Representation of a spline regression - it is better to plot y axis in log scale?

Question

I have a quick (perhaps very naive) question here.

Suppose I have a Cox Regression model in which I have modeled a spline curve on a Predcitor. I want to plot the results of this regression (i.e., predicted Hazard Ratios across the Predictor spectrum).

I have to option:

1. to plot the y-axis in linear scale (as following):

2. to transform the y-axis in log-scale (as following):

From a theoretical point of view, and assuming both are suitable option, which is better? On one side, I am thinking that the log scale may be "more right" than the linear one (as one would do with forest plot), but I would also like to listen to a more expert opinion.

Answer 1

In terms of the y-axis scaling, you can choose whichever will be more useful to your audience. The log transformation is just re-expressing the hazard ratios into something like the scale of the original Cox model regression coefficients, which were exponentiated to get the hazard ratios in the first place. There's no theoretical "best" way to proceed on that, so long as you clearly explain the transformation in the figure legend.

In either case you might, however, make a different choice of the reference level for the y axis. All of your displayed hazard ratios are less than 1, so it's hard to gauge the relative hazard between a typical predictor value, say 50, and a more extreme value like 35 or 65. It's often useful to express these hazard ratios in a way that the mean or the median of the predictor has a reference hazard ratio of 1. Then other predictor values can be compared to it more directly.