Sample size calculation for non-inferiority survival analysis

[Josan Rueda]

Dear list,

This is my first post here, so, my apologies in advance for the mistakes I will surely do.

I'm using Stata BE 17.0. I'm trying to reproduce the sample size calculation made by the authors in this article: Polypill Strategy in Secondary Cardiovascular Prevention, where they state they're also using Stata 17.0.

Keeping it brief, they are comparing an experimental treatment (E) to a reference (R) with a non-inferiority trial. They consider E to be non-inferior if the upper boundary of a 97.5 CI for the primary outcome HR is lower than 1.373. Once the criterion for noninferiority had been met, a test for superiority with respect to the primary outcome was performed. For the primary composite outcome, an annual event rate of 7.2% was expected in the usual-care group. They determined that a sample size of 3206 patients with a minimum 2 years of follow-up would provide 90% power to reject a finding of noninferiority and 80% power to detect a 21% relative risk reduction in the polypill group, with a two-sided alpha level of 0.05, assuming 5% loss to follow-up.

Well... using the power cox command I don't get anywhere near those 3206 patients.

This is what I ask Stata to do:

power cox, hratio(0.79) failprob(0.258) wdprob(0.05)

I'm assuming HR is (1-0.21=0.79) and the event probability is 0.258 (assuming a constant rate of events, that number comes from 0.072*2 for the R group and 2*0.0569 for the E group).

Are some of my assumptions wrong? Am I using the wrong command?

Thank you SO much for your help.

[Rich Goldstein]

I'm not sure I completely follow your description of the article but your command has nothing to do with non-inferiority; you can use the user-written artsurv for non-inferiority; it is part of the art package and be found and downloaded using -search-; did the authors say what command they used?

[Josan Rueda]

Hello Rich,

The authors don't say anything about the command they have used.

This is the exact thing they report in the New England article:

The primary composite outcome was evaluated for noninferiority, which was defined as an upper boundary of the one-sided 97.5% confidence interval of less than 1.373 for the hazard ratio. Once the criterion for noninferiority had been met, a test for superiority with respect to the primary outcome was performed. A test for superiority for the key secondary outcome would be performed only if superiority for the primary outcome was confirmed. For the primary composite outcome, an annual event rate of 7.2% was expected in the usual-care group. We determined that a sample size of 3206 patients with a minimum 2 years of follow-up would provide 90% power to reject a finding of noninferiority and 80% power to detecta 21% relative risk reduction in the polypill [i.e. experimental treatment] group, with a two-sided alpha level of 0.05, assuming 5% loss to follow-up.

What I tried to reproduce with my command is the calculation for the 80% power to detect 21% RRR with 2-sided 5% alpha and 5% loss to follow-up, which apparently should yield a result of 3206 patients.

Thank you.