How to calculated the sample size for three groups (or >2 groups) by log-rank test in SAS

[Dennisky]

We plan to conduct a study for comparing the survival rate between three different types of surgery for total knee arthroplasty. Thus, the sample size for the study should be estimated.

We could calculate the sample size for two groups by log-rank test in SAS as follow:

%let pt=0.65;
%let pc=0.40;
%let alpha=0.05;
%let beta=0.15;
data aa;
theta=log10(1-&pt)/log10(1-&pc);
thetal=round(theta,0.001);
e=((theta+1)/(theta-1))**2*(probit(1-&alpha/2)+probit(1-&beta))**2;
el=int(e)+1;
n=2/(&pt+&pc)*e;
nl=int(n)+1;
file print;
run;

But, how to calculated  the sample size for three groups (or >2 groups) by log-rank test?

Thanks!

[Norman21 · Accepted solution]

I suppose it depends on your hypothesis - all three groups are the same, or all three groups are different, or one group is different from the other two...?

The following describes running simulations, you might find this helpful:

https://www.lexjansen.com/pharmasug/2004/StatisticsPharmacokinetics/SP08.pdf

Also this, especially the example:

https://onlinelibrary.wiley.com/doi/pdf/10.1002/sim.4780142010

[Dennisky]

Thank you very much for your generous help!
Pairwise multiple comparisons test the difference between each pair.
Could we perform multiple pairwise log-rank tests for three groups (3 pairs) and calculated the sample size for each pair ( we set our significance level α at 0.017（0.05/3=0.017), β=0.2) ) ? Then we choose the group with the largest sample size, which is the sample size required in each group ?
Thanks!