Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-22T02:59:32.975Z Has data issue: false hasContentIssue false
  • English
  • Français

Simulating Duration Data for the Cox Model

Published online by Cambridge University Press:  24 May 2018

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

Abstract

The Cox proportional hazards model is a popular method for duration analysis that is frequently the subject of simulation studies. However, no standard method exists for simulating durations directly from its data generating process because it does not assume a distributional form for the baseline hazard function. Instead, simulation studies typically rely on parametric survival distributions, which contradicts the primary motivation for employing the Cox model. We propose a method that generates a baseline hazard function at random by fitting a cubic spline to randomly drawn points. Durations drawn from this function match the Cox model’s inherent flexibility and improve the simulation’s generalizability. The method can be extended to include time-varying covariates and non-proportional hazards.

Type
Research Notes
Information
Political Science Research and Methods , Volume 7 , Issue 4 , October 2019 , pp. 921 - 928
Copyright
© The European Political Science Association 2018 

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

*

Jeffrey J. Harden is an Assistant Professor in the Department of Political Science, University of Notre Dame, 2055 Jenkins Nanovic Halls, Notre Dame, IN 46556 ([email protected]). Jonathan Kropko is an Assistant Professor of in the Department of Politics, University of Virginia, S383 Gibson Hall, 1540 Jefferson Park Avenue, Charlottesville, VA 22904 ([email protected]). The methods described here are available in the coxed R package. To view supplementary material for this article, please visit https://doi.org/10.1017/psrm.2018.19

References

Austin, Peter C. 2012. ‘Generating Survival Times to Simulate Cox Proportional Hazards Models with Time-Varying Covariates’. Statistics in Medicine 31(29):3946–3958.Google Scholar
Benaglia, Tatiana, Jackson, Christopher H., and Sharples, Linda D.. 2015. ‘Survival Extrapolation in the Presence of Cause Specific Hazards’. Statistics in Medicine 34(5):796–811.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
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., Linn, Suzanna, and Smidt, Corwin D.. 2014. ‘Analyzing the Robustness of Semi-Parametric Duration Models for the Study of Repeated Events’. Political Analysis 22(2):183–204.Google Scholar
Chastang, Claude, Byar, David, and Piantadosi, Steven. 1988. ‘A Quantitative Study of the Bias in Estimating the Treatment Effect Caused by Omitting a Balanced Covariate in Survival Models’. Statistics in Medicine 7(12):1243–1255.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
Crowther, Michael J., and Lambert, Paul C.. 2013. ‘Simulating Biologically Plausible Complex Survival Data’. Statistics in Medicine 32(23):4118–4134.Google Scholar
Desmarais, Bruce A., and Harden, Jeffrey J.. 2012. ‘Comparing Partial Likelihood and Robust Estimation Methods for the Cox Regression Model’. Political Analysis 20(1):113–115.Google Scholar
Hendry, David J.. 2014. ‘Data Generation for the Cox Proportional Hazards Model with Time-Dependent Covariates: A Method for Medical Researchers’. Statistics in Medicine 33(3):436–454.Google Scholar
Hyman, James M.. 1983. ‘Accurate Monotonicity Preserving Cubic Interpolation’. SIAM Journal on Scientific and Statistical Computing 4(4):645–654.Google Scholar
Jackson, Dan, White, Ian R., Seaman, Shaun, Evans, Hannah, Baisley, Kathy, and Carpenter, James. 2014. ‘Relaxing the Independent Censoring Assumption in the Cox Proportional Hazards Model Using Multiple Imputation’. Statistics in Medicine 33(27):4681–4694.Google Scholar
Keele, Luke. 2010. ‘Proportionally Difficult: Testing for Nonproportional Hazards in Cox Models’. Political Analysis 18(2):189–205.Google Scholar
Kropko, Jonathan, and Harden, Jeffrey J.. 2018. ‘Beyond the Hazard Ratio: Generating Expected Durations from the Cox Proportional Hazards Model’. British Journal of Political Science (Forthcoming). https://doi.org/10.1017/S000712341700045X.Google Scholar
Leemis, Lawrence M.. 1987. ‘Variate Generation for Accelerated Life and Proportional Hazards Models’. Operations Research 35(6):892–894.Google Scholar
Leemis, Lawrence M., Shih, Li-Hsing, and Reynertson, Kurt. 1990. ‘Variate Generation for Accelerated Life and Proportional Hazards Models with Time Dependent Covariates’. Statistics & Probability Letters 10(4):335–339.Google Scholar
Shih, Li-Hsing, and Leemis, Lawrence M.. 1993. ‘Variate Generation for a Nonhomogeneous Poisson Process with Time Dependent Covariates’. Journal of Statistical Computation and Simulation 44(3–4):165–186.Google Scholar
Sylvestre, Marie-Pierre, and Abrahamowicz, Michal. 2008. ‘Comparison of Algorithms to Generate Event Times Conditional on Time-Dependent Covariates’. Statistics in Medicine 27(14):2618–2634.Google Scholar
Zhou, Mai. 2001. ‘Understanding the Cox Regression Models with Time-Change Covariates’. The American Statistician 55(2):153–155.Google Scholar
Supplementary material: Link

Harden and Kropko Dataset

Dataset

https://doi.org/10.7910/DVN/1YG7BI
Link
Supplementary material: PDF

Harden and Kropko supplementary material

Harden and Kropko supplementary material

Download Harden and Kropko supplementary material(PDF)
PDF 143.1 KB