I have a survival-time dataset where entities (countries) are measured at discrete intervals (years). I'm interested in examining the effect of some fixed treatments (i.e. ones that occur at the beginning of each entity's spell and remain constant until failure time). I've fit a Cox proportional hazards model (using Stata's stcox command).
The main effect of my variable of interest is statistically significant, but when I test the proportional hazards assumption, I find that this variable fails. Next I re-run the model with time-varying covariates (using the tvc and texp(ln(_t)) commands). When I have done this before, the time-varying covariates have usually been significant, but in this case neither the main effect or the time-varying effect are statistically significant when both are included. If I run the model again with the variable as a time-varying covariate but with no main effect, the time-varying covariate is significant.
I'm not sure what conclusion to draw from this. Given that the variable fails the proportional hazards assumption, I don't read too much into the statistically significant main effect. But does the its failure when both are included mean that the variable is just not statistically significant? Or is there any meaning to the fact that it's statistically significant if the main effect is not included?
