# Interpretation of effect of exp(coeff) Cox PH on survival time

I performed a Cox PH estimation of an experiment with a treatment and control group. Survival time is measured in days. The exponentiated coefficient for the treatment group is 1.105. If I understand correctly, this means that a person in the treatment group has a 10.5% higher probability of not surviving at any given time than a person in the control group, all other variables remaining the same. However, I'm trying to quantify this effect in a number of days shortened.

1. Is it correct to calculate this as 'for each in individual in the treatment group the expected survival days are 10.5% shorter than if they had been in the control group'?
2. And if so, would it be sufficient to multiply their number of survival days by 1.105 to simulate their number of survival days had they been in the control group?

$\exp(\beta_{\text{trt}})$ must be interpreted as a hazard ratio.

As a reminder, the hazard gives the instantaneous rate at which events occur in time for susceptible patients.

$\exp(\beta_{\text{trt}}) = 1.105$ means that the hazard of the event under treatment is 10.5% higher then under control.

Proposal 1: To answer your question, you can calculate the survival rate at 30 days (for example) in the control group and see how many days are needed in the treatment group to achieve the same survival rate.

Proposal 2: Compare the median survival times.

• Thanks for you suggestions. I'll try your first proposal. The second one I found risky, because the two groups were not randomly selected, there are significant differences in for example the % of females in control vs treatment. What I tried instead was taking the median of the treatment group (10 days) and dividing that by 1.105 to get the treatment impact on the median number of days. – DaReal Mar 14 '17 at 10:03
• You should add gender as a covariate. Then assessments are made conditional on the covariates. Happy that it helps. – ocram Mar 14 '17 at 10:19
• I added it as a covariate to Cox PH, but that doesn't affect the original 'within group' medians right? So then the question would be what a clean median would be after correcting for covariates, where I can single out the effect of the treatment group on the median survival days. – DaReal Mar 14 '17 at 11:02