# How to calculate number of events in each treatment arm given hazard ratio and CI?

I have a question regarding calculating event numbers for survival analysis. I have a trial where the hazard ratio of treatment arm compared to control arm is 0.75 (95% CI: 0.59-0.96). I know the number of patients enrolled in arm A and Arm B were 355, respectively. I was trying to calculate the number of events in both arm. This is what I did. Could you please tell me if this is right or wrong? I would appreciate any feedback and guidance. Thanks in advance.

Fsk = (exp(0.75)-1)/exp(0.75) = 0.527.
Number of events in control arm = qbinom(0.527, n = 355, p=0.5).
SE_ln[HR] = (log(0.96) - log(0.59)) / (2 * qnorm(1 - 0.05/2)).
Total no. of events = 4/SE_ln[HR].
Number of events in treatment arm = Total number of events - Number of events in control arm

1 Like

Look at the R `Hmisc` package `spower` function which helps with these kinds of problems. Also `cpower` .

Hi! In your example Number of events in control arm = 178, SE_ln[HR] = 0.1241887, Total no. of events = 4/0.1241887 = 32 (why 4?), so Number of events in treatment arm = 32 - 178 - it is negative value. Something wrong?!