# Re: st: equivalence trial power calculation

 From Constantine Daskalakis <[email protected]> To [email protected] Subject Re: st: equivalence trial power calculation Date Tue, 07 Oct 2003 20:23:32 -0400

```At 04:38 PM 10/7/2003, you wrote:
```
```Dear list

Using Stata 8.1

I'm unsure on how to calculate the required sample for the following trial,

We are planning to do a 2 year equivalence trial.The current standard of
treatment has a 2 year failure rate of 7%: In our trial of a new drug, the
treatments will be considered equivalent if the 95% confidence interval are
within the bound of -12% to 12%, which we believe is the  the largest
difference that would be considered clinically acceptable.
```
First off, it would seem that what is appropriate here is a non-inferiority setup (1-sided) rather than (bio)equivalence (2-sided). If the new drug is much much better, that's good and acceptable, no? Why would you want to bound the efficacy difference from both sides? It's only when the new drug is worse that you might need to impose bounds. It comes down to what exactly you want to prove:

(i) equivalence -- TO PROVE that drug and standard treatment have "similar" failure probabilities; but
(ii) non-inferiority -- TO PROVE that drug is "at least as good as" ("no worse than") standard treatment.

If the difference in true failure probabilities is p = p{drug} - p{standard}, then

(i)
H0: |p| >= 0.12
H1: |p| < 0.12

(ii)
H0: p >= 0.12
H1: p < 0.12

In both cases, the "delta" (0.12 here) determines what is "similar" or "as good as".

You need equivalence power calculations for (i) but the usual 1-sided superiority/inferiority power calculations for (ii).

In (i), you give up the opportunity to infer anything about differences (ie, if one treatment is much different than the other, you'll still simply infer that they are not "similar" enough -- end of story).

In (ii), you give up the opportunity to infer that the drug is "better" than standard treatment if that turns out to be the case (ie, you'll simply have to say that the drug is not worse than treatment). If this "better" kind of statement is of interest, then the usual 2-sided superiority/inferiority setup should be used instead.

That said, I don't even see how the 12% bound for the difference is reasonable for the one side (drug better). Bounds refer to the TRUE parameter values. If the hypothesized failure probability for standard treatment is 7%, the biggest difference in one direction can only be 7% (ie, 0% failure for drug, 7% failure for standard treatment, p = -7%). On the other hand, the 12% bound for the other side seems huge (ie, 19% failure for the drug vs. 7% failure for standard tretament, an almost 3-fold increase!). I'll take your word that this would be an "acceptable" drug... I suppose if the disease is not serious but the standard treatment has serious side effects (but the new drug doesn't), it could be ok...

```any suggestions?

Jannik Helweg-Larsen
```

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