The forthcoming article “Reassessing Schoenfeld Residual Tests of Proportional Hazards in Political Science Event History Analyses” by Sunhee Park and David J. Hendry is summarized by the authors here:
In a 2001 AJPS article, Janet Box-Steffensmeier and Chris Zorn introduced the political science audience to Patricia Grambsch and Terry Therneau’s method of testing and correcting for violations of the proportional hazards assumption in applications of the Cox model. The test allows researchers to identify specific covariates in a multivariate Cox regression model that do not satisfy the proportional hazards assumption. In recent years, the number of applications of the Cox model and other proportional hazards models has exploded in the political science literature, and the Grambsch-Therneau method advocated by Box-Steffensmeier, Zorn, and colleagues has become the disciplinary standard. The test works by comparing a type of covariate-specific regression residual to the time scale in order to determine whether the effect of a covariate differs depending on when in the process under study the researcher is looking. If it does, this indicates a violation of the proportional hazards assumption, and suggests the need to take corrective measures in order to make valid inferences.
In our new article, we identify an important issue that often goes overlooked in applications of the Grambsch-Therneau method. Specifically, the test requires the researcher to make a choice about a transformation of the time scale (or not to transform at all). The idea is that a small number of cases with relatively long observation times (a not uncommon feature of political science data) can have a disproportionate impact on the test results, and using a transformation offers researchers a way to avoid this pitfall. If the choice of whether or not to transform and, if so, which transformation to choose, did not have an impact on the test results, it would not be an important issue. However, we use an extensive set of simulations and replications of published work to demonstrate that the choice of a time transformation often does have serious consequences for the conclusions reached.
We argue that researchers using the Grambsch-Therneau tests of proportional hazards need to combine them with exploratory data analysis in order to make appropriate choices about transformations of the time scale. Our replications in particular show that researchers who are unaware of the need to transform would often be better served by a transformation, and that researchers who are aware often do not make the ideal choice. And most importantly, better choices could be made by simply doing the type of data exploration that researchers should be doing anyway in the name of best practices. We hope that our findings will make researchers aware of this issue moving forward, and help take practitioners a modest step toward greater consistency in methodological standards.