I’m analysing the functional form of a continuous covariate to the hazard ratio in a Cox proportional hazard model. I’d like to compare a linear model to a model where the covariate is log transformed. I have two specific questions:
- What is the appropriate method for visual inspection?
- Apart from visual inspection, should I do a formal test to compare the two models?
Fe, this paper (link to paper) used martingale residuals for visual inspection, and a partial likelihood ratio test to compare a model with linear terms and a model using fractional polynomials.