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Reassessing Schoenfeld Residual Tests of Proportional Hazards in Political Science Event History Analyses
The authors contributed equally to this work. Author ordering was chosen at random. We are grateful to Janet Box-Steffensmeier, Wendy Cho, Kyle Joyce, Philip Chen, Han Dorussen, Charles Gregory, Zein Murib, Maron Sorenson, and participants in the event history ITV course held at the Ohio State University, the University of Illinois, the University of Minnesota, and the University of Wisconsin for offering helpful comments on earlier versions of this project. We are indebted to the current and previous editors and anonymous reviewers of AJPS, who provided invaluable suggestions during the review process. We also thank Jason Morgan for providing critical suggestions with respect to the simulation algorithm, as well as Kyle Beardsley, Scott Bennett, Kathleen Cunningham, Zachary Elkins, Scott Gartner, Hein Goemans, John Huber, Cecilia Martinez-Gallardo, Michaela Mattes, Maria Victoria Murillo, Stephen Quackenbush, Burcu Savun, Dan Smith, Paul Warwick, and Christopher Zorn for helpful correspondence with respect to replication materials. Thanks also go to all of the authors, too numerous to list here, who have made their data and replication code publicly available. Any and all errors are our own. Replication materials are available in the AJPS Data Archive on Dataverse (http://dvn.iq.harvard.edu/dvn/dv/ajps) and from the authors' websites.
Abstract
An underlying assumption of proportional hazards models is that the effect of a change in a covariate on the hazard rate of event occurrence is constant over time. For scholars using the Cox model, a Schoenfeld residual-based test has become the disciplinary standard for detecting violations of this assumption. However, using this test requires researchers to make a choice about a transformation of the time scale. In practice, this choice has largely consisted of arbitrary decisions made without justification. Using replications and simulations, we demonstrate that the decision about time transformations can have profound implications for the conclusions reached. In particular, we show that researchers can make far more informed decisions by paying closer attention to the presence of outlier survival times and levels of censoring in their data. We suggest a new standard for best practices in Cox diagnostics that buttresses the current standard with in-depth exploratory data analysis.