Hi, first of all, I want to thank all active members here, I found many useful tips and insights here, beside the fact that I learned a lot.
Now its time to ask a maybe „easy“ question, which came up, while I was analysing survival data.
The study is not that complex, I am using a ph cox model with 5 parameters and ph assumption is fulfilled.
Now my results showed, that 1 variable has a HR of 1.0003 (CI: 1.00011.0008). Corresponding to the CI it is significant.
The parameter is continuous and has the 2nd highest Chi2 in the model. Beside this, the histogram shows, that it is highly rightskewed, although I already logtransformed it cause of not normal distributed residuals.
Now my question: How do I interpret and report a HR so close to 1? (especially in this logtransformed case)
Could the restricted mean survival time (RMST) maybe be a „better“ measurement?
1 Like
I’m certain that is a meaningless hazard ratio. Were X=male/female, antilogging \hat{\beta} to get an HR would have been OK. I’ll bet that the HR is the antilog of a coefficient for a predictor whose range is very, very different from 01. That’s why I default to using interquartilerange HRs in the R rms
package.
1 Like
Well I get it, and you are completely right.
The interpretation in the way for example 10 increase in the variable means xhazardincrease would be definitely better than the one with 1 increase.
And meanwhile I also understood that it is the potency of hazard ratio in this computation.
But now I have two more question:

Is there any solution, how one can implement this interquartilerange HR into the use of ggforest?

Is there a way to transform the HR back to interpret it on the original scale of the logarithmized variable?
Thank you already for your time!
The R rms
summary
function and its plot method gives you a kind of forest plot with one axis per predictor showing a hazard ratio. You can probably program a transformation of the summary
(full name summary.rms
) function to send data to ggforest
with some work.
It is best to present HR, but using a log scale for tick marks. plot(summary(...), antilog=TRUE)
gives you that.
1 Like
Given how small this CI is, I suspect it’s artifactual. What is the sample size here? I once came across a case where misapplication of a clustered variance estimator resulted in an incredibly small CI.
I wouldn’t call it artifactual but would rather call it an inappropriate use of a [0,1] scale for a covariate in computing the HR.
1 Like
The sample size is 2490. 3 of the parameters in the model are categorical, then I have age as continuous and the one with the small hazard ratio (as a logarithmized one).
What is the range of values for the predictor on the logarithmized scale? You mentioned it was still strongly rightskewed.
1 Like
So you mean that a 0 vs 1 contrast was effectively infinitesimal, relative to the whole range of the covariate?
I do not know what you are measuring. However, check whether the scale is appropriate as the HR is per 1 unit increase in your scale. E.g. if your variable is lung volume measured in millilitres your HR and CI will be quite different compared to a model with lung volume measured in litres.