Bioequivalence and Bioavailability Forum

Hi MGR,

❝ Is this type of analysis can be done by WinNonlin 5.2 or 6.3?

WinNonlin 5.2 is history (released in 2007, end of support of v5.2.1 was already in June 2011). In the following the procedure in Phoenix/WinNonlin’s 6.3 BE tool (EMA’s all fixed effects method and the addi­tional term in the second stage according to the Q&A-document Rev.7) and Example 2 from Potvin’s paper:

• Stage 1
  Map variables as usual.
  Navigate to [Options] and change the Confidence Level to 94.12%.
  Navigate to [Random 1] and delete Subject(Sequence).
  Navigate to [Fixed Effects], modify the model specification to Sequence+Treatment+Period+Subject(Sequence).
  You should get:
  Ratio_%Ref:    108.76
CI_User_Lower:  92.93
CI_User_Upper: 127.28
  With this coding we don’t get the intrasubject-CV in the output (I think it will be available in the next release this summer).
  Output Data → Final Variance Parameters → Send To → Data → Data Wizard:
  Add Transformation → Custom → New Column Name: CVintra → Formula: sqrt(exp(Estimate)-1)
  You should get:
  CVintra: 0.1821 (=18.21%)
  
  
• Stage 2
  Map variables as usual; additionally map Stage to Classification.
  Navigate to [Options] and change the Confidence Level to 94.12%.
  Navigate to [Random 1] and delete Subject(Sequence).
  Navigate to [Fixed Effects], modify the model specification to Stage+Sequence+Sequence*Stage+Sequence*Stage*Subject+Period(Stage)+Treatment.
  You should get:
  Ratio_%Ref:    101.45
CI_User_Lower:  88.45
CI_User_Upper: 116.38
  

These results agree with the ones reported by Potvin et al.

Intermediate power after stage 1 and sample size estimation for stage 2 in with PowerTOST:

• library(PowerTOST)
power.TOST(alpha=0.0294, theta0=0.95, CV=0.1821, n=12, design='2x2')
  You should get:
  [1] 0.5253565
  Since 52.54% < 80%, initiate the second stage (if ≥80% stop; study failed to show BE).
  
  
• sampleN.TOST(alpha=0.0294, targetpower=0.80, theta0=0.95, CV=0.1821, design='2x2')
  You should get:
  +++++++++++ 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 = 0.1821

Sample size (total)
 n     power
20   0.829292
  Perform the second stage in 20–12=8 subjects like in the example.

BTW, recently it was shown* that EMA’s modification of the model is irrelevant for the BE assess­ment – which is not sur­prising, since Sequence*Stage is a between-subject term. If anybody has a clue why EMA introduced it, please enlighten me. Furthermore, there is not difference in results irrespective whether subjects are treated as a fixed or random effect (unless T/R >1.20).

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• Karalis V, Macheras P. On the Statistical Model of the Two-Stage Designs in Bioequivalence Assessment. J Pharm Pharmacol. 2014;66(1):48–52. doi 10.1111/jphp.12164