: An Introduction with R. Boca Raton, FL: Chapman & Hall/CRC.Google Scholar
Wood, Simon N. 2011. Fast Stable Restricted Maximum Likelihood and Marginal Likelihood Estimation of Semiparametric Generalized Linear Models. Journal of the Royal Statistical Society: Series B (Methodological) 73 (1):3–36.Google Scholar
Supplementary material: Link

Kropko and Harden Supplementary Material

Dataset

http://dx.doi.org/10.7910/DVN/ELT9VD
Link
Supplementary material: PDF

Kropko and Harden supplementary material

Kropko and Harden supplementary material 1

Download Kropko and Harden supplementary material(PDF)
PDF 259.3 KB