I'm currently working with event history data studying how long after implementation countries abolish certain policies. Regarding the policies I also have an index on how far the countries went with their policies ranging from 0 to 100.
I wanted to control for this, in order be able to control for their point of departure. However the coefficient violates the proportionality assumption.
Can I stratify for the continuous variable of that index? I understand it so, that this would allow every country to have a different baseline hazard with respect to their point of departure. Playing around with the data this didn't produce an error.
Could anyone tell me if I can trust these results or if I have to categorize the variable first?
The CoxPH model allows using continuous predictors. The only point to take care of is that the relationship between predictor and log hazard ratio should be approximately linear.
https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_survival/BS704_Survival6.html
Jochen Wilhelm thank you for your answer. Just one quick follow-up question: Is it also possible to stratify on this continuous variable if it violates the PH assumption?
Yes, it is possible. Sometimes the proportional hazard assumption is violated for some covariate. In such cases, it is possible to stratify taking this variable into account and use the proportional hazards model in each stratum for the other covariates (https://bookdown.org/sestelo/sa_financial/non-proportional-hazards-and-now-what.html). This paper (https://www.lexjansen.com/phuse/2013/sp/SP07.pdf) describes two different methods: introducing interactions of selected covariates with the function of time and stratification model.
The following is an excellent paper (https://jamanetwork.com/journals/jama/article-abstract/2763185). The authors are saying the hazards are never proportional unless the treatment has a zero causal effect on survival.
The PH assumption relates to the entire model, including all predictors and covariables deemd interesting or relevant. "Restoring" PH by irgnoring or removing a covariable is not ok, as it likely demonstates that the inclusion of the covariable is relevant because it explains so much of the variance in the data that deviation from the PH assumption becomes clear.
If you have non-PH, you might start investigating if the effects of the predictors/covariables in the model are not linear. If this is not successful, an appropriate partition of the time axis might be the key (early effects are different from late effects, but the hazards are proportional within the early as well as within the late phases). If this also does not help, you might really think of stratification (what, by definition, is possible only for categorical variables). I don't consider it a good idea to categorize a continuous variable just to be able to use it for stratification. But if nothing else works, this might be a last rescue. But I would then check if the violation of the PH assumption really does more harm than the categorization of the continuous variable.
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