Bioequivalence and Bioavailability Forum

Dear Helmut,

❝ ...The documentation of PASS refers to Julious¹ (see esp. pp1961–2). Given that, the approxi­ma­tion by the noncentral t-distribution is used.

IMHO here you err. They also refer to Phillips. And this would mean Owen's Q or some sort of.
Since non-central t is a very good approximation in most not-extrem cases it's not that easy to find an example for a numeric inspection.
But remember our Captn's extremal question: power in a 2,2,2-BE trial at N=6, CV=65% and T/R=95% which lead to such famous R-implementations like "EatMyShorts" and "Apfelstrudel" . And was also the jump start of PowerTOST.

Method                power
PowerTOST exact       0.00162
PowerTOST nct         0       (forced to zero, naively calculated negative)
PowerTOST shifted t   0       (forced to zero)
PASS 12               0.00162 

On the other hand PASS uses in the module for "Higher-Order Cross-Over Design" the crude shifted central t-approximation as described in the help pages, although they refer also to Phillips, but later to Chow and Liu (2000?, 1999)^*. Numerical inspection gives not so good agreement with f.i. their example 1:
Design = 2x2x3, theta0=0.96, CV=0.4
                PowerTOST
n    PASS12  shifted t  exact   
10   0       0         0.02852
20   0.3051  0.30603   0.31264 
30   0.5858  0.58615   0.58895
40   0.7483  0.74840   0.75025 
...
The reason of the not so good numerical agreement is the different degrees of freedom. PASS uses a model with carry-over included exactly as described in the literature cited below^* which reduces the df by 1 compared to PowerTOST.

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^*Chow, S.C. and Liu, J.P.
Design and Analysis of Bioavailability and Bioequivalence Studies.
Marcel Dekker. New York 1999

Chen, K.W.; Chow, S.C.; and Li, G.
A Note on Sample Size Determination for Bioequivalence Studies with Higher-Order Crossover Designs.
J. Pharmacokinetics and Biopharmaceutics, Volume 25, No. 6, pages 753-765. 1997