# Bioequivalence and Bioavailability Forum 05:23 CET

Balaji
Junior

India,
2015-11-23 13:39

Posting: # 15653
Views: 7,335

## Inter subject vari­ability for parallel [Software]

Can anyone tell me how to calculate Inter subject variability for parallel design using phoenix winnonlin or manually i can find only Var(Residual) in final variance parameters sheet in Winnonlin while calculating average bioequivalence

Helmut
Hero

Vienna, Austria,
2015-11-23 15:07

@ Balaji
Posting: # 15655
Views: 6,469

## Phoenix/WinNonlin: Total subject vari­ability in parallel designs

Hi Balaji,

» Can anyone tell me how to calculate Inter subject variability for parallel design

That’s a common misconception. The fact that you administered products only once does not mean that the intra-subject variability does not exist (you observed only one occasion). You can calculate the inter-subject variability only in a crossover design. In a parallel design you get only the total (or pooled) vari­abi­li­ty, which con­sists of both inter- and intra-subject components. Talking of inter-subject variability in paral­lel designs is sloppy terminology.

» … using phoenix winnonlin or manually i can find only Var(Residual) in final variance parameters sheet in Winnonlin while calculating average bioequivalence

Correct. I would not suggest to assume equal variances in groups (see the FDA’s 2001 guidance). Example dataset:

```subj trt  var   1   T  2.52   2   T  8.87   3   T  0.79   4   T  1.68   5   T  6.95   6   T  1.05   7   T  0.99   8   T  5.60   9   T  3.16  10   R  4.98  11   R  7.14  12   R  1.81  13   R  7.34  14   R  4.25  15   R  6.66  16   R  4.76  17   R  7.16  18   R  5.52```

With PHX/WNL’s default method (fixed: trt) you get
PE 48.58% (90% CI: 27.15–86.94%).
Levene’s test for equality of variances is significant (p 0.0229). The conventional t-test is liberal in the case of unequal variances and even more sensitive to unequal group sizes. Personally I would not apply pre-test­ing and use the Welch-Satterthwaite adjustment in all cases. In PHX/WNL add a column “period” to the data (containing 1 in all rows). Map `trt` to `Formulation`, `var` to `Dependent`, `subj` and `period` to `Classification`. Keep `trt` as the fixed effect and add a repeated specification to the variance structure: `repeated` = `period`, `variance blocking variables` = `subj`, `group` = `trt`, `type` = `variance components`. This specification gives:
PE 48.58% (90% CI: 26.78–88.14%) – which is wider (conservative).

In the conventional analysis the total CV is 100√Var(Residual)–1 = 80.54%.
In the modified analysis you can estimate the total CV separately for T and R, where in PHX/WNL `Var(period*trt*subj)_11` is the one of R and `Var(period*trt*subj)_12` the one of T. From these variances we get a total CV of 46.23% for R and 111.34% for T.
Variances (but not CVs) are additive. Since group sizes are equal, we don’t have to worry about weighting by the degrees of freedom. The residual variance in the default model is 0.5000. The one of R is 0.1937 and the one of T 0.8063. Hence, (0.1937+0.8063)/2=0.5000.

Cheers,
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. ☼
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Balaji
Junior

India,
2015-11-24 07:14

@ Helmut
Posting: # 15657
Views: 6,147

## Phoenix/WinNonlin: Total subject vari­ability in parallel designs

Thanks Helmut

so we can use total variability instead of (inter subject variability and intra subject variability) for parallel design using this 100√ℯVar(Residual)–1 but winnonlin wont calculate total cv we have to calculate manually
am I right
Helmut
Hero

Vienna, Austria,
2015-11-24 12:58

@ Balaji
Posting: # 15661
Views: 6,129

## Manually?

Hi Balaji,

» so we can use total variability instead of (inter subject variability and intra subject variability) for parallel design…

Not instead of… In a parallel design the total variability is all we have.
Again: Inter- and intra-subject variabilities are not accessible, only their sum!

» …using this 100√ℯVar(Residual)–1

I strongly advise to use the modified setup (see the “Phoenix WinNonlin 6.4 User’s Guide”, p85–6).

» …but winnonlin wont calculate total cv we have to calculate manually

Manually? Set up a custom transformation in the Data Wizard.
• Default model (not recommended)
Final Variance Parameters [right click] Send To ► Data ► Data Wizard | Add Transformation
Transformation Type: Custom
Transformation: Custom Function
New Column Name: CVp
Formula: 100*sqrt(exp(Estimate)-1))
Gives for my example above 80.54%.
• Modified model (adjusting for unequal variances and group sizes)
Same procedure as above.
Gives 46.23% for Reference and 111.34% for Test.

Cheers,
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. ☼
Science Quotes
Balaji
Junior

India,
2015-11-24 13:44

@ Helmut
Posting: # 15663
Views: 6,138

## Manually?

Again Thanks Helmut

So your saying by using data wizard is the only way to calculate total cv

we wont get it by changing some settings
Helmut
Hero

Vienna, Austria,
2015-11-24 14:09

@ Balaji
Posting: # 15664
Views: 6,219

## RTFM!

Hi Balaji,

» So your saying by using data wizard is the only way to calculate total cv

Correct.

» we wont get it by changing some settings

Yes. Why are you confused? What about RTFMs?
Relevant ones: “Phoenix WinNonlin 6.4 User’s Guide” and “Data Tools and Plots Guide”. 784 pages. There is no free lunch.
If you have difficulties with the setup, I suggest to register at Certara’s forum. There you could upload your project-file.

Cheers,
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. ☼
Science Quotes
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