Bioequivalence and Bioavailability Forum

Dear all,

I read a bit about the power calculation methods (exact, approximation) and are wondering about some details (I couldn't find the answer already in old posts).
On slide 31 from Helmut's lecture it's written that exact methods rely on AS 243 (or AS 184). I thought the exact method stands for solving the integral defined by Owens Q function (see also this post); but AS 243 (and AS 184) are algorithms to compute cumulative probabilities of the noncentral t-distribution (aren't they?) and hence are only applicable in the case where the approximation via noncentral t-distribution is being used. So one cannot talk about using the exact method and AS 243 in one sentence. Or am I wrong here?

Also, the nQuery v7 user manual (Appendix 7-5, page 153) says that an algorithm due to Owen is used in order to calculate the power, therefore on slide 33 I don't understand why the algorithm from nQuery is "AS 184" (well, if the algorithm from Owen is exactly AS 184, then it's ok...). Coming from another point of view it's getting clear why it cannot be the algorithm of Owen (like in the row above: Diletti et al (1991)): the sample sizes for example in case of CV=0.075 from Diletti et al (1991) and nQuery Advisor 7 do not match. So what about the user manual...?

Another thing is: AS 184 is older than AS 243, but is it worse? For example if the true ratio=1, CV=0.075 and n=4 (see also this post) the exact method from PowerTOST gives a power of 0.7290143. nQuery 7 (see the table in the post just mentioned) gives 71.559% whereas FARTSSIE 1.6 (with AS 243) gives 66.674%. The result from nQuery is closer to the "exact" result, although it uses an older algorithm.

Thank you in advance for all your thoughts on that.
-Ben

PS
Dear d_labes, while playing around with PowerTOST I saw the following happen:
> sampleN.TOST(theta0=1, CV=0.075, targetpower=0.6, method="noncentral", details=FALSE)

+++++++++++ Equivalence test - TOST +++++++++++
            Sample size estimation
-----------------------------------------------
Study design:  2x2 crossover
log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.6
BE margins        = 0.8 ... 1.25
Null (true) ratio = 1,  CV = 0.075
4   0.666742

Sample size (total)
 n     power
4   0.666742

Approximate power calculation with
non-central t-distribution.

There is this extra line (shown in red) stating the sample size and power (for all methods and details=FALSE). I guess this is just a bug...