Covariate Functional Form in Cox Models

In most event history models, the effect of a covariate on the hazard is assumed to have a log-linear functional form. For continuous covariates, this assumption is often violated as the effect is highly nonlinear. Assuming a log-linear functional form when the nonlinear form applies causes specification errors leading to erroneous statistical conclusions. Scholars can, instead of ignoring the presence of nonlinear effects, test for such nonlinearity and incorporate it into the model. I review methods to test for and model nonlinear functional forms for covariates in the Cox model. Testing for such nonlinear effects is important since such nonlinearity can appear as nonproportional hazards, but time varying terms will not correct the misspecification. I investigate the consequences of nonlinear function forms using data on international conflicts from 1950-1985. I demonstrate that the conclusions drawn from this data depend on fitting the correct functional form for the covariates.