Bioequivalence and Bioavailability Forum

Dear D. Labes & Maura,

❝ This gives among the [SAS Proc mixed] output:

❝ ...

❝                    The Mixed Procedure

❝

❝                    Covariance Parameter

❝                        Estimates

❝

❝                  Cov Parm      Estimate

❝

❝                   Subj(SEQ)      0.02788

❝                   Residual       0.03344

❝ ...

❝              Type 3 Tests of Fixed Effects

❝

❝                    Num     Den

❝      Effect         DF      DF    F Value    Pr > F

❝

❝      Droga           2      18       3.44    0.0543

❝      Per             2      18       1.27    0.3037

❝      SEQ             5    6.32       1.56    0.2956

❝      Carry           2      18       1.21    0.3204

❝ This is very close to your results with Proc GLM, as I had expected.

❝

❝ Thus I can't figure out why WNL gives distinct F-tests.

❝ Check your model specifications and data thoroughly.

OK, here my results (Phoenix/WinNonlin 6.1):
Model Specification and User Settings
       Dependent variable : lnAUC
                Transform : Data already ln-transformed
              Fixed terms : int+Sequence+Droga+Period+Carry
    Random/repeated terms : Sequence*Subject

Final variance parameter estimates:
    Var(Sequence*Subject)    0.0278831
            Var(Residual)    0.0334379
          Intersubject CV    0.168153
          Intrasubject CV    0.1844

     REML log(likelihood)      2.96255
 -2* REML log(likelihood)     -5.92511
 Akaike Information Crit.     22.0749
   Schwarz Bayesian Crit.     38.5676

Partial Tests of Model Effects
              Hypothesis    Numer_DF    Denom_DF      F_stat     P_value
------------------------------------------------------------------------
                     int           1        7.78     920.601      0.0000
                Sequence           5        6.31     1.55832      0.2957
                   Droga           2          18     3.44086      0.0543
                  Period           2          18     1.27404      0.3037
                   Carry           2          18     1.21312      0.3204

Partial Sum of Squares
              Hypothesis          DF          SS          MS      F_stat     P_value
------------------------------------------------------------------------------------
                Sequence           5           2         0.4   0.0852022      1.2740
        Sequence*Subject        6.31     4.04403    0.640933     19.1678      0.0000
                   Droga           2     0.23011    0.115055     3.44086      0.0543
                  Period           2   0.0852022   0.0426011     1.27404      0.3037
                   Carry           2   0.0852022   0.0426011     1.27404      0.3037
                   Error          18    0.601883   0.0334379

❝ Maybe that WNL partial F-tests do not correspond to SAS type III tests?

They are almost (!) the same.

❝ Any of the WNL owners out there with an opinion?

I would say wrong coding. The model should be specified with:
Fixed Effects Sequence+Droga+Period+Carry
Variance Structure / Random 1 Subject(Sequence) Type Variance Components

Chow/Liu reported carryover effects at p=0.32 and further results (3^rd ed. 2009, Tables 10.3.15/16, p322):
Carryover   R      T      S
  Yes      5.67   7.24   6.30
  No       6.01   7.06   6.45

Comparison  Carryover       90% CI
T vs R        Yes      107.20%, 134.41%
              No       104.75%, 129.92%
S vs R        Yes       94.47%, 119.68%
              No        92.62%, 119.79%
T vs S        Yes      101.63%, 129.83%
              No        97.54%, 122.72%
I followed Maura's coding here; R=solution (R), T=domestic tablet (T₁), S=European tablet (T₂). According to footnote (a): Calculations were based upon [...] an estimate of solution formulation mean which is 5.97 (??) in the presence of carryover effects and is 6.01 in the absence of carryover effects.

I got:
Carryover   R      T      S
  Yes      5.77   7.16   6.22
  No       5.77   6.83   6.26

Comparison  Carryover       90% CI
T vs R        Yes      107.35%, 143.40%
              No       103.95%, 134.86%
S vs R        Yes       93.30%, 124.63%
              No        95.29%, 123.62%

No idea whether the LSM of the reference in Chow/Liu contains another typo (5.67 ↔ 5.97) - and which value they have actually used in calculating the 90% CI.

@Maura: Where did you get the coding of carryover from?