Bioequivalence and Bioavailability Forum

Dear all colleagues,

We like to announce the release of bear v2.3.0 and share it with all colleagues of this Forum. The new release has the following updates and new functions:

• add sample estimation and lme (mixed model) data analysis for the parallel BE study
  
• add References into bear's output (such as sample estimation, outliers detection, etc.)
  
• label outliers' subjects number for boxplot only if there is any (see crossover demo)
  
• add input data summary of BA measurement (class level information, means, etc.)
  
• add interpretations for some statistical tests (such as Hotelling T² test)
  
• add add Two One-Sided Tests (TOST) and Anderson-Hauck's tests (for educational purposes ONLY)
  
• allow users to change BE acceptance range now (not fixed on 80%-125% any more!); different countries have different regulatory guideline.
  
• show MSResidual and MSSubject(seq) values when calculating inter- and intra-subject CVs
  
• change Hotelling T² test layout

Please use "Update packages" function to upgrade your bear if you have already installed any previous version of bear. For new installation, please refer R website for "How to install R add-on packages" and also browse bear website. Previous version of bear announced in the Forum are listed as follows: bear v2.2.0, v2.1.0, v2.0.1, v1.1.4, v1.0.0.

Here are some results generated from bear v2.3.0.
<<Sample Size Estimation>>
 Upper acceptance limit = 125 %
 Lower acceptance limit = 80 %
     Expected ratio T/R = 95.00 %
           Target power = 80.00 %
Inter- or Intra-subj CV = 20.0 %

 study    2x2x1         2x2x2        2x2x3        2x2x4
design   parallel     crossover   replicated   replicated
------- ----------- ------------ ------------ ------------
   N       36            20           16           10

Estimated power = 80.99398 % (for parallel study)
Estimated power = 83.46802 % (for crossover/replicate study)
where 2x2x2 means 2-treatment, 2-sequence, and 2-period crossover study.

Data Summary of BA measurement (...)             
--------------------------------------------------------------------------
   subj drug seq prd Cmax    AUC0t   AUC0INF   lnCmax   lnAUC0t lnAUC0INF
1     1    1   2   2 1739 14445.27 14925.656 7.461066  9.578123  9.610837
2     2    1   1   1 1481 12516.14 13134.553 7.300473  9.434774  9.483002
3     3    1   2   2 1780 15371.40 15999.744 7.484369  9.640264  9.680328
4     4    1   1   1 1374 11063.10 11647.240 7.225481  9.311371  9.362824
5     5    1   2   2 1555 13971.45 14556.963 7.349231  9.544771  9.585825
6     6    1   1   1 1756 15376.35 15950.591 7.470794  9.640586  9.677251
(...)


  Class Level Information                 
--------------------------------------------------------------------------
  Class       Levels      Values
  SUBJECT      14          1 2 3 4 5 6 7 8 9 10 11 12 13 14
  DRUG          2          1 2
  SEQUENCE      2          1 2
  PERIOD        2          1 2
-----------
DRUG 1: the Ref. product; DRUG 2: the Test product
SEQUENCE 1:  Ref. -> Test, and SEQUENCE 2: Test -> Ref.
-------------------------------------------------------

 Means                 
--------------------------------------------------------------------------
  SEQUENCE     Cmax    AUC0t  AUC0INF  lnCmax  lnAUC0t lnAUC0INF
1        1 1602.071 14109.25 14713.39 7.37045 9.538976  9.582570
2        2 1589.786 13357.85 13970.66 7.36052 9.487205  9.532541


   SUBJECT SEQUENCE   Cmax    AUC0t  AUC0INF   lnCmax  lnAUC0t lnAUC0INF
1        1        2 1686.0 13369.59 13950.10 7.429620 9.497491  9.540791
2        2        1 1659.0 13907.39 14645.04 7.408181 9.535147  9.586510
3        3        2 1926.5 15277.70 15838.53 7.560560 9.634131  9.670149
4        4        1 1501.5 12522.38 13133.29 7.310602 9.428436  9.476462
5        5        2 1470.0 12911.54 13523.30 7.291343 9.462496  9.509240
6        6        1 1639.0 14607.04 15146.74 7.399287 9.587870  9.624130
(...)

  PERIOD     Cmax    AUC0t  AUC0INF   lnCmax lnAUC0t lnAUC0INF
1      1 1632.714 13855.25 14531.50 7.390958 9.52988  9.577774
2      2 1559.143 13611.85 14152.54 7.340011 9.49630  9.537337


  DRUG     Cmax    AUC0t  AUC0INF  lnCmax  lnAUC0t lnAUC0INF
1    1 1539.643 13171.14 13781.86 7.32951 9.474286  9.519987
2    2 1652.214 14295.97 14902.19 7.40146 9.551895  9.595125

(...)    BE Summary Report                           
--------------------------------------------------------------------------
  Dependent Variable: lnCmax                                               
--------------------------------------------------------------------------
        n1(R=>T) = 7
        n2(T=>R) = 7
        N(n1+n2) = 14
  Lower criteria = 80 %
  Upper criteria = 125 %
        MEAN-ref = 7.32951
       MEAN-test = 7.40146
             MSE = 0.01780339
              SE = 0.05043155
Diff. (test-ref) = 0.07195028

**************** Classical (Shortest) 90% C.I. for lnCmax ****************

  CI90_lower Point_estimated CI90_upper
1     98.223         107.460    117.566

---------------------- Two One-Sided Tests (TOST) -------------------------

     TOST   T value   P value
1 T_lower   -5.8514    0.0000
2 T_upper   -2.9980    0.0056

**Interpretation:
Ho: Theta =<  0.8  or  Theta >=  1.25
Ha:  0.8  < Theta <  1.25
Theta = Mean_test/Mean_ref 
Because all P values are less than 0.05, we will reject the null hypothesis (Ho).
BE acceptance range is set at 80 % -  125 % .

------------------------ Anderson-Hauck Test ------------------------------

          P value = 0.005515

**Interpretation:
Ho: Theta =<  0.8  or  Theta >=  1.25
Ha:  0.8  < Theta <  1.25
Theta = Mean_test/Mean_ref 
Because all P values are less than 0.05, we will reject the null hypothesis (Ho).
BE acceptance range is set at 80 % -  125 % .

---------------------------------------------------------------------------
Ref.:
1. Chow SC and Liu JP. Design and Analysis of Bioavailability-       
   Bioequivalence Studies. 3rd ed., Chapman & Hall/CRC, New York (2009).
2. Schuirmann DJ. On hypothesis testing to determine if the mean of a 
   normal distribution is continued in a known interval. Biometrics, 37,
   617(1981).                                                           
3. Schuirmann DJ. A comparison of the two one-sided tests procedure and the
   power approach for assessing the equivalence of average bioavailability.
   Journal of Pharmacokinetics and Biopharmaceutics, 15, 657-680 (1987).
4. Anderson S and Hauck WW.  A new procedure for testing equivalence in
   comparative bioavailability and other clinical trials. Communications
   in Statistics-Theory and Methods, 12, 2663-2692 (1983).     
--------------------------------------------------------------------------
(...)

Please let us know if you have any question about bear. Thank you all.

All the best,
Hsin-ya Lee, Yung-jin Lee
College of Pharmacy,
Kaohsiung Medical University,
Kaohsiung, Taiwan