Abstract
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.
Publisher
Cambridge University Press (CUP)
Subject
Political Science and International Relations,Sociology and Political Science
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4. Many texts also outline a graphical approach to the diagnosis of nonlinear functional forms (Hosmer and Lemeshow 1999; Therneau and Grambsch 2000; Box-Steffensmeier and Jones 2004). Under this method, martingale residuals from a null model are plotted against each covariate and a scatterplot smoother is added to the plot. If the scatterplot smoother fit is nonlinear, this provides evidence of a nonlinear functional form. As Therneau and Grambsch (2000) outline, this method often fails if the various predictors are correlated.
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