Stratify Cox Proportional Hazard Model on continuous variable

Question

I have a question regarding Cox proportional hazard models. I've been working with data with some time-varying variables and some that are fixed over time. In total 79 units are surveyed giving around ~ 8500 total observations. However one of the continuous variables doesn't conform with the proportionality assumption. I would like to stratify the model on this variable. However I'm not sure if I can stratify on a continuous variable, as one of the books I'm working with says you should factorize before, whereas I found other texts stratifying on continuous variables.

Does someone know if it is okay to stratify on a continuous variable?

Answer 1

It is OK to stratify a continuous predictor to deal with violation of proportional hazards (PH). Harrell says on page 501 of the second edition of Regression Modeling Strategies:

When a factor violates the PH assumption and a test of association is not needed, the factor can be adjusted for through stratification ... For continuous predictors, one may want to stratify into quantile groups. The continuous version of the predictor can still be adjusted for as a covariable to account for any residual linearity within strata.

Before you jump to that solution, however, consider some alternatives first. Mis-specification of the functional form of a continuous covariate can show up as a violation of PH. Plots of martingale residuals from a model omitting such a continuous covariate against the value of the covariate can show the correct form of its relationship with outcome, if it's not too strongly associated with other predictors. Spline modeling of the covariate in the regression might identify a close enough approximation to the correct functional form to remove the PH violation. Try for better specification of the model before you settle for stratification.