Goodness of fit – Testing Cox proportional hazard assumption in R I am performing survival analysis on credit data.  I created a simple model with using interest rate:
cox <- coxph(Surv(periods,charged_off) ~ int_rate, data=notes)
I assumed that int_rate was a time-independent variable, but the following test rejects HA:
> cox.zph(cox)
            rho chisq        p
int_rate 0.0446  14.2 0.000169

Same result for other variables such as loan amount:
> cox <- coxph(Surv(periods,charged_off) ~ int_rate + loan_amnt, data=notes)
> cox.zph(cox)
             rho chisq        p
int_rate  0.0364  9.31 2.28e-03
loan_amnt 0.0317  8.84 2.95e-03
GLOBAL        NA 26.28 1.97e-06

Plot for int_rate:

Why would these covariates be considered time dependent?  Am I doing something wrong? Thanks.  
 A: The distinction one has to make is between time-varying covariate and a covariate whose coefficient changes over time. Both violate the proportionality assumption, but do not have to be drawbacks. Rather, they can and are often theoretically meaningful (see Singer & Willett's book on Longitudinal Data Analysis and their 1991 paper in Psychological Bulletin). They just have to be included in the model.
In your plot, it looks like the coefficient for that time-invariant predictor changes over time (becomes less strong) and therefore violates the proportionality assumption. Including an interaction with that covariate and time would solve things and get around the proportionality assumption. Again, Singer and Willett's book is a classic--and highly accessible. The companion website also has code and examples for software implementation.
A: The cox.zph function is measuring the overall effects of relaxing the assumption that the effect is constant in time. It telling you that the effect is probably not constant, but it's not telling you much more.
The plot is giving you further information about the time course and shows that the effect is maximal at intermediate values of time. I'm guessing that the outcome is loan default and that you are seeing a result that implies the probability of loan default is highest when the interest rate was high at loan origination and during intervals when the loan has been on the books for between 1 and 3 years. The impact of the interest rate then tapers off. This all seems perfectly sensible.
For further information on how the authors of the survival package use cox.zph, I recommend Chapter 6:"Testing Proportional Hazards" in their book, "Modeling Survival Data". Your result resembles their illustration of the time dependence of the Karnofsky performance measure. They consider various options for using a transformed time scale.
I wonder if you might have additional information such as the time-dependent covariate which would be the interest rates in periods after the loan origination? 
