Skip to main content Accessibility help
×
Home
Hostname: page-component-7ccbd9845f-dxj8b Total loading time: 0.342 Render date: 2023-01-29T09:27:33.294Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

Simulating Duration Data for the Cox Model

Published online by Cambridge University Press:  24 May 2018

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
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 (jeff.harden@nd.edu). 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 (jkropko@virginia.edu). 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):39463958.CrossRefGoogle ScholarPubMed
Benaglia, Tatiana, Jackson, Christopher H., and Sharples, Linda D.. 2015. ‘Survival Extrapolation in the Presence of Cause Specific Hazards’. Statistics in Medicine 34(5):796811.CrossRefGoogle ScholarPubMed
Bender, Ralf, Augustin, Thomas, and Blettner, Maria. 2005. ‘Generating Survival Times to Simulate Cox Proportional Hazards Models’. Statistics in Medicine 24(11):17131723.CrossRefGoogle ScholarPubMed
Box-Steffensmeier, Janet M., and Jones, Bradford S.. 2004. Event History Modeling: A Guide for Social Scientists. New York: Cambridge University Press.CrossRefGoogle 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):183204.CrossRefGoogle 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):12431255.CrossRefGoogle ScholarPubMed
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):43524374.CrossRefGoogle ScholarPubMed
Crowther, Michael J., and Lambert, Paul C.. 2013. ‘Simulating Biologically Plausible Complex Survival Data’. Statistics in Medicine 32(23):41184134.CrossRefGoogle ScholarPubMed
Desmarais, Bruce A., and Harden, Jeffrey J.. 2012. ‘Comparing Partial Likelihood and Robust Estimation Methods for the Cox Regression Model’. Political Analysis 20(1):113115.CrossRefGoogle 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):436454.CrossRefGoogle ScholarPubMed
Hyman, James M.. 1983. ‘Accurate Monotonicity Preserving Cubic Interpolation’. SIAM Journal on Scientific and Statistical Computing 4(4):645654.CrossRefGoogle 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):46814694.CrossRefGoogle ScholarPubMed
Keele, Luke. 2010. ‘Proportionally Difficult: Testing for Nonproportional Hazards in Cox Models’. Political Analysis 18(2):189205.CrossRefGoogle 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.CrossRefGoogle Scholar
Leemis, Lawrence M.. 1987. ‘Variate Generation for Accelerated Life and Proportional Hazards Models’. Operations Research 35(6):892894.CrossRefGoogle 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):335339.CrossRefGoogle 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):165186.CrossRefGoogle 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):26182634.CrossRefGoogle ScholarPubMed
Zhou, Mai. 2001. ‘Understanding the Cox Regression Models with Time-Change Covariates’. The American Statistician 55(2):153155.CrossRefGoogle Scholar
Supplementary material: Link

Harden and Kropko Dataset

Link
Supplementary material: PDF

Harden and Kropko supplementary material

Harden and Kropko supplementary material

Download Harden and Kropko supplementary material(PDF)
PDF 143 KB
16
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Simulating Duration Data for the Cox Model
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Simulating Duration Data for the Cox Model
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Simulating Duration Data for the Cox Model
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *