Bioequivalence and Bioavailability Forum

Hi John!

❝ I back-computed the intra-CV from the single dose interaction study and it was 13-14%. I decided to go with 20% CV as the basis for my sample size estimation. I hope that's not an overkill...

You can take the uncertainty of the CVs into account (smaller for larger studies). Play around in Detlew’s PowerTOST-package (T/R 0.95, 90% power, CV 14% derived from studies with 12 and 24 subjects):

require(PowerTOST)
expsampleN.TOST(targetpower=0.9, CV=0.14, dfCV=12-2, design="2x2")
++++++++ Equivalence test - TOST ++++++++
   Sample size est. with uncertain CV
-----------------------------------------
Study design:  2x2 crossover
log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.9
BE margins        = 0.8 ... 1.25
Null (true) ratio = 0.95
CV                 = 0.14 with 10 df
one-sided upper CL = 0.2247103 (level = 95%)

Sample size (ntotal)
 n    exp. power
18   0.921907

expsampleN.TOST(targetpower=0.9, CV=0.14, dfCV=24-2, design="2x2")
++++++++ Equivalence test - TOST ++++++++
   Sample size est. with uncertain CV
-----------------------------------------
Study design:  2x2 crossover
log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.9
BE margins        = 0.8 ... 1.25
Null (true) ratio = 0.95
CV                 = 0.14 with 22 df
one-sided upper CL = 0.1876612 (level = 95%)

Sample size (ntotal)
 n    exp. power
16   0.931383

So n=20 is reasonable even if the CV was obtained in a small study.

❝ Another question, for truncated AUC0-72 hours, what is your experience in terms of setting the limit for 72 hr blood draw time deviation?

Personally I use the estimated AUC₇₂ whatever the actual sampling time was.

❝ The drug has a half-life of 20-30 hours. The clinic allows the subjects to return for the 72 hour return blood draw with a +4 hour time limit (i.e, if they come back after 76 hours then they will not collect it).

Great for the CRO. You loose power (exclude the subject), the study is more likely to fail, the CRO will perform another study with a larger sample size. Bad idea IMHO.

❝ Is that a bit too late?

Yes; especially if we use the measured C_t. Example: A -100, B 100, t_½,α 1 h, t_½,β 25 h, T/R 100%, simple trapezoidal.
  t       C
 0        BQL
 0.5     27.91
 1       47.27
 2       69.61
 3       79.52
 4       83.25
 5       83.93
 6       83.11
 9       77.72
12       71.67
16       64.17
24       51.41
36       36.86
48       26.43
72       13.58
AUC₇₂ 2996

Let’s assume that after the reference the last sample is drawn at 72 h and after the test at 73 h. AUC₇₃ is 3011, T/R 100.5% – acceptable bias. If the last sample is drawn at 76 h, AUC₇₆ is 3056, T/R 102.0%.
If you are able to estimate λ_z you can use the estimated concentration at 72 h:

Ĉ₇₂ = C_tz · ℯ^{–λ_z(72–t_z)}

From the last three concentrations we get half lives of 24.99 h and 25.00 h, pretty close to the theoretical 25 h. Estimated 72 h-concentrations are 13.58 (last sample 73 h) and 13.59 (last sample 76 h) leading to estimated AUC₇₂ of 2996 for both schedules. T/R 100% – bingo.

❝ I would either set the limit to 1 hour or keep the subject for 72 hours in house.

Better (see above). I would prefer the latter – especially if you don’t want to deal with estimated values.