## CVs (borderline OT) [RSABE / ABEL]

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 (CVWR). 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 CVWR, 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 CVWR from the first n/2 group of subjects (one sequence) and CVWT 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