## total (pooled) variance: examples [Power / Sample Size]

Dear Nav!

Some more references and explanations.

In a parallel design we have no direct access to inter-subject variability, what we see is the

From a 2×2×2 crossover design we may estimate

I give you two examples from my 2×2 cross-over studies (for low/medium/high intra-subject CV) to get an impression about the lacking relationship of CV-intra/-inter/-total:

Methyphenidate 20 mg MR single dose sprinkled, AUC

CV-intra

CV-inter

CV-total

Paroxetine 30 mg IR steady state, AUC

CV-intra

CV-inter

CV-total

Lansoprazole 30 mg single dose fasting, C

CV-intra

CV-inter

CV-total

I can’t see this rule of thumb of

❝ […] But how would you get the inter-subject variability from the ANOVA for parallel design in order to calculate the sample size.

Some more references and explanations.

In a parallel design we have no direct access to inter-subject variability, what we see is the

*total*(sometimes called*pooled*) variability.From a 2×2×2 crossover design we may estimate

- intra-subject variability as

\(CV_e(\%)=100\sqrt{e^{MS_e}-1}\)

- inter-subject variability as

\(CV_s(\%)=100\sqrt{e^{(MS_s{\color{Red} -}ME_e)/2}-1}\)

- total (pooled) variability as

\(CV_p(\%)=100\sqrt{e^{(MS_s{\color{Red} +}ME_e)/2}-1}\)

- Midha KK, Ormsby ED, Hubbard JW, McKay G, Hawes EM, Gavalas L, McGilveray IJ.
*Logarithmic Transformation in Bioequivalence: Application with Two Formulations of Perphenazine.*J Pharm Sci. 1993;82(2):138–44.

- Hauschke D, Steinijans VW, Diletti E.
*Presentation of the intrasubject coefficient of variation for sample size planning in bioequivalence studies.*Int J Clin Pharmacol Ther. 1994;32(7):376–8.

^{1}So I would*guess*you may simply use formulas and software intended for inter-subject CV (although you have the total CV). At least it’s a conservative approach (in other words, you will only loose some money because your study will be slightly overpowered)❝ Re: 60% of inter to estimate the intra: I am a statistician and I routinely see the PK individuals taking 60% of inter to be the intra for estimating sample size for a crossover design and always wondered about the validity of the approach.

I give you two examples from my 2×2 cross-over studies (for low/medium/high intra-subject CV) to get an impression about the lacking relationship of CV-intra/-inter/-total:

^{2}Methyphenidate 20 mg MR single dose sprinkled, AUC

_{t}, n=12CV-intra

` `

7.00% [=36% of inter, 34% of total] CV-inter

` `

19.1%CV-total

` `

20.4%Paroxetine 30 mg IR steady state, AUC

_{tau}, n=32CV-intra

` `

25.2% [=46% of inter, 41% of total] **≈**CV-inter

` `

55.1%CV-total

` `

62.1%Lansoprazole 30 mg single dose fasting, C

_{max}, n=47CV-intra

` `

47.0% [=187% (!) of inter, 86% of total] CV-inter

` `

25.1%CV-total

` `

54.6%I can’t see this rule of thumb of

*‘CV-intra = 60% CV-inter’*to be applicable …- Intra-subject variability does not ‘disappear’ just because you made only one observation.

- See also this thread.

—

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

*Dif-tor heh smusma*🖖🏼 Довге життя Україна!_{}Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

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### Complete thread:

- Sample size estimation for parallel design Nav Coelho 2007-07-20 16:14 [Power / Sample Size]
- Parallel designs (total variance) Helmut 2007-07-20 16:29
- Parallel designs (total variance) Nav Coelho 2007-07-20 18:38
- CV-intra # 60% CV-inter Helmut 2007-07-22 01:17
- total (pooled) variance: examplesHelmut 2007-07-23 17:44
- total (pooled) variance: examples Nav Coelho 2007-07-23 19:58
- total (pooled) variance: examples BEQool 2023-04-18 09:59
- Higher-Order Crossovers Helmut 2023-04-20 10:19
- Higher-Order Crossovers BEQool 2023-04-21 07:53

- total (pooled) variance: examples zizou 2023-04-21 21:23
- total (pooled) variance: examples BEQool 2023-04-22 18:20
- total (pooled) variance: examples zizou 2023-04-22 21:06
- total (pooled) variance: examples BEQool 2023-04-25 10:57
- total (pooled) variance: examples zizou 2023-04-25 22:43
- total (pooled) variance: examples BEQool 2023-05-04 08:17

- total (pooled) variance: examples zizou 2023-04-25 22:43

- total (pooled) variance: examples BEQool 2023-04-25 10:57

- total (pooled) variance: examples zizou 2023-04-22 21:06

- total (pooled) variance: examples BEQool 2023-04-22 18:20

- Higher-Order Crossovers Helmut 2023-04-20 10:19

- Parallel designs (total variance) Nav Coelho 2007-07-20 18:38
- Sample size estimation for parallel design Dipesh Jayswal 2007-07-24 08:52

- Parallel designs (total variance) Helmut 2007-07-20 16:29