I fitted a Cox proportional hazard model and checked the proportionality assumption using R's cox.zph function, with the following output:
chisq df p
Var1 0.0324 1 0.857
Var2 0.1972 1 0.657
log(var3) 4.1552 1 0.042
Var4 4.6903 1 0.030
Var5 0.6472 1 0.421
Var6 1.2257 1 0.268
Var7 4.9311 1 0.026
Var8 0.3684 1 0.544
Var9 2.0905 1 0.148
Var10 0.0319 1 0.858
Var11 4.0771 1 0.043
GLOBAL 14.2625 11 0.219
In the study, Variable 1 and 2 are the ones I'm actually interested in, whereas the others are only controls. As you can see, the PH assumptions seems to hold for these two covariates, but most prominently not for Var3. Can I still interpret my findings on Var1 and 2 and talking about Var3 add, that this is displays the average effect over the study-time? Or will my coefficients for Var1 and 2 be biased/incorrect?
Thanks in advance!
Yes, the results will be incorrect. Stratify by taking Var3 into account and use the proportional hazards model in each stratum for the other covariates. Check this paper whether relevant for you to back up your claims: https://jamanetwork.com/journals/jama/article-abstract/2763185
Obviously, there is time interaction with some of your covariates (control variables). Their interactions with time also need to be added to the model for an appropriate interpretation. Also, since there are quite a few variables in your model, the analysis might be subject to multiple comparisons bias that would require P value significance cutoff adjustment with methods such as false discover rate (FDR) adjustment.
If what you are interested in is the effect (hazard ratio) for var 1 and var 2 while adjusting for others (covariates) then you are fine. You don't need every covariate to also fulfill the assumption.
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