What should be reported as Hazard Ratio in Kaplan Meier curve?

Question

[Raheleh]

Hello all, I did survival analysis for my data and used log rank to test if there is significant difference between the high-risk and low-risk group. This my script and image:

k <- ggsurvplot(survfit(recsurv~T1_signature, data = MSKCC),
           data = MSKCC,
           risk.table = TRUE,
           pval = TRUE,
           conf.int = TRUE,
           ggtheme = theme_minimal(),
           risk.table.y.text.col = TRUE,
           risk.table.y.text = FALSE)

I want to add the HR in the graph as well. I did cox proportional hazards in R. This is the script:

hr <- coxph(recsurv~T1_signature, data = MSKCC)
summary(hr)

and this is the result:

Call:
coxph(formula = recsurv ~ T1_signature, data = MSKCC)

  n= 159, number of events= 6 

                    coef exp(coef) se(coef)      z Pr(>|z|)    
T1_signatureLow -2.89660   0.05521  0.87006 -3.329 0.000871 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

                exp(coef) exp(-coef) lower .95 upper .95
T1_signatureLow   0.05521      18.11   0.01003    0.3038

Concordance= 0.794  (se = 0.09 )
Likelihood ratio test= 11.17  on 1 df,   p=8e-04
Wald test            = 11.08  on 1 df,   p=9e-04
Score (logrank) test = 21.08  on 1 df,   p=4e-06

As far as I found out, for HR I need to subtract the amount of exp(coef) from 1 (1 – 0.05). In this case HR will be 0.95.

It means that the hazar ratio in my low-risk group decreased by 95%. Am I right? I want to use annotate to add HR in my plot. I am not sure should I report it as 0.05 0r 0.95?

I really appreciate any help!

Answer 1

[discombobulated]

Hi. Yes you are correct but you need to be careful in how you explain it. Your hazard ratio is 0.05 (ie 0.05:1) but you reduce your hazard by a factor of 95% (ie your hazard ratio as such hasn't decreased). It is only a nuance but it changes the meaning. I suggest reporting the hazard ratio (HR = 0.05 (95% C.I 0.01, 0.30)) in the graph and expand on this reporting a hazard reduction of 95% in text. also check your rounding :)

Answer 2

[huynguyen96.dnu]

Sorry, but I have a question on the interpretation of HR value. According to your above result, High is Reference and HR of Low is 0.06. So I will explain that Low is significantly associated with better outcome than High? Am I right?

Answer 3

[discombobulated]

looking at your output, low has been coded as 1 (your outcome) and high as 0 (the reference). So you are correct that the hazard ratio is reported for Low - i.e HR of Low is 0.06. As the HR is less than 1, Low has a hazard reduction. While it is often reported as risk, technically this is not correct. There are several papers on interpretation of survival analysis which may help you formulate the interpretation of your results. Have a look at these papers written for clinicians: https://journals.lww.com/anesthesia-analgesia/Fulltext/2018/09000/Survival_Analysis_and_Interpretation_of.32.aspx https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5388384/