Bioequivalence and Bioavailability Forum

Hi everybody and nobody.

Firstly I have not many experiences with replicate designs, so I may be wrong.

But I have doubts about the degrees of freedom in the post above. When we are calculating the within-subject variability of the reference product (CV_WR). The ANOVA model is quite reduced, as EMA stated in Questions & Answers (with errors in red):

The following code removes all the test data from the data-set and then fits a model where the residual variance corresponds to the within subject variance for the test product.

data var;
set replicate;
if formulation='R';
run;

proc glm data=var;
class subject period sequence;
model logDATA= sequence subject_(sequence) period;
run;

Of course there is no formulation effect. (For TRT/RTR design there is even no sequence effect because for this design R is replicated only in one sequence.)

So I think, the degrees of freedom incoming to R function CVCL() should be changed (as shown in rows below with "-->"):

TRT|RTR
Degrees of Freedom of ANOVA for 2x2x3 replicate crossover design:
   Source of variation   df            df from ANOVA with reference data only
   Formulations          1             NA
   Periods               2             1
   Subjects              n – 1         n/2 – 1
      Sequences          1             NA
      Subjects(SEQ)      n – 2         NA
   Error                 2n – 3  -–>  n/2 – 1
   Total                 3n – 1        n – 1

TRR|RTR|RRT
Degrees of Freedom of ANOVA for 2x3x3 replicate crossover design:
   Source of variation   df            df from ANOVA with reference data only
   Formulations          1             NA
   Periods               2             2
   Subjects              n – 1         n – 1
      Sequences          2             2
      Subjects(SEQ)      n – 3         n – 3
   Error                 2n – 3  -–>  n – 2
   Total                 3n – 1        2n – 1

TRTR|RTRT
Degrees of Freedom of ANOVA for 2x2x4 replicate crossover design:
   Source of variation   df            df from ANOVA with reference data only
   Formulations          1             NA
   Periods               3             3
   Subjects              n – 1         n – 1
      Sequences          1             1
      Subjects(SEQ)      n – 2         n – 2
   Error                 3n – 4  -–>  n – 3
   Total                 4n – 1        2n – 1

No questions about df of designs (namely df of MSE: 2n-3 for 2x2x3, 2n-3 for 2x3x3, 3n-4 for 2x2x4). I'm only pointing to degrees of freedom used for function CVCL().

I don't know how much it will change the width of CI of CV_WR, so I am not making conclusions.

But in general, TRT|RTR design looks interesting, we get estimates of test and reference variability (each from half of subjects). But I am not convinced if there is right to compare (everyone can see) which variability T or R is higher, when it is comparison of CV_WR from the first n/2 group of subjects (one sequence) and CV_WT from the second n/2 group (second sequence, i.e. different subjects) - difference of T and R variability can be caused by different subjects - it looks like little bit as comparison of results from two studies performed in the same time/place/conditions with different subjects. Of course this comparison is not the goal of average BE, where we calculate GMR + 90% CI, but still many readers want to compare variabilities T versus R (maybe). For me this design looks like a "demo version" of the full replicate design TRTR|RTRT with only half of subjects for expanding Cmax acceptance limits.

Best regards,
zizou