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Analyzing the Robustness of Semi-Parametric Duration Models for the Study of Repeated Events

  • Janet M. Box-Steffensmeier (a1), Suzanna Linn (a2) and Corwin D. Smidt (a3)


Estimators within the Cox family are often used to estimate models for repeated events. Yet, there is much we still do not know about the performance of these estimators. In particular, we do not know how they perform given time dependence, different censoring rates, and a varying number of events and sample sizes. We use Monte Carlo simulations to demonstrate the performance of a variety of popular semi-parametric estimators as these data aspects change and under conditions of event dependence and heterogeneity, both, or neither. We conclude that the conditional frailty model outperforms other standard estimators under a wide array of data-generating processes, and data limitations rarely alter its performance.


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Authors' note: Thanks to Neal Beck and anonymous reviewers for helpful comments on drafts of the article.



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Andersen, P. K., and Gill, R. D. 1982. Cox's regression model for counting processes: A large sample study. Annals of Statistics 10: 11001120.
Baccini, L. 2012. Democratization and trade policy: An empirical analysis of developing countries. European Journal of International Relations 18(3): 455–79.
Beardsley, K. 2008. Agreement without peace? International mediation and time inconsistency problems. American Journal of Political Science 52(4): 723–40.
Bender, R., Augustin, T., and Blettner, M. 2005. Generating survival times to simulate Cox proportional hazards models. Statistics in medicine 24(11): 1713–23.
Boehmke, F., Morey, D., and Shannon, M. 2006. Selection bias and continuous-time duration models: Consequences and a proposed solution. American Journal of Political Science 50(1): 192207.
Boehmke, F. J., and Skinner, P. 2012. State policy innovativeness revisited. State Politics and Policy Quarterly 12: 304–30.
Boehmke, F. J., and Witmer, R. 2004. Disentangling diffusion: The effects of social learning and economic competition on state policy innovation and expansion. Political Research Quarterly 57(1): 3951.
Box-Steffensmeier, J. M., and De Boef, S. 2006. Repeated events survival models: The conditional frailty model. Statistics in Medicine 25(20): 3518–33.
Brancati, D., and Snyder, J. 2011. Rushing to the polls: The causes of premature postconflict elections. Journal of Conflict Resolution 55(3): 469–92.
Brown, M. 1996. The international dimensions of internal conflict. Cambridge, MA: MIT Press.
Cheung, Y., Xu, Y., Tan, S., and Milligan, P. 2010. Estimation of intervention effects using first or multiple episodes in clinical trials: The Andersen-Gill model re-examined. Statistics in Medicine 29(3): 328–36.
Cook, R. J., Lawless, J., and Nadeau, C. 1996. Robust tests for treatment comparisons based on recurrent event responses. Biometrics 52(2): 557–71.
Cook, R. J., and Lawless, J. F. 1997. An overview of statistical methods for multiple-failure time data in clinical trials: Discussion. Statistics in Medicine 16(8): 841–43.
Curini, L. 2011. Government survival the Italian way: The core and the advantages of policy immobilism during the first republic. European Journal of Political Research 50(1): 110–42.
Dugan, L., LaFree, G., and Piquero, A. 2005. Testing a rational choice model of airline hijackings. Intelligence and Security Informatics 3495: 513–29.
Fernandez, J. 2010. Economic crises, high public pension spending, and blame-avoidance strategies: Pension policy retrenchments in 14 social-insurance countries, 1981–2005. Technical report, MPIfG Discussion Paper.
Gray, G. R. 1992. Flexible methods for analyzing survival data using splines, with application to breast cancer prognosis. Journal of the American Statistical Association 87(420): 942–51.
Greig, J. M. 2001. Moments of opportunity: Recognizing conditions of ripeness for international mediation between enduring rivals. Journal of Conflict Resolution 45(6): 691718.
Harezlak, J., and Tu, W. 2006. Estimation of survival functions in interval and right censored data using STD behavioral diaries. Statistics in Medicine 25(23): 4053–64.
Henderson, R., and Oman, P. 1999. Effect of frailty on marginal regression estimates in survival analysis. Journal of the Royal Statistical Society. Series B, Statistical Methodology 61(2): 367–79.
Kelly, P. J., and Lim, L. L.-Y. 2000. Survival analysis for recurrent event data: An application to childhood infectious disease. Statistics in Medicine 19: 1333.
Kuhn, U. 2009. Stability and change in party preference. Swiss Political Science Review 15(3): 463–94.
Leighley, J. E., and Nagler, J. 2013. Who votes now? Demographics, issues, inequality, and turnout in the United States. Princeton, NJ: Princeton University Press.
Li, Q., and Lagakos, S. 1997. Use of the Wei-Lin-Weissfeld method for the analysis of a recurring and a terminating event. Statistics in Medicine 16(8): 925–40.
Maoz, Z. 1996. Domestic sources of global change. Ann Arbor, MI: University of Michigan Press.
Martin, L., and Vanberg, G. 2003. Policing the bargain: Coalition government and parliamentary scrutiny. American Journal of Political Science 48(1): 1327.
Metcalfe, C., and Thompson, S. 2006. The importance of varying the event generation process in simulation studies of statistical methods for recurrent events. Statistics in Medicine 25(1): 165–79.
Oakes, D. 1992. Frailty models for multiple event times. In Survival analysis, state of the art, eds. Klein, John P. and Goel, P. K. The Netherlands: Kluwer Academic Publishers.
Pepe, M., and Cai, J. 1993. Some graphical displays and marginal regression analysis for recurrent failure times and time dependent covariates. Journal of the American Statistical Association 88(423): 811–20.
Plutzer, E. 2002. Becoming a habitual voter: Inertia, resources, and growth in young adulthood. American Political Science Review 96(1): 4156.
Prentice, R., Williams, B., and Peterson, A. 1981. On the regression analysis of multivariate failure time data. Biometrika 68(2): 373–9.
Rohde, D. W., and Simon, D. M. 1985. Presidential vetoes and congressional response: A study of institutional conflict. American Journal of Political Science 29: 397427.
Schneider, G., and Wiesehomeier, N. 2008. Rules that matter: Political institutions and the diversity: Conflict nexus. Journal of Peace Research 45(2): 183203.
Stukel, T. 1993. Comparison of methods for the analysis of longitudinal interval count data. Statistics in Medicine 12(14): 1339–51.
Suciu, G. P. 2002. Nonparametric survival comparison methods. Typescript.
Sun, J., and Yang, I. 2000. Nonparametric tests for stratum effects in the Cox model. Lifetime Data Analysis 6(4): 321–30.
Therneau, T. M., and Grambsch, P. M. 2000. Modeling survival data: Extending the Cox model. Statistics for Biology and Health. New York: Springer.
Therneau, T. M., and Hamilton, S. A. 1997. rhDNase as an example of recurrent event analysis. Statistics in Medicine 16(18): 2029–47.
Wei, L. J., Lin, D. Y., and Weissfeld, L. 1989. Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. Journal of the American Statistical Association 84(408): 1065–73.
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Analyzing the Robustness of Semi-Parametric Duration Models for the Study of Repeated Events

  • Janet M. Box-Steffensmeier (a1), Suzanna Linn (a2) and Corwin D. Smidt (a3)


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