Skip to main content Accessibility help
Hostname: page-component-cf9d5c678-m9wwp Total loading time: 0.181 Render date: 2021-07-30T22:49:15.813Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

A Bayesian Split Population Survival Model for Duration Data With Misclassified Failure Events

Published online by Cambridge University Press:  25 March 2019

Benjamin E. Bagozzi
Assistant Professor, Dept. of Political Science & International Relations, University of Delaware, USA. Email:
Minnie M. Joo
Assistant Professor, Dept. of Political Science, University of Massachusetts Lowell, USA. Email:
Bomin Kim
Ph.D. Candidate, Dept. of Statistics, Penn State, USA. Email:
Bumba Mukherjee
Professor, Dept. of Political Science, Penn State, USA. Email:


We develop a new Bayesian split population survival model for the analysis of survival data with misclassified event failures. Within political science survival data, right-censored survival cases are often erroneously misclassified as failure cases due to measurement error. Treating these cases as failure events within survival analyses will underestimate the duration of some events. This will bias coefficient estimates, especially in situations where such misclassification is associated with covariates of interest. Our split population survival estimator addresses this challenge by using a system of two equations to explicitly model the misclassification of failure events alongside a parametric survival process of interest. After deriving this model, we use Bayesian estimation via slice sampling to evaluate its performance with simulated data, and in several political science applications. We find that our proposed “misclassified failure” survival model allows researchers to accurately account for misclassified failure events within the contexts of civil war duration and democratic survival.

Copyright © The Author(s) 2019. Published by Cambridge University Press on behalf of the Society for Political Methodology. 

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.)


Authors’ note: Earlier versions of this paper were presented as a poster at the 2014 Society For Political Methodology Annual Meeting in Athens, GA, USA and the 2018 Asian Political Methodology Conference in Seoul, South Korea, and as a paper at the 2018 Penn State Department of Political Science Brown Bag seminar series in State College, PA, USA, and the 2018 Visions in Methodology Conference at Ohio State University, in Columbus, OH, USA. Bagozzi’s contribution is partly based upon the work supported by the National Science Foundation under Grant Nos. SBE-SMA-1539302 and DMS-1737865. The authors wish to thank Jeff Gill, two anonymous reviewers, Lee Ann Banaszak, Liz Carlson, Bruce Desmarais, Kentaro Fukumoto, Simon Heuberger, Nahomi Ichino, Kosuke Imai, Azusa Katagiri, Fridolin Linder, Elizabeth Menninga, Shawna K. Metzger, Sara Mitchell, Inken von Borzyskowski, Michael Ward, Joe Wright, and Teppei Yamamoto for their helpful comments and suggestions. See Bagozzi et al. (2019) for replication materials.

Contributing Editor: Jeff Gill


Bagozzi, B., Joo, M., Kim, B., and Mukherjee, B.. 2019. “Replication Data for: A Bayesian Split Population Survival Model for Duration Data With Misclassified Failure Events.”, Harvard Dataverse, V1.CrossRefGoogle Scholar
Balcells, L., and Kalyvas, S. N.. 2014. “Does Warfare Matter? Severity, Duration, and Outcomes of Civil Wars.” Journal of Conflict Resolution 58(8):13901418.CrossRefGoogle Scholar
Balch-Lindsay, D., and Enterline, A. J.. 2000. “Killing Time: The World Politics of Civil War Duration, 1820–1992.” International Studies Quarterly 44(4):615642.CrossRefGoogle Scholar
Beger, A., Dorff, C. L., and Ward, M. D.. 2014. “Ensemble Forecasting of Irregular Leadership Change.” Research & Politics , 1–14.CrossRefGoogle Scholar
Beger, A., Dorff, C. L., and Ward, M. D.. 2016. “Irregular Leadership Changes in 2014: Forecasts Using Ensemble, Split-population Duration Models.” International Journal of Forecasting 32(1):98111.CrossRefGoogle Scholar
Beger, A., Hill, D. W., Metternich, N. W., Minhas, S., and Ward, M. D.. 2017. “Splitting It Up: The spduration Split-Population Duration Regression Package for Time-Varying Covariates.” The R Journal 9(2):474486.CrossRefGoogle Scholar
Box-Steffensmeier, J. M., and Zorn, C.. 1999. “Modeling Heterogeneity in Duration Models.” Paper presented at the 1999 Summer Meeting of The Political Methodology Society.Google Scholar
Box-Steffensmeier, J. M., Radcliffe, P. M., and Bartels, B. L.. 2005. “The Incidence and Timing of PAC Contributions to Incumbent U.S. House Members, 1993–94.” Legislative Studies Quarterly 30(4):549579.CrossRefGoogle Scholar
Box-Steffensmeier, J. M., De Boef, S., and Joyce, K.. 2007. “Event Dependent and Heterogeneity in Duration Models: the Conditional Frailty Model.” Political Analysis 15(3):237256.CrossRefGoogle Scholar
Brandt, P. T., Mason, T. D., Gurses, M., Petrovsky, N., and Radin, D.. 2008. “When and How the Fighting Stops: Explaining the Duration and Outcome of Civil Wars.” Defence and Peace Economics 19(6):415434.CrossRefGoogle Scholar
Buhaug, H., and Gates, S.. 2002. “The Geography of Civil War.” Journal of Peace Research 39(4):417433.CrossRefGoogle Scholar
Buhaug, H., Gates, S., and Lujala, P.. 2009. “Geography, Rebel Capability, and the Duration of Civil Conflict.” Journal of Conflict Resolution 53(4):544569.CrossRefGoogle Scholar
Carlin, B. P., and Louis, T. A.. 2000. Bayes and Empirical Bayes Methods for Data Analysis , 2nd edition. New York: Chapman and Hall/CRC.CrossRefGoogle Scholar
Carter, D. B., and Signorino, C. S.. 2013. “Good Times, Bad Times: Left Censoring in Grouped Binary Duration Data.” Presented at the Meeting of the International Studies Association, 3–6 April, 2013.Google Scholar
Cioffi-Revilla, C., and Lai, D.. 1995. “War and Politics in Ancient China, 2700 B.C. to 722 B.C.: Measurement and Comparative Analysis.” Journal of Conflict Resolution 39(3):467494.CrossRefGoogle Scholar
Cioffi-Revilla, C., and Landman, T.. 1999. “Evolution of Maya Polities in the Ancient Mesoamerican System.” International Studies Quarterly 43(4):559598.CrossRefGoogle Scholar
Collier, P. 2003. “The Market for Civil War.” Foreign Policy (136):3845.CrossRefGoogle Scholar
Collier, P., Hoeffler, A., and Söderbom, M.. “On the Duration of Civil War.” Journal of Peace Research 41(3):253273.CrossRefGoogle Scholar
Cress, D. M., McPherson, J. M., and Rotolo, T.. 1997. “Competition and Commitment in Voluntary Memberships: The Paradox of Persistence and Participation.” Sociological Perspectives 40(1):6179.CrossRefGoogle Scholar
Cunningham, D. E. 2006. “Veto Players and Civil War Duration.” American Journal of Political Science 50(4):875892.CrossRefGoogle Scholar
Fearon, J. D., and Laitin, D.. 2003. “Ethnicity, Insurgency, and Civil War.” American Political Science Review 97(1):7590.CrossRefGoogle Scholar
Geweke, J. 1992. “Evaluating the Accuracy of Sampling Based Approaches to the Calculation of Posterior Moments.” In Bayesian Statistics, vol. 4 , edited by Bernardo, J. M., Berger, J. O., Dawid, A. P., and Smith, A. F. M., 169193. New York: Oxford University Press.Google Scholar
Heidelberger, P., and Welch, P. D.. 1983. “Simulation Run Length Control in Presence of an Initial Transient.” Operations Research 31:11091144.CrossRefGoogle Scholar
Jin, S., and Boehmke, F. J.. 2017. “Proper Specification of Nonproportional Hazards Corrections in Duration Models.” Political Analysis 25(1):138144.CrossRefGoogle Scholar
Keele, L. 2010. “Proportionally Difficult: Testing for Nonproportional Hazards in Cox Models.” Political Analysis 18(2):189205.CrossRefGoogle Scholar
Kreutz, J. 2010. “How and When Armed Conflicts End: Introducing the UCDP Conflict Termination Dataset.” Journal of Peace Research 47(2):243250.CrossRefGoogle Scholar
Larmer, M., Laudati, A., and Clark, J. F.. 2013. “Neither War Nor Peace in the Democratic Republic of Congo (DRC): Profiting and Coping Amid Violence and Disorder.” Review of African Political Economy 40:112.CrossRefGoogle Scholar
Licht, A. A. 2011. “Change Comes with Time: Substantive Interpretation of Nonproportional Hazards in Event History Analysis.” Political Analysis 19(2):227243.CrossRefGoogle Scholar
Lischer, S. K. 2015. Dangerous Sanctuaries: Refugee Camps, Civil War, and the Dilemmas of Humanitarian Aid . Ithaca, NY: Cornell University Press.Google Scholar
Metzger, S. K., and Jones, B. T.. 2016. “Surviving Phases: Introducing Multistate Survival Models.” Political Analysis 24(4):457477.CrossRefGoogle Scholar
Neal, R. M. 2003. “Slice Sampling.” The Annals of Statistics 31(3):705741.CrossRefGoogle Scholar
Puddephatt, A.2006. “Conflict and the Role of the Media.” Copenhagen: International Media Support Report.Google Scholar
Ruhe, C. 2018. “Quantifying Change Over Time: Interpreting Time-varying Effects In Duration Analyses.” Political Analysis 26(1):90111.CrossRefGoogle Scholar
Shimray, U. A. 2001. “Ethnicity and Socio-political Assertion: the Manipur Experience.” Economic and Political Weekly 36(39):36743677.Google Scholar
Svolik, M. W. 2008. “Authoritarian Reversals and Democratic Consolidation.” American Political Science Review 102(2):153168.CrossRefGoogle Scholar
Themnér, L., and Wallensteen, P.. 2014. “Armed conflicts, 1946–2013.” Journal of Peace Research 51(4):541554.CrossRefGoogle Scholar
Thyne, C. L. 2012. “Information, Commitment, and Intra-War Bargaining: The Effect of Governmental Constraints on Civil War Duration.” International Studies Quarterly 56(2):307321.CrossRefGoogle Scholar
Young, J. K., and Dugan, L.. 2014. “Survival of the Fittest: Why Terrorist Groups Endure.” Perspectives on Terrorism 8(2):223.Google Scholar
Supplementary material: File

Bagozzi et al. supplementary material

Bagozzi et al. supplementary material 1

Download Bagozzi et al. supplementary material(File)
File 1 MB
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure 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 sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ 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.

A Bayesian Split Population Survival Model for Duration Data With Misclassified Failure Events
Available formats

Send article to Dropbox

To send 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 use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

A Bayesian Split Population Survival Model for Duration Data With Misclassified Failure Events
Available formats

Send article to Google Drive

To send 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 use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

A Bayesian Split Population Survival Model for Duration Data With Misclassified Failure Events
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? *