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Event Dependence and Heterogeneity in Duration Models: The Conditional Frailty Model

Published online by Cambridge University Press:  04 January 2017

Janet M. Box-Steffensmeier ,
Suzanna De Boef  and
Kyle A. Joyce
Janet M. Box-Steffensmeier
Affiliation:
Department of Political Science, 2140 Derby Hall, 154 North Oval Mall, The Ohio State University, Columbus, OH 43210. e-mail: [email protected] (corresponding author)
Suzanna De Boef
Affiliation:
Department of Political Science, 219 Pond Laboratory, The Pennsylvania State University, University Park, PA 16802. e-mail: [email protected]
Kyle A. Joyce
Affiliation:
Department of Political Science, 219 Pond Laboratory, The Pennsylvania State University, University Park, PA 16802. e-mail: [email protected]
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Abstract

We introduce the conditional frailty model, an event history model that separates and accounts for both event dependence and heterogeneity in repeated events processes. Event dependence and heterogeneity create within-subject correlation in event times thereby violating the assumptions of standard event history models. Simulations show the advantage of the conditional frailty model. Specifically they demonstrate the model's ability to disentangle the sources of within-subject correlation as well as the gains in both efficiency and bias of the model when compared to the widely used alternatives, which often produce conflicting conclusions. Two substantive political science problems illustrate the usefulness and interpretation of the model: state policy adoption and terrorist attacks.

Type
Research Article
Information
Political Analysis , Volume 15 , Issue 3 , Summer 2007 , pp. 237 - 256
Copyright
Copyright © The Author 2007. Published by Oxford University Press on behalf of the Society for Political Methodology 

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References

Aalen, Odd O. 1988. Heterogeneity in survival anlaysis. Statistics in Medicine 7: 1121–37.Google Scholar
Andersen, Per Kragh, Klein, John P., and Zhang, Mei-Jie. 1999. Testing for centre effects in multi-centre survival studies: A monte carlo comparison of fixed and random effects tests. Statistics in Medicine 18: 1489–1500.Google Scholar
Andersen, P. K., and Gill, R. D. 1982. Cox's regression model for counting processes: A large sample study. The Annals of Statistics 10: 1100–20.Google Scholar
Berry, Francis Stokes, and Berry, William D. 1990. State lottery adoptions as policy innovations: An event history analysis. American Political Science Review 84: 395–415.Google Scholar
Blossfeld, Hans-Peter, and Rohwer, Götz. 1995. Techniques of event history modeling. Mahwah, NJ: Lawrence Erlbaum.Google Scholar
Bowman, Michael E. 1996. An evaluation of statistical models for the analysis of recurrent events data: With application to needlestick injuries among a cohort of female veterinarians. PhD diss., Ohio State Univ.Google Scholar
Box-Steffensmeier, Janet M., and Zorn, Christopher. 2002. Duration models for repeated events. Journal of Politics 64: 1069–94.Google Scholar
Box-Steffensmeier, Janet M., and De Boef, Suzanna. 2006. Repeated events survival models: The conditional frailty model. Statistics in Medicine 25: 3518–33.Google Scholar
Clayton, David. 1994. Some approaches to the analysis of recurrent event data. Statistical Methods in Medical Research 3: 227–62.Google Scholar
Cleves, Mario. 1999. Analysis of multiple failure-time data using Stata. Stata Technical Bulletin 49: 30–9.Google Scholar
Cook, Richard J., Ng, Edmund T. M., Mukherjee, Jayanti, and Vaughn, David. 1999. Two-state mixed renewal processes for chronic disease. Statistics in Medicine 18: 175–88.Google Scholar
Cook, Richard J., and Lawless, Jerald F. 1997. Marginal analysis of recurrent events and a terminating event. Statistics in Medicine 16: 841–51.Google Scholar
Cook, Richard J., and Lawless, Jerald F. 2002. Analysis of repeated events. Statistical Methods in Medical Research 11: 141–66.Google Scholar
Cox, D. R. 1972. Regression models and life tables. Journal of the Royal Statistical Society B34: 187–220.Google Scholar
Fong, Daniel Y.T., Lam, K. F., Lawless, J. F., and Lee, Y. W. 2001. Dynamic random effects models for times between repeated events. Lifetime Data Analysis 7: 345–62.Google Scholar
Gail, M. H., Santner, T. J., and Brown, C. C. 1980. An analysis of comparative carcinogenesis experiments based on multiple times to tumor. Biometrics 36: 255–66.Google Scholar
Gao, Feng, Manatunga, Amita K., and Chen, Shande. 2007. Non-parametric estimation for baseline hazards function and covariate effects with time-dependent covariates. Statistics in Medicine 26: 857–68.Google Scholar
Gao, Sujuan, and Zhow, Xiao-Hua. 1997. An empirical comparison of two semi-parametric approaches for the estimation of covariate effects from multivariate failure time data. Statistics in Medicine 16: 2049–62.Google Scholar
Hausman, Jerry A. 1978. Specification tests in econometrics. Econometrica 46: 1251–71.Google Scholar
Hougaard, Philip. 1991. Modelling heterogeneity in survival data. Journal of Applied Probability 28: 695–701.Google Scholar
Hougaard, Philip. 2000. Analysis of multivariate survival data. New York: Springer-Verlag.Google Scholar
Hurvich, Clifford M., Simonoff, Jeffrey S., and Tsai, Chih-Ling. 1998. Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. Journal of Royal Statistical Society B60: 271–93.Google Scholar
Jones, Bradford S., and Branton, Regina P. 2005. Beyond logit and probit: Cox duration models of single, repeating, and competing events for state policy adoption. State Politics and Policy Quarterly 5: 420–43.Google Scholar
Keiding, Niels, Andersen, Per Kragh, and Klein, John P. 1997. The role of frailty models and accelerated failure time models in describing heterogeneity due to omitted covariates. Statistics in Medicine 16: 215–24.Google Scholar
Kelly, Patrick J., and Lim, Lynette L.-Y. 2000. Survival analysis for recurrent event data: An application to childhood infectious disease. Statistics in Medicine 19: 13–33.Google Scholar
Klein, John P., and Moeschberger, Melvin L. 1997. Survival analysis: Techniques for censored and truncated data. New York: Springer-Verlag.Google Scholar
Kosorok, Michael R., Lee, Bee Leng, and Fine, Jason P. 2004. Robust inference for univariate proportional hazards frailty regression models. Annals of Statistics 32: 1448–91.Google Scholar
Lawless, Jerald F. 2002. Statistical models and methods for lifetime data. 2nd ed. New York: Wiley.Google Scholar
Lawless, J. F., and Nadeau, C. 1995. Some simple robust methods for the analysis of recurrent events. Technometrics 37: 158–68.Google Scholar
Li, Quan, and Schaub, Drew. 2004. Economic globalization and transnational terrorism: A pooled time-series analysis. Journal of Conflict Resolution 48: 230–58.Google Scholar
Li, Yi, and Lin, Xihong. 2003. Functional inference in frailty measurement error models for clustered survival data using the SIMEX approach. Journal of the American Statistical Association 98: 191–203.Google Scholar
Lin, D. Y. 1994. Cox regression analysis of multivariate failure time data: The marginal approach. Statistics in Medicine 13: 2233–47.Google Scholar
Mintrom, Michael, and Vergari, Sandra. 1998. Policy networks and innovation diffusion: The case of state education reforms. Journal of Politics 60: 126–48.Google Scholar
Mooney, Christopher Z., and Lee, Mei-Hsien. 1995. Legislative morality in the American states: The case of pre-Roe abortion regulation reform. American Journal of Political Science 39: 599–627.Google Scholar
Nelson, Wayne B. 2003. Recurrent events data analysis for product repairs, disease recurrences, and other applications. Philadelphia, PA: Society for Industrial and Applied Mathematics.Google Scholar
Oakes, D. 1992. Frailty models for multiple event times. In Survival analysis: State of the art, ed. Klein, John P. and Goele, Prem K., 371–9. Dordrecht, Netherlands: Kluwer Academic Publishers.Google Scholar
Oakes, D. A. 1997. Model based and or marginal analysis for multiple event time data. In Proceedings of the first Seattle symposium in biostatistics: Survival analysis, ed. Lin, D. Y. and Fleming, T. R., 85–98. New York: Springer-Verlag.Google Scholar
Ohman-Strickland, Pamela. 2003. Fitting the frailty distribution using empirical Bayes. International Conference on Reliability and Survival Analysis, Columbia, SC.Google Scholar
Prentice, R. L., Williams, B. J., and Peterson, A. V. 1981. On the regression analysis of multivariate failure time data. Biometrika 68: 373–9.Google Scholar
R Development Core Team. 2007. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. http://www.R-project.org.Google Scholar
Sastry, Narayan. 1997. A nested frailty model for survival data, with an application to the study of child survival in Northeast Brazil. Journal of the American Statistical Association 92: 426–35.Google Scholar
Therneau, Terry M. 2000. Practical frailty models. Technical report. Mayo Clinic.Google Scholar
Therneau, Terry M., and Grambsch, Patricia M. 2000. Modeling survival data: Extending the Cox model. New York: Springer-Verlag.Google Scholar
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: 1065–73.Google Scholar