Bioequivalence and Bioavailability Forum

Hi Dan,

❝ There are some People who recommend to use a very small alpha in the first stage and a large alpha in the next.

❝

❝ Stage I:  0.001 leading to 99.8% CI

❝ Stage II: 0.049 leading to 90.2% CI

Your values are according to Haybittle/Peto. However, like Pocock’s “magic 0.0294” these numbers were derived for superiority testing in group sequential designs (normal distributed data, parallel groups). I know some companies routinely applying this “method” but obviously never ever assessed the type I error in the BE setting (equivalence, crossover). The GL is clear:

… appropriate steps must be taken to preserve the overall type I error of the experiment …
… the choice of how much alpha to spend at the interim analysis is at the company’s discretion.

“is at the company’s discretion” should read “has to be justified by the applicant” since – with one exception* – nothing is pub­lished so far! 0.001/0.049 may lead to unacceptable inflation of the TIE. Example (location of the maxi­mum TIE in the assessed grid of n₁ 12–72, CV 10–80%):

library(Power2Stage)
power.2stage(method="B", alpha=c(0.001, 0.049), n1=12, GMR=0.95,
  CV=0.22, targetpower=0.8, theta0=1.25, nsims=1e6)

# Method B: alpha (s1/s2) = 0.001 0.049
# Target power in power monitoring and sample size est. = 0.8
# BE margins = 0.8 ... 1.25
# CV = 0.22; n(stage 1)= 12; GMR = 0.95
# GMR = 0.95 and mse of stage 1 in sample size est. used
# Futility criterion Nmax = Inf

# 1e+06 sims at theta0 = 1.25 (p(BE)='alpha').
# p(BE)    = 0.058031

In our pile of half-baked manuscripts we explored adjusted alphas which maintain the TIE. For a “type 1” TSD, GMR 0.95, target power 80%, α₁ 0.001 we found an adjusted α₂ of 0.0413 suitable to maintain the patient’s risk:

library(Power2Stage)
power.2stage(method="B", alpha=c(0.001, 0.0413), n1=12, GMR=0.95,
  CV=0.22, targetpower=0.8, theta0=1.25, nsims=1e6)

# Method B: alpha (s1/s2) = 0.001 0.0413
# Target power in power monitoring and sample size est. = 0.8
# BE margins = 0.8 ... 1.25
# CV = 0.22; n(stage 1)= 12; GMR = 0.95
# GMR = 0.95 and mse of stage 1 in sample size est. used
# Futility criterion Nmax = Inf

# 1e+06 sims at theta0 = 1.25 (p(BE)='alpha').
# p(BE)    = 0.049939

Zheng’s 0.01/0.04 at the location of maximum inflation:

library(Power2Stage)
power.2stage(method="B", alpha=c(0.01, 0.04), n1=12, GMR=0.95,
  CV=0.24, targetpower=0.8, theta0=1.25, nsims=1e6)

Method B: alpha (s1/s2) = 0.01 0.04
Target power in power monitoring and sample size est. = 0.8
BE margins = 0.8 ... 1.25
CV = 0.24; n(stage 1)= 12; GMR = 0.95
GMR = 0.95 and mse of stage 1 in sample size est. used
Futility criterion Nmax = Inf

1e+06 sims at theta0 = 1.25 (p(BE)='alpha').
p(BE)    = 0.048782

❝ Chance of approval in the first go is low, but you will have a comfortable CI in the second stage.

Correct. If one does not want to take the chance to show BE already in the first stage and has enough time to almost always proceed to the second stage, why not? The first stage serves only to get an estimate of the CV and can be seen as an “internal pilot study”. Compared to published methods with an equal split of alphas the sample size penalty is lower.

❝ However, as I learned from our famous captain, it is almost impossible to argue that it makes a practical difference.

Ahoy! Difference to what?

❝ What is your experience?

See above for the thoughtless application of 0.001/0.049 which leads to an inflated TIE. Sooner or later the BSWP (which has TSDs on their work-plan for 2015) will realize this problem. Consequences? Re­cal­cu­late studies with a wider CI? What if a study fails with a 91.74% CI which passed with the reported 90.20% CI?

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• Zheng C, Zhao L, Wang J. Modifications of sequential designs in bioequivalence trials. Pharm Stat. 2015;14(3):180–8. doi:10.1002/pst.1672.