# Bioequivalence and Bioavailability Forum

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ViPraj
Junior

India,
2017-07-27 05:05

Posting: # 17618
Views: 579

## within-subject variance vs within-subject variability [General Sta­tis­tics]

Dear
Is there any difference between within-subject variance and within-subject variability ?
If yes, how to calculate one from another ?

Regards
VP
Helmut
Hero

Vienna, Austria,
2017-07-27 16:08

@ ViPraj
Posting: # 17619
Views: 472

## Variability for non-statisticians

Hi VP,

» Is there any difference between within-subject variance and within-subject variability ?

Variability is a term statisticians use when desperately trying to communicate with members of the real world (phy­sicians, patients, the boss).
In statistics two parameters describe a distribution. One gives the location (mean, median, …) and the other dispersion (variance or standard deviation, interquartile range, …). You have to figure out yourself from the context what is meant. In BE (log-transformed data) most common: CVw = √w – 1.

All the best,
Helmut Schütz

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

India,
2017-08-01 04:31

@ Helmut
Posting: # 17639
Views: 323

## Variability for non-statisticians

Dear Helmut
Actually while reading the USFDA reference scaled BE guidance of Progesterone and Warfarin this question came in my mind.I was thinking that S2w (S square w) is within subject variance and Sw is within subject variability (assumption was based on the formula mentioned for variance and standard deviation in various literature) . Pl. confirm if it is true or false. Also i was interested in knowing how we can calculate S2w (S square w) from available Sw value.

Regards
VP
Shuanghe
Regular

Spain,
2017-08-01 08:07

@ ViPraj
Posting: # 17640
Views: 312

## Variability for non-statisticians

Hi Vipraj,

» I was thinking that S2w (S square w) is within subject variance and Sw is within subject variability (assumption was based on the formula mentioned for variance and standard deviation in various literature) . Pl. confirm if it is true or false.

Yes. In fact, the step 1 of method description before the SAS code in FDA's guidance already clearly mentioned it as "Determine SWR, the within-subject standard deviation (SD) of the reference product, for the pharmacokinetic (PK) parameters AUC and Cmax. ..."

» Also i was interested in knowing how we can calculate S2w (S square w) from available Sw value.

Now I'm lost. You mean other way than just square it?

» Is there any difference between within-subject variance and within-subject variability ?

Like Helmut said, depending on the context. Sometimes they mean the same thing, sometimes they don't.

In the "additional comments" of the same FDA guidance, they tell us in order to apply the scaled method the criterion is "within-subject variability ≥ 30%)", so clearly here the variability is not equal to variance since you need to do `sqrt(exp(s2w) - 1)` to get it.

All the best,
Shuanghe
Helmut
Hero

Vienna, Austria,
2017-08-01 14:55

@ Shuanghe
Posting: # 17643
Views: 281

## swR 0.294 ≠ CVwR 30%

Hi Shuanghe,

» In the "additional comments" of the same FDA guidance, they tell us in order to apply the scaled method the criterion is "within-subject variability ≥ 30%)", so clearly here the variability is not equal to variance since you need to do `sqrt(exp(s2w) - 1)` to get it.

Yep, sloppy as usual.

[…] please provide evidence of high variability […] (i.e., within-subject variability ≥ 30%).
If swR ≥ 0.294, use the reference-scaled procedure to determine BE for the individual PK parameter(s)

log(0.30²+1) = 0.2935604  0.294
100√0.294²–1 = 30.04689%  30%
Who cares about the fourth significant digit…

Regulators love simple numbers.
What does the EMA tell us? The switching variability is clearly defined as CVwR 30% (based on the paper of the two Lászlós). That would translate into a regulatory σ0 of 0.29356… and a switching condition θS of log(1.25)∕σ0 = –log(0.80)∕σ0 = 0.760128… Well, what do we have to use? 0.760. IIRC, Panos Macheras complained about it in one his papers about reference-scaling.

Picky: In code assessing ABEL (SAS, Phoenix/WinNonlin) only the 90% CI should be rounded to two digits, not the expanded limits themselves. Otherwise a discontinuity will appear close to CVwR 50%:

All the best,
Helmut Schütz

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