Bioequivalence and Bioavailability Forum

Hi Khaoula,

I’m too lazy to check with my old installation of Kinetica. But there are some points to note:

❝ SOURCE       D.F      SS         MS        F        p

❝ Period         1  0.0264787  0.0264787   0.56186  0.4669    NS

❝ Subject(Seq)  13  4.8517     0.373208    7.91934  0.0003379 ***

❝ Formulation    1  0.211625   0.211625    4.4906   0.05391   NS

❝ Sequence       1  0.686301   0.686301   14.5631   0.002141  ***

❝ Error         13  0.61264    0.0471261

❝ Total         29  6.38875

Old story. Kinetica calculates the sequence effect wrong – since ages. See this thread.
Instead of F=0.686301/0.0471261=14.5631 (which is highly significant with p=0.002141) the correct test is against Subject(Seq): F=0.686301/0.373208=1.8389 (which is not sig­nificant with p=0.1982).

❝ Root Mean Square Error = 0.217086

The RMSE is a crude estimate of the CV and should be avoided.

❝                                   ; CV = 0.0347883

That’s nonsense! Is this part of Kinetica’s original output?* Why didn’t you bother to manu­ally calculate the CV according to the formula I gave you above?
\(CV\% = 100\sqrt{e^{0.0471261}-1} = 21.97\%\)

❝ Power of the test = 0.500777

❝ 1 - ( Power of the test ) = 0.499223

Wrong. If you insist in post hoc power: 0.09885. With a T/R-ratio close to the upper limit of the acceptance range would you really expect a ~50% chance to pass BE in 15 subjects?

❝ around the ratio:[test form]/[ref form])=[1.028, 1.3612]

Yes, but around which ratio? I would guess: \(\sqrt{1.028 \times 1.3612} = {\color{Red} {1.829\ldots}}\) The geometric mean of Test is 559.01 and the one of Reference 461.21. As a first guess of the T/R-ratio we get 461.21/559.01=1.2121. Since this is an imbalanced dataset, we have to use the least squares (or adjusted) means instead, which are 552.58 and 456.58. Therefore, T/R=1.2103. What does Kinetica “calculate” here?

Due to the bug in Kinetica this is likely wrong. In Phoenix/WinNonlin I got:

Hypothesis       DF    SS        MS       F_stat  P_value
Period            1  0.027982  0.027982  0.07021  0.79519
Sequence*Patient 13  5.181510  0.398578  7.49434  0.00045
Sequence          1  0.105223  0.105223  1.97847  0.18300
Formulation       1  0.271883  0.271883  5.11214  0.04155
Error            13  0.691389  0.053184

T/R 121.02% [90% CI: 104.22%, 140.53%]

BTW:
Parameter              Estimate
Var(Sequence*Patient)  0.172697
Var(Residual)          0.053184
Intersubject CV        0.434173
Intrasubject CV        0.233717

Check: \(CV\% = 100\sqrt{e^{0.053184}-1} = 23.37\%\). Low for omeprazole, but possible.

If you want an independent evaluation by noncommercial software: In (you find the script in my lectures) I got:
121.02% [104.22–140.53%] CV 23.37%

❝ I havnt randomisation of subject 15, and then they put the result in kinetica they excluded him,

The randomization of an excluded subject is not required anyhow.

---

• Confirmed. I don’t have the slightest idea how Kinetica gets this number.
  Discovered this interesting post at David’s PKPD-list.

Dear Khaoula,

I re-calculated your C_max-data in Kinetica v5.0.10. I didn’t import the “all missing” row of subject #15 and asked for log-transformed analysis. Now I’m even more confused. Below my results:

            ------------------------------------------
            LATIN SQUARE DESIGN : ANOVA TABLE for Cmax
            ------------------------------------------
LATIN SQUARE with Log (neperian) option


SOURCE       D.F    SS         MS          F         p
Period         1  0.0092314  0.0092314   0.174967  0.6826    NS
Subject(Seq)  13  5.18151    0.398578    7.55441   0.0004324 ***
Formulation    1  0.277381   0.277381    5.25731   0.03917   ***
Sequence       1  0.788575   0.788575   14.9462    0.001947  ***
Error         13  0.685892   0.0527609
Total         29  6.94259
---------------------------------------------------------------------
                     N   Mean     SD         SEM     GeoMean  Geo SD
Formulation:num = R 15  6.13386  0.498125  0.128615  461.211  1.64563
Formulation:num = T 15  6.32617  0.477449  0.123277  559.01   1.61196
---------------------------------------------------------------------
Root Mean Square Error = 0.229697 ; CV = 0.0368695

phi = 1.62131
Power of the test = 0.564385
1 - ( Power of the test ) = 0.435615
Minimum detectable difference = 0.192312
---------------------------------------------------------------------
BIOEQUIVALENCE TESTS FOR
Level R and level T

Reference Confidence Interval: [0.8, 1.25]
Geomean Ratio (Test/Reference) = 1.21205
90% standard confidence interval
(around the ratio:[test form]/[ref form])=[1.0448, 1.4061]
t(0.05 - 13df) = 1.7709

  Cannot conclude equivalence.

Still wrong in many places, but closer to Phoenix/WinNonlin and R.
                 PE        90% CI       MSE     CV
PHX/WNL and R  121.02  104.22–140.53  0.053184 23.37
Kinetica 5     121.20  104.48–140.61  0.052761 23.28 (manually from MSE)