Proportionally Difficult: Testing for Nonproportional Hazards in Cox Models

The Cox proportional hazards model is widely used to model durations in the social sciences. Although this model allows analysts to forgo choices about the form of the hazard, it demands careful attention to the proportional hazards assumption. To this end, a standard diagnostic method has been developed to test this assumption. I argue that the standard test for nonproportional hazards has been misunderstood in current practice. This test detects a variety of specification errors, and these specification errors must be corrected before one can correctly diagnose nonproportionality. In particular, unmodeled nonlinearity can appear as a violation of the proportional hazard assumption for the Cox model. Using both simulation and empirical examples, I demonstrate how an analyst might be led astray by incorrectly applying the nonproportionality test.

[1]  P. Grambsch,et al.  Proportional hazards tests and diagnostics based on weighted residuals , 1994 .

[2]  Sanford C. Gordon,et al.  Stochastic dependence in competing risks , 2002 .

[3]  Nancy Reid,et al.  On “A conversation with Sir David Cox” , 1994, Issue 5.2, Spring 2023.

[4]  B. Ripley,et al.  Semiparametric Regression: Preface , 2003 .

[5]  Sunil J Rao,et al.  Regression Modeling Strategies: With Applications to Linear Models, Logistic Regression, and Survival Analysis , 2003 .

[6]  R. Michael Alvarez,et al.  Event History Modeling: A Guide for Social Scientists , 2004 .

[7]  L. R. Reed,et al.  A unified statistical model of conflict onset and escalation American Journal of Political Science 4 , 2000 .

[8]  Nathaniel Beck,et al.  Taking Time Seriously: Time-Series-Cross-Section Analysis with a Binary Dependent Variable , 1998 .

[9]  Guohua Pan,et al.  Local Regression and Likelihood , 1999, Technometrics.

[10]  S W Lagakos,et al.  Properties of proportional-hazards score tests under misspecified regression models. , 1984, Biometrics.

[11]  Alan Y. Chiang,et al.  Generalized Additive Models: An Introduction With R , 2007, Technometrics.

[12]  Janet M. Box-Steffensmeier,et al.  Duration models and proportional hazards in political science , 2001 .

[13]  John D. Kalbfleisch,et al.  Misspecified proportional hazard models , 1986 .

[14]  Nathaniel N. Beck,et al.  Beyond linearity by default: Generalized additive models , 1998 .

[15]  L. Keele.  Semiparametric Regression for the Social Sciences , 2008 .

[16]  Thomas R. Fleming,et al.  Model misspecification in proportional hazards regression , 1995 .

[17]  H. E. Goemans,et al.  International Conflict and the Tenure of Leaders: Is War Still Ex Post Inefficient? , 2004 .

[18]  Richard D. Deveaux,et al.  Applied Smoothing Techniques for Data Analysis , 1999, Technometrics.

[19]  Per Kragh Andersen,et al.  Regression Modeling Strategies with Applications to Linear Models, Logistic Regression and Survival Analysis. Frank E. Harrell, Jun, Springer‐Verlag, New York, 2001. No. of pages: 568. ISBN 0‐387‐95232‐2 , 2003 .

[20]  Daniel Carpenter,et al.  Groups, the Media, Agency Waiting Costs, and FDA Drug Approval , 2002 .

[21]  Janet M. Box-Steffensmeier,et al.  Duration Models for Repeated Events , 2002, The Journal of Politics.

[22]  P. Grambsch,et al.  Martingale-based residuals for survival models , 1990 .

[23]  M. Wand.  Local Regression and Likelihood , 2001 .

[24]  D.,et al.  Regression Models and Life-Tables , 2022 .

[25]  David W. Hosmer,et al.  Applied Survival Analysis: Regression Modeling of Time-to-Event Data , 2008 .

[26]  M LeBlanc,et al.  Adaptive Regression Splines in the Cox Model , 1999, Biometrics.

[27]  J. O'neal,et al.  The Classical Liberals Were Right: Democracy, Interdependence, and Conflict, 1950–1985 , 1997 .

[28]  S. Wood.  Generalized Additive Models: An Introduction with R , 2006 .