Duration Models and Proportional Hazards in Political Science

Abstract

period. In recent years political scientists have increasingly adopted a wide range of techniques for modeling duration data. But while the use of duration models by political scientists has increased dramatically, a concomitant examination of the modeling assumptions underlying these methods has not accompanied this growth. An important characteristic of most of these models is the assumption that the relative hazards over different covariate values are proportional. This consideration is important because, as has been widely shown in the statistics literature, estimation of proportional hazards models when hazards are, in fact, nonproportional can result in biased estimates, incorrect standard errors, and faulty inferences about the substantive impact of independent variables (e.g., Kalbfleisch and Prentice 1980; Schemper 1992; Collett 1994; Klein and Moeschberger 1997). But while the proportional hazards assumption is central to the proper estimation and interpretation of these models, it has received little attention by political scientists modeling duration data. This is unfortunate because, absent explicit examinations of the validity of these assumptions, the reader is often unable to infer whether or not the assumption holds for any particular analysis. This difficulty is exacerbated by the fact that, in many circumstances, both substantive theories and empirical data suggest that the assumption itself is of dubious accuracy. In fact, it is often the case that many substantively interesting hypotheses imply time-dependence or other forms of nonproportionality in the conditional probability of failure. Thus, it is important that, as political scientists begin to use these models more often in applied research, they take care to examine the extent to which this assumption is consistent with their data and to be aware of methods for analyzing duration data in which hazards are not proportional.

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