Bioequivalence and Bioavailability Forum

Hi John John,

❝ We have worked with CI of 94.12 and alpha 0.0294

Which software did you use? The phrase

Power at 20%

smells of an outdated version of WinNonlin, which reports power for the FDA’s prehistoric “80/20 Rule” (i.e., power to detect a difference in least square means equal to 20% of the reference least squares mean). Since Phoenix/WinNonlin 6.4 additionally the much more relevant “Power_TOST” is reported. However, even if you have v6.4 you cannot specify a GMR of 0.95 (as required by Mme Potvin). The reported value is always given for the observed GMR. In your case it would be ex­tre­me­ly low for C_max (⇒ 0.043) and should be calculated for a GMR of 0.95 (⇒ 0.377) – as pointed out by Detlew above.

Now for the nasty part. I recalculated your CVs and PEs from the CIs in order to increase precision. Your data make clear that C_max is the crucial point (higher CV, worse PE).

library(PowerTOST)
n  <- 36
lo <- 0.70162
hi <- 0.94529
CV <- signif(CI2CV(lower=lo, upper=hi, n=n, design="2x2x2"), 5)
PE <- sqrt(lo*hi)
sampleN.TOST(alpha=0.0294, CV=CV, theta0=0.95, targetpower=0.8, design="2x2x2")

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

alpha = 0.0294, target power = 0.8
BE margins        = 0.8 ... 1.25
Null (true) ratio = 0.95,  CV = 0.38744

Sample size (total)
 n     power
74   0.802127


Potvin B (which you stated in the protocol) would mandate to initiate the second stage with 74 – 36 = 38 subjects. But: Does it make sense to still assume a GMR of 0.95 when you have observed 0.8144 (‼) in stage 1? That’s one of the drawbacks of TSDs. Generally they are not fully adaptive (i.e., re-estimate the sample size only based on the CV, not the GMR). Let’s play the devil’s ad­vo­cate and assume that both the CV and GMR in the final analysis (74 subjects) will be exactly what we observed in stage 1. Which power can we expect?

power.TOST(alpha=0.0294, CV=CV, n=74, theta0=PE, design="2x2x2")
[1] 0.05443928

Oops! Not surprising since the PE is that close to the lower limit of the acceptance range. Which sample size would we really need?

sampleN.TOST(alpha=0.0294, CV=CV, theta0=PE, targetpower=0.8, design="2x2x2")

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

alpha = 0.0294, target power = 0.8
BE margins        = 0.8 ... 1.25
Null (true) ratio = 0.814392,  CV = 0.38744

Sample size (total)
 n     power
6566   0.800031

I’m sure that your protocol states somewhere (not in the statistical section) that the study might be stopped by the sponsor. Think twice whether it makes sense to dose additional subjects given the information you have from the first stage (i.e., the keep-one’s-fingers-crossed approach).

In the future consider to add a futility criterion for early stopping and don’t perform TSDs if you are unsure about the GMR. Sorry, but I have to quote myself¹

The entire arsenal of obtaining a reliable ‘educated guess’ (e.g. dissolution similarity for immediate release formulations of biopharmaceutics classification system class I/III drugs, established in vivo-in vitro correlation for controlled release products) should be used as well. If no reliable estimate can be derived, a—sufficiently large—pilot study should be performed. Subsequently, a TSD would still support dealing with the uncertain CV.

Be aware that futility rules deteriorate power. This was shown by Fuglsang² for an upper total sample size, but is valid for any other rule as well. It would make sense to perform own simulations to get an idea about the impact of GMRs substantially deviating from 1.

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References:
1. Schütz H. Two-stage designs in bioequivalence trials. Eur J Clin Pharmacol. 2015;71(3):271-81. doi:10.1007/s00228-015-1806-2
   
2. Fuglsang A. Futility rules in bioequivalence trials with sequential designs. AAPS J. 2014;16(1):79–82. doi:10.1208/s12248-013-9540-0