Should the curve be around zero when assessing the smoothed scaled Schoenfeld residual plot for proportional hazard assumption?

Question

I'm using the smoothed scaled Schoenfeld residual plot to assess the proportional hazard assumption. I have a decent understanding of what a smoothed scaled Schoenfeld residual plot shows, but I'm still a bit confused about some details. Where exactly should the line be for assuming that the proportional hazard assumption is not violated? I previously read on Stack Exchange that I should look for an almost flat smoothed curve that doesn't deviate much from the coxph() coefficient value.

However, I've also been told that the line should be close to 0, as the test of correlation between the Schoenfeld residuals and survival time should be zero (the null hypothesis), indicating that the proportional hazard assumption is not violated. I hope someone can elaborate.

Thanks in advance!

Answer 1

Although it's called a "scaled Schoenfeld residuals plot," for each predictor variable it's really a plot of the sum of those residuals plus the (constant) log-hazard ratio reported by the model. That's explained toward the middle of this answer. The plot is often accompanied by a smoothed interpolation (loess) of those "residuals," which is what you want to be reasonably flat. Remember that for correlations you first subtract the mean from all the individual values anyway, so the constant offset due to adding in the log-hazard ratio doesn't matter. Also, newer versions of the R survival package no longer use the correlation per se in cox.zph(); it's been replaced by a score test. See this answer.