Bioequivalence and Bioavailability Forum

Dear Oiinkie, dear Helmut,

❝ ... For a two-stage crossover design both the CRO and I have calculated sample sizes with the following parameters:

❝ alpha = 0.049

❝ PE = 0.8969

❝ CV = 0.1149

❝ ...

❝ With both PowerTOST and FARTSSIE (and even StudySize) I come to a sample size of 16 (power=0.8474), while the CRO gives a sample size of 14 (power=0.820).

❝ According to the file I received from the CRO, the Power procedure (Equivalence Test for Mean Ratio) was used with distribution set as lognormal and method as exact.

Which statement (module) in Proc Power they (your CRO) really had used? twosamplemeans or pairedmeans?

Both are not correct! twosamplemeans is for a parallel group design and pairedmeans for a "paired design", i.e. a study with the paired t-test as the basic statistical method. The latter can be used for a 2x2 crossover but only if it is assumed that no period effects occur.
This is described in one of the examples (Example 67.3 Simple AB/BA Crossover Designs) in the help file of Proc Power.

Seems to me your CRO has used the first because only then I obtain (within SAS Proc Power) their figures for sample size and power. You can check this with PowerTOST if you choose design="parallel".
> sampleN.TOST(alpha=0.049,CV=0.1149,theta0=0.8969,design="parallel")

+++++++++++ Equivalence test - TOST +++++++++++
            Sample size estimation
-----------------------------------------------
Study design:  2 parallel groups
log-transformed data (multiplicative model)

alpha = 0.049, target power = 0.8
BE margins        = 0.8 ... 1.25
Null (true) ratio = 0.8969,  CV = 0.1149

Sample size
(n is sample size per group)
 n     power
14   0.820209
But see my emphasis!

The difference of the paired means case to the procedure taking into account the period effects lies mainly in the degrees of freedom, namely n-1 for the "paired" design compared to n-2 for the 2x2 cross-over. This will give you different results between PowerTOST (with design="2x2") and SAS Proc Power with pairedmeans. Regarding the sample size they usually will be small (around +2 subjects), but they exists and can be higher in extrem cases.
> sampleN.TOST(alpha=0.049,CV=0.1149,theta0=0.8969,design="paired")

+++++++++++ Equivalence test - TOST +++++++++++
            Sample size estimation
-----------------------------------------------
Study design:  paired values
log-transformed data (multiplicative model)

alpha = 0.049, target power = 0.8
BE margins        = 0.8 ... 1.25
Null (true) ratio = 0.8969,  CV = 0.1149

Sample size
 n     power
14   0.800631
Don't try this by your own. It's my un-validated extended code for PowerTOST . All you out there: Drop me an E-mail if this is helpful for you and I will incorporate the code in the next release. Guaranteed.
The above result is identical to SAS Proc Power, statement pairedmeans.

Regarding the statement:

❝ but they want to stick with SAS (because “they have always used it)”

I can only add: There was no possibility within before version 9.1 (was rolled out around 2003 I think) for sample size estimation for a 2x2 cross-over beside the ugly Analyst application (had to be extra licensed, i.e. extra money) which was also only able to handle the paired values case and the parallel group design and used the undocumented OwenQ function.
Less than 10 years SAS experience is not "always". It takes some time longer to know the , definitely!

@Helmut: OwenQ is up to now not findable in the function dictionary of SAS 9.2 TS2M0, which I have to use (released last year if I remember correctly). They call Proc Power meanwhile production .

BTW: Oiinkie, where does your 'unusual' alpha came from? Two-stage design with nominal alpha's according to Haybittle-Peto? If yes, how do you satisfy the use of them?