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Comparing Partial Likelihood and Robust Estimation Methods for the Cox Regression Model

Published online by Cambridge University Press:  04 January 2017

Bruce A. Desmarais  and
Jeffrey J. Harden
Bruce A. Desmarais
Affiliation:
Department of Political Science, University of Massachusetts Amherst, 420 Thompson Hall, 200 Hicks Way, Amherst, MA 01003. e-mail: desmarais@polsci.umass.edu
Jeffrey J. Harden*
Affiliation:
Department of Political Science, University of North Carolina at Chapel Hill, 312 Hamilton Hall, CB No. 3265, Chapel Hill, NC 27599
*
e-mail: jjharden@unc.edu (corresponding author)
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Abstract

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The Cox proportional hazards model is ubiquitous in time-to-event studies of political processes. Plausible deviations from correct specification and operationalization caused by problems such as measurement error or omitted variables can produce substantial bias when the Cox model is estimated by conventional partial likelihood maximization (PLM). One alternative is an iteratively reweighted robust (IRR) estimator, which can reduce this bias. However, the utility of IRR is limited by the fact that there is currently no method for determining whether PLM or IRR is more appropriate for a particular sample of data. Here, we develop and evaluate a novel test for selecting between the two estimators. Then, we apply the test to political science data. We demonstrate that PLM and IRR can each be optimal, that our test is effective in choosing between them, and that substantive conclusions can depend on which one is used.

Information

Type
Research Article
Information
Political Analysis , Volume 20 , Issue 1 , Winter 2012 , pp. 113 - 135
Copyright
Copyright © The Author 2011. Published by Oxford University Press on behalf of the Society for Political Methodology 

Footnotes

Edited by Jonathan N. Katz

References

Arjas, Elja. 1988. A graphical method for assessing goodness of fit in Cox's proportional hazards model. Journal of the American Statistical Association 83(401): 204–12.Google Scholar
Bednarski, Tadeusz. 1989. On sensitivity of Cox's estimator. Statistics and Decisions 7(3): 215–28.Google Scholar
Bednarski, Tadeusz. 1993. Robust estimation in Cox's regression model. Scandinavian Journal of Statistics 20(3): 213–25.Google Scholar
Bednarski, Tadeusz, and Borowicz, Filip. 2006. coxrobust: Robust Estimation in Cox Model, R package version 1.0.Google Scholar
Box-Steffensmeier, Janet M., and Jones, Bradford S. 1997. Time is of the essence: Event history models in political science. American Journal of Political Science 41(4): 1414–61.CrossRefGoogle 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., and Zorn, Christopher J. W. 2001. Duration models and proportional hazards in political science. American Journal of Political Science 45 (4): 972–88.Google Scholar
Box-Steffensmeier, Janet M., and Zorn, Christopher. 2002. Duration models for repeated events. Journal of Politics 64(4): 1069–94.CrossRefGoogle 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): 324–38.Google Scholar
Brambor, Thomas, Clark, William Roberts, and Golder, Matt. 2006. Understanding interaction models: Improving empirical analyses. Political Analysis 14 (1): 63–82.Google Scholar
Cai, Jianwen, Sen, Pranab K., and Zhou, Haibo. 1999. A random effects model for multivariate failure time data from multicenter clinical trials. Biometrics 55(1): 182–89.Google Scholar
Clarke, Kevin A. 2003. Nonparametric model discrimination in international relations. Journal of Conflict Resolution 47(1): 72–93.Google Scholar
Clarke, Kevin A. 2007. A simple distribution-free test for nonnested hypotheses. Political Analysis 15(3): 347–63.Google Scholar
Cook, R. Dennis. 1977. Detection of influential observation in linear regression. Technometrics 19(1): 15–8.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): 269–76.CrossRefGoogle Scholar
Desmarais, Bruce A., and Harden, Jeffrey J. 2011. Replication data for: Comparing partial likelihood and robust estimation methods for the Cox regression model. IQSS Dataverse Network [Distributor]. Vol. 1. http://hdl.handle.net/1902.1/16638.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): 609–26.CrossRefGoogle Scholar
Genz, Alan, Bretz, Frank, Hothorn, Torsten, Miwa, Tetsuhisa, Mi, Xuefei, Leisch, Friedrich, and Scheipl, Fabian. 2008. mvtnorm: Multivariate Normal and t Distributions, R package version 0.9-3.Google Scholar
Golder, Sona N. 2010. Bargaining delays in the government formation process. Comparative Political Studies 43(1): 3–32.Google Scholar
Harden, Jeffrey J., and Desmarais, Bruce A. 2011. Linear models with outliers: Choosing between conditional-mean and conditional-median methods. State Politics & Policy Quarterly doi:10.1177/1532440011408929.Google Scholar
Hartzell, Caroline, and Hoddie, Matthew. 2003. Institutionalizing peace: Power sharing and post-civil war conflict management. American Journal of Political Science 47 (2): 318–32.Google Scholar
Laver, Michael, and Ben Hunt, W. 1992. Policy and party competition. New York: Routledge.Google Scholar
Longini, Ira M., and Elizabeth Halloran, M. 1996. A frailty mixture model for estimating vaccine efficacy. Journal of the Royal Statistical Society Series C (Applied Statistics) 45(2): 165–73.Google Scholar
Martin, Lanny W. 2004. The government agenda in parliamentary democracies. American Journal of Political Science 48(3): 445–61.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): 323–44.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): 511–24.Google Scholar
Minder, Christopher E., and Bednarski, Tadeusz. 1996. A robust method for proportional hazards regression. Statistics in Medicine 15(10): 1033–47.Google Scholar
R Development Core Team. 2011. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.Google Scholar
Reid, Nancy, and Crépeau, Helene. 1985. Influence functions for proportional hazards regression. Biometrika 72(1): 1–9.Google Scholar
Therneau, Terry, and Lumley, Thomas. 2009. survival: Survival analysis, including penalised likelihood, R package version 2.35-4.Google Scholar
Verweij, Pierre J.M., and Van Houwelingen, Hans C. 1993. Cross-validation in survival analysis. Statistics in Medicine 12(24): 2305–14.Google Scholar
Yu, Chi Wai, and Clarke, Bertrand. 2011. Median loss decision theory. Journal of Statistical Planning and Inference 141(2): 611–23.Google Scholar
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