Bioequivalence and Bioavailability Forum

Dear all,

the usual suspects have layed another egg:

Jialin Xu, Charles Audet, Charles E. DiLiberti, Walter W. Hauck, Timothy H Montague, Alan F. Parr, Diane Potvin and Donald J. Schuirmann
"Optimal adaptive sequential designs for crossover bioequivalence studies"
Pharm Stat. 2015 Nov 5. doi: 10.1002/pst.1721. Epub ahead of print

First impression:
Decision tree of Method E = identical to method B with arbitrary alphas + futility check
Decision tree of Method F = identical to method C + futility check

The futility check is based on the 90% CI of the point estimate outside a futility range.

There is a maximum sample size max.n in the sense that if the sample size adaption leads to n(total) > max.n then max.n is used as n(total). This differs from a futility criterion Nmax.

What they have done with 'optimizing' alpha1, alpha2, futility range and n1 is beyond my intellectual reach.

Their claim that they have chosen from designs with TIE controlled at <=0.05 and power > 80% has to be checked. Especially with max.n = 42 for the low CV range 10-30% I don't believe in power > 80%:

library(Power2Stage)
power.2stage.fC(method="B",alpha=c(0.0249,0.0363), n1=18, CV=0.3, max.n=42, fCrit="CI", fClower=0.9374)
TSD with 2x2 crossover
Method B: alpha (s1/s2) = 0.0249 0.0363
Interim power monitoring step included
Target power in power monitoring and sample size est. = 0.8
Power calculation via non-central t approx.
CV1 and GMR = 0.95 in sample size est. used
Maximum sample size max.n = 42
Futility criterion 90% CI outside 0.9374 ... 1.06678
BE acceptance range = 0.8 ... 1.25

CV = 0.3; n(stage 1) = 18; GMR= 0.95

1e+05 sims at theta0 = 0.95 (p(BE)='power').
p(BE)    = 0.75239
p(BE) s1 = 0.1785
Studies in stage 2 = 77.79%

Distribution of n(total)
- mean (range) = 34.3 (18 ... 42)
- percentiles
 5% 50% 95%
 18  42  42


BTW: This result was verified independently by our Ol'Captain using compiled C-code.