How can I communicate hazard ratios from log-transformed biomarkers in a clinically interpretable way?

I’m not sure if my understanding is correct. Log transformation is often used when the original scale changes proportionally rather than numerically. It flattens the multiplicative curve into an additive straight line. If you’re looking for an interpretation of the log transformed value as if it were an additive continuous value, the simple approach is to use a base of 2 instead of a natural number. This calculates the hazard ratio as the risk changes when the original scale doubles. For example, a hazard ratio of 1.2 means the risk change when the original scale increases from 10 to 20 (from x to x * 2). This is commonly used when antibody titers are significantly left-skewed and have a very large range. If the variable’s range isn’t very large, you can use the ln(1+ x) power of the hazard ratio. For example, if x is 10%, this means the change in hazard ratio when the original scale increases by 10%. In other words, it converts the additive interpretation of the hazard ratio into an interpretation based on the proportional change of the original scale. This applies if the original scale changes proportionally. If not, I guess a nonlinear RCS might be better.