Elena777
☆

Belarus,
2018-01-20 13:31
(1832 d 09:31 ago)

(edited by Elena777 on 2018-01-20 20:44)
Posting: # 18231
Views: 13,750

## CV values in BE studies: intra, or inter, or total? [Study As­sess­ment]

Hello to all.

There is data about CV values (often these values are placed into brackets) in many published reports of BE studies.

I'll provide two examples in order to make my BIG question clear:

1. In a single dose, randomised 3-way cross-over bioequivalence study, comparing the proposed 160 mg product with two reference 160mg tablets from France (Sotalex, Bristol Myers Squibb, France) and Australia (Sotacor, Bristol Myers Squibb, Australia) in healthy adult male volunteers under fasting conditions such results were obtained:

Ln Cmax(ng/ml) for Sotalex-French Reference tablets 160 mg: Mean (CV) = 1212.09 (28.7)

The link to the source: http://www.mhra.gov.uk/home/groups/par/documents/websiteresources/con2031163.pdf

2. In a another randomized two-dose two-period crossover study on the bioequivalence of oral and intravenous sotalol CV for Cmax (oral route of administration) was 0.41. This value was performed in a separate cell of a table (that table contained data about individual levels of PK parameters of participants, min, max, mean, median as well; you can check it here: https://www.accessdata.fda.gov/drugsatfda_docs/nda/2009/022306s000ClinPharmR.pdf)

The question:

Which kind of CV is performed in my examples? And in general which kind of CV is usually performed in reports of BE studies? Is it CVintra, or CVinter, or CVtotal?

jag009
★★★

NJ,
2018-01-20 20:18
(1832 d 02:43 ago)

@ Elena777
Posting: # 18232
Views: 12,511

## CV values in BE studies: intra, or inter, or total?

Hi

❝ Ln Cmax(ng/ml) […]: Mean (CV) = 1212.09 (28.7)

I checked the table... That's not the intrasubject CV. That's just the CV from (SD/Mean)*100.
Same answer from your 2nd question (I didn't look but I assume you were referring to a result that has similar output format as in Mean(CV)).

❝ Which kind of CV is performed in my examples? And in general which kind of CV is usually performed in reports of BE studies? Is it CVintra, or CVinter, or CVtotal?

In the world of BE we deal with CVintra because that's what we are interested in since that's one of the driving force in computing the 90% CI goal post for BE. We do care about inter and CVtotal as well depending on the type of BE study design we are going after (crossover or parallel).

J
Elena777
☆

Belarus,
2018-01-20 22:10
(1832 d 00:52 ago)

@ jag009
Posting: # 18233
Views: 12,441

## CV values in BE studies: intra, or inter, or total?

jag009, thank you for your answer and for revision of my link. But what does it mean "simple CV"? Why can't we say that this is CVinter?
I understood that CVintra is a value important in planning and realization of BE studies. But I need your consultation once more: after all which kind of CV we usually observe in reports of BE studies (when CV is performed in the way like in my examples)?

jag009
★★★

NJ,
2018-01-21 04:17
(1831 d 18:44 ago)

@ Elena777
Posting: # 18235
Views: 12,441

## CV values in BE studies: intra, or inter, or total?

What is simple CV?
IntraCV is called within subject CV. To keep it simple yes this is the one we usually focus on (and yes observe mostly) on in the BE report.
J
Elena777
☆

Belarus,
2018-01-21 09:21
(1831 d 13:40 ago)

@ jag009
Posting: # 18237
Views: 12,372

## CV values in BE studies: intra, or inter, or total?

jag009, sorry, I was wrong with my text input. Sometimes it is quite uncomfortable to input text on my tablet, I used a wrong word. I wanted to ask which CV did you mean in the following sentence of you previous message:

❝ That's just the CV from (SD/Mean)*100."

So I wanted to write: what is "just the CV..."? Not "simple CV". Sorry once more.

Helmut
★★★

Vienna, Austria,
2018-01-21 18:33
(1831 d 04:28 ago)

@ Elena777
Posting: # 18240
Views: 12,618

## CV values in BE studies: intra, or inter, or total?

Hi Elena,

❝ […] in general which kind of CV is usually performed in reports of BE studies? Is it CVintra, or CVinter, or CVtotal?

It depends on the design of the study. See this presentation (slides 17–18).

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
ElMaestro
★★★

Denmark,
2018-01-21 19:17
(1831 d 03:44 ago)

@ Elena777
Posting: # 18242
Views: 12,709

## CV values in BE studies: intra, or inter, or total?

Hi Elena

perhaps not a direct answer to your actual question but a general comment to the general question you aired:
1. For a crossover trial with 2 treatments, 2 sequences and 2 periods we use the "within subject variance" to construct the confidence interval. The CV is derived from this variance. We can call it a within-subject CV but it is not treatment-specific; you can say it is an estimate of a common intra-subject variance or CV. CV = sqrt(exp(Variance)-1). We get that variance as the residual error from a linear model with various factors.
2. For a crossover trial with replication of the reference treatment the important CV, but not the only one, is the CV associated with the reference treatment.
3. For a parallel trial we derive a total variance and total CV for the construction of a confidence interval. If the trial is done in batches, then the CV is somehow a kind of total CV excluding the component of the influence of batch, if calculated correctly. Yes, cosmic mindf%cker but BE often is.
When you read study reports or assessment reports you often come across descriptive statistics. Here the CV is simply the (sample) sd divided by (sample) mean.

If you want to use a CV for sample size calculation, then you need to know which model you applied in the dataset where the CV came from and what the model is the design you want to apply - the model is dependent on the study design itself. If you have a CV from a 222BE trial, then obviously this could be directly used for sample size calculation in another 222BE trial assuming your assay and other factors are as good as in the other trial. If you want to apply the CV from a 222BE trial to a replicated trial then that is still a decent guess in my opinion and vice versa. What you should not do is to apply the CV from descriptive stats to any sample size calculation, or to confuse CV's from parallel trial with CV's from crossovers.

Intra-subject CVs are generally (=most often) lower than between-subject CVs which are lower than total CVs.

Pass or fail!
ElMaestro
Elena777
☆

Belarus,
2018-01-27 10:57
(1825 d 12:04 ago)

@ ElMaestro
Posting: # 18294
Views: 12,275

## CV values in BE studies: intra, or inter, or total?

jag009, Helmut and ElMaestro, thank you so much for the information, you've provided here. It is really useful for me.
Louis52
☆

2018-02-07 21:22
(1814 d 01:40 ago)

@ Elena777
Posting: # 18372
Views: 11,863

## CV values in BE studies: intra, or inter, or total?

Just to follow up with a question regarding the total CV...as in the case of the sampleN.TOST function for "parallel" design. We supposed to use the total CV in that case, right? That means we should have prior knowledge of both MSEw and MSEb.
Helmut
★★★

Vienna, Austria,
2018-02-07 21:31
(1814 d 01:30 ago)

@ Louis52
Posting: # 18373
Views: 12,116

## CV values in BE studies: intra, or inter, or total?

Hi Louis,

❝ […] the sampleN.TOST function for "parallel" design. We supposed to use the total CV in that case, right?

Correct.

❝ That means we should have prior knowledge of both MSEw and MSEb.

Again correct (you get them from crossover designs). If the previous study had a parallel design the CV (calculated from the ANOVA’s residual error) is already CVtotal (aka CVpooled) anyway and you can plug it in directly.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
Rosy
☆

Mexico,
2019-02-19 19:33
(1437 d 03:28 ago)

@ Helmut
Posting: # 19934
Views: 9,574

## CV values in BE studies: intra, or inter, or total?

Dear Helmut,

Accordig to the first post, i have a doubt. If i found an article of a BABE study in which 3 formulation where evaluated against to reference (A) in a 4 way crossover study, but in a bioequivalence table appears for example A vs B treatment and its respective Geometric Mean Ratio (IC 90%). If i wanna calculate CV% intrasubject ussing POWER.TOST which desing i have to pick up (4x4 or parallel)? Of course 4x4 is the real design but the comparative A vs B is technically a parallel study.

Kind Regards
Helmut
★★★

Vienna, Austria,
2019-02-20 14:00
(1436 d 09:01 ago)

@ Rosy
Posting: # 19937
Views: 9,460

## PowerTOST: CVfromCI

¡Hola Rosy!

❝ Dear Helmut,

Not interested in other members’ opinions?

❝ If i found an article of a BABE study in which 3 formulation where evaluated against to reference (A) in a 4 way crossover study, …

So far, so good.

❝ … but in a bioequivalence table appears for example A vs B treatment and its respective Geometric Mean Ratio (IC 90%).

Being A the reference, it should be B vs A, right?

❝ If i wanna calculate CV% intrasubject ussing POWER.TOST which desing i have to pick up (4x4 or parallel)? Of course 4x4 is the real design but the comparative A vs B is technically a parallel study.

Parallel‽
You have to find out whether the study was evaluated with a “pooled ANOVA” or according to the “Two‐at‐a‐Time Principle” (see this post).
Example: 4×4 crossover, n 24, 90% CI 85.00–106.18%.

############################################# n    <- 24        # total sample size l    <- 0.8500    # lower 90% CL u    <- 1.0618    # upper 90% CL ############################################# library(PowerTOST) des  <- "4x4"     # design and 1st evaluation eval <- "2x2"     # 2nd evaluation pe   <- sqrt(l*u) # calculate the PE CV.1 <- CVfromCI(lower=l, upper=u, design=des, n=n)  # 1 CV.2 <- CVfromCI(lower=l, upper=u, design=eval, n=n) # 2 cat(paste0("\n", des, " design, n = ", n,            sprintf("%s %.2f%%%s", "\n90% CI =", 100*l, "\u2013"),            sprintf("%.2f%%", 100*u),            sprintf(" %s %.2f%%)", "(PE =", 100*pe),            sprintf("\n  Pooled ANOVA           : CVintra = %.2f%%",                    100*CV.1),            sprintf("\n  Two-at-a-Time Principle: CVintra = %.2f%%",                    100*CV.2)), "\n")

You will get:

4x4 design, n = 24 90% CI = 85.00%–106.18% (PE = 95.00%)   Pooled ANOVA           : CVintra = 23.41%   Two-at-a-Time Principle: CVintra = 22.73%

How to discover which method was used?
Work backwards, i.e., see with which CV you can reproduce the reported results for each comparison. (Nonsense: See Detlews post below)

res.1 <- CI.BE(pe=pe, CV=CV.1, n=n, design=des) res.2 <- CI.BE(pe=pe, CV=CV.2, n=n, design=eval) cat(paste0("\nBack-calculated 90% CI by",     "\n  Pooled ANOVA           : ",     sprintf("%.2f%%%s", 100*res.1[["lower"]], "\u2013"),     sprintf("%.2f%%", 100*res.1[["upper"]]),     "\n  Two-at-a-Time Principle: ",     sprintf("%.2f%%%s", 100*res.2[["lower"]], "\u2013"),     sprintf("%.2f%%", 100*res.2[["upper"]]), "\n")) Back-calculated 90% CI by   Pooled ANOVA           : 85.00%–106.18%   Two-at-a-Time Principle: 85.00%–106.18%

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
d_labes
★★★

Berlin, Germany,
2019-02-20 15:12
(1436 d 07:50 ago)

@ Helmut
Posting: # 19938
Views: 9,161

## PowerTOST: CVfromCI -> CI.BE

Dear Helmut,

❝ ...

❝ How to discover which method was used?

❝ Work backwards, i.e., see with which CV you can reproduce the reported results for each comparison.

res.1 <- CI.BE(pe=pe, CV=CV.1, n=n, design=des)

❝ res.2 <- CI.BE(pe=pe, CV=CV.2, n=n, design=eval)

❝ cat(paste0("\nBack-calculated 90% CI by",

 ❝     "\n  Pooled ANOVA           : ", ❝     sprintf("%.2f%%%s", 100*res.1[["lower"]], "\u2013"), ❝     sprintf("%.2f%%", 100*res.1[["upper"]]), ❝     "\n  Two-at-a-Time Principle: ", ❝     sprintf("%.2f%%%s", 100*res.2[["lower"]], "\u2013"), ❝     sprintf("%.2f%%", 100*res.2[["upper"]]), "\n"))❝ ❝ Back-calculated 90% CI by ❝   Pooled ANOVA           : 85.00%–106.18% ❝   Two-at-a-Time Principle: 85.00%–106.18%

IMHO this suggestion is an orouboros.
Calculating the CV from the CI and using this CV to calculate the CI will give you always the CI used in the starting step. Regardless of the design used in both steps.
As you has demonstrated with your calculations .

Regards,

Detlew
Helmut
★★★

Vienna, Austria,
2019-02-20 16:32
(1436 d 06:30 ago)

@ d_labes
Posting: # 19940
Views: 9,465

## Oops!

Dear Detlew,

❝ IMHO this suggestion is an orouboros.

Oh dear, it is!

❝ Calculating the CV from the CI and using this CV to calculate the CI will give you always the CI used in the starting step. Regardless of the design used in both steps.

❝ As you has demonstrated with your calculations .

Shit. Not that easy. Second try with a simple example. My data:

sub per seq  trt   PK  1   1  ACBD  A  1.0793  1   2  ACBD  C  1.1324  1   3  ACBD  B  0.9422  1   4  ACBD  D  0.7828  2   1  BADC  B  1.0005  2   2  BADC  A  1.1138  2   3  BADC  D  0.7245  2   4  BADC  C  0.9690  3   1  CDAB  C  0.8392  3   2  CDAB  D  0.8110  3   3  CDAB  A  1.1333  3   4  CDAB  B  1.0058  4   1  DBCA  D  0.7478  4   2  DBCA  B  0.8006  4   3  DBCA  C  1.1432  4   4  DBCA  A  0.9911  5   1  ACBD  A  1.4136  5   2  ACBD  C  0.8082  5   3  ACBD  B  1.3025  5   4  ACBD  D  1.4506  6   1  BADC  B  1.0167  6   2  BADC  A  0.9470  6   3  BADC  D  1.5021  6   4  BADC  C  1.2398  7   1  CDAB  C  1.3904  7   2  CDAB  D  1.2809  7   3  CDAB  A  1.3593  7   4  CDAB  B  1.3605  8   1  DBCA  D  1.0852  8   2  DBCA  B  0.9390  8   3  DBCA  C  1.2467  8   4  DBCA  A  1.2721  9   1  ACBD  A  1.3878  9   2  ACBD  C  1.2703  9   3  ACBD  B  1.5533  9   4  ACBD  D  1.3324 10   1  BADC  B  1.1792 10   2  BADC  A  0.9035 10   3  BADC  D  1.1517 10   4  BADC  C  1.1225 11   1  CDAB  C  1.1025 11   2  CDAB  D  1.0596 11   3  CDAB  A  1.5024 11   4  CDAB  B  0.8432 12   1  DBCA  D  1.1236 12   2  DBCA  B  1.3696 12   3  DBCA  C  0.6106 12   4  DBCA  A  0.6973

Running the models gives in the comparisons vs A:

 Test    Method        PE     90% CI     CVintra  B   pooled ANOVA   96.62  83.41 111.91  21.45      Two-at-a-Time  96.62  80.90 115.39  23.72  C   pooled ANOVA   93.16  80.43 107.91  21.45      Two-at-a-Time  93.16  82.48 105.23  16.15  D   pooled ANOVA   93.79  80.97 108.64  21.45      Two-at-a-Time  93.79  79.44 110.74  22.47

Say the CIs of the three comparisons are published but not the method. Two cases:
1. The analysis was performed by the pooled ANOVA.
If we plug in the CIs of B/A, C/A, and D/A we get in all comparisons 21.45% for the pooled ANOVA and 20.06% for the Two-at-a-Time Principle (TaaTP).
2. The analysis was performed by the TaaTP.
We get different results, namely for
B/A: 26.05% and 24.35%
C/A: 17.71% and 16.57%
D/A: 24.32% and 22.73%
Now I think we have sumfink to work with. If we get identical results, it means that a pooled analysis was performed and the TaaTP otherwise.
What puzzles me is that in the latter case the calculated CVs don’t match the models’ (24.35↔23.72, 16.57↔16.15, 22.73↔22.47). Knapp vorbei ist auch daneben. Degrees of freedom?

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
d_labes
★★★

Berlin, Germany,
2019-02-20 20:45
(1436 d 02:16 ago)

@ Helmut
Posting: # 19946
Views: 9,213

## Oops! df?

Dear Helmut,

❝ What puzzles me is that in the latter case the calculated CVs don’t match the models’ (24.35↔23.72, 16.57↔16.15, 22.73↔22.47). Knapp vorbei ist auch daneben.

My grandma had another sentence in some sort of Plattdütsch language: Dicht doarnebn is ok vorbü.

❝ Degrees of freedom?

Presumable YES. Since you have already done the Two-at-a-Time evaluation, look at the error degrees of freedom. And be so kind to post them here, and pay attention to look at the df's for all comparisons. Maybe they are or can be different, IIRC. Why ever.

Regards,

Detlew
Helmut
★★★

Vienna, Austria,
2019-02-20 21:43
(1436 d 01:18 ago)

@ d_labes
Posting: # 19947
Views: 8,914

## Oops! df?

Dear Detlew,

❝ ❝ Degrees of freedom?

❝ Presumable YES. Since you have already done the Two-at-a-Time evaluation, look at the error degrees of freedom. And be so kind to post them here, and pay attention to look at the df's for all comparisons. Maybe they are or can be different, IIRC. Why ever.

ANOVA: 30 (well…)
TaaTP:
B/A 8
C/A 8
D/A 9

8? 9?? What the heck? Checked my setup until my eyes got dry. In all datasets for the TaaTP I have 12 subjects. Each of the four sequences is allocated to three subjects: ACBD (1, 5, 9), BADC (2, 6, 10), CDAB (3, 7, 11), DBCA (4, 8, 12). Each subject is allocated to exactly two (and the correct) treatments. I don’t get it.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
d_labes
★★★

Berlin, Germany,
2019-02-21 11:54
(1435 d 11:07 ago)

@ Helmut
Posting: # 19956
Views: 9,084

## Oops! df!

Dear Helmut,

❝ ❝ ❝ Degrees of freedom?

❝ ❝

❝ ❝ Presumable YES. ... Maybe they are or can be different, IIRC. Why ever.

❝ ANOVA: 30 (well…)

❝ TaaTP:

❝   B/A 8

❝   C/A 8

❝   D/A 9

❝ 8? 9?? What the heck? ... I don’t get it.

Ok, something like that I have expected.
Let's try a 'theoretical' approach. Since we do not recode the periods and / or sequences the df can be obtained via (model without decomposition of the subjects effect into sequence and subject within sequence, design 4x4)

source    df ------------------------------- Total    2*n-1 = 23 treat    t-1   =  1 period   p-1   =  3 subject  n-1   = 11 ------------------------------- error    n-4   = 23-1-3-11 = 8 -------------------------------

So far so good. Two numbers of three 'explained'. Why the heck the comparison D/A has one degree of freedom more: Duno .
We have already noticed a similar effect for the EMA 'crippled' model for replicate designs. See this post.

Nevertheless: The degrees of freedom are different for the 2x2 design and the design of the TaaTP. We can mimic the df's, at least approximately, if we use the robust df's.

Regards,

Detlew
zizou
★

Plzeň, Czech Republic,
2019-02-21 12:33
(1435 d 10:28 ago)

@ Helmut
Posting: # 19957
Views: 8,910

## Oops! df?

Hello everybody and nobody.

It reminds me of this discussion.

Best regards,
zizou
nobody
nothing

2019-02-21 13:42
(1435 d 09:19 ago)

@ zizou
Posting: # 19958
Views: 9,088

## Oops! df?

❝ Hello everybody and nobody.

... I'm not a "Mensch mit Migränehintergrund" but I feel a very strong headache crawling up my neck and this forum is apparently not really helpful with my chronic insomnia...

Kindest regards, nobody
d_labes
★★★

Berlin, Germany,
2019-02-21 15:49
(1435 d 07:12 ago)

@ zizou
Posting: # 19959
Views: 8,878

## All the answers are here

Dear Zizou,

THX for reminding me that post I had totally forgotten.

As I said numerous times: All the answers are here in the Forum.
Even for questions not asked .

Regards,

Detlew
Rosy
☆

Mexico,
2019-02-20 16:25
(1436 d 06:36 ago)

@ Helmut
Posting: # 19939
Views: 9,143

## PowerTOST: CVfromCI

❝              Not interested in other members’ opinions?

I'm sorry if I looked rude, I was just trying to follow the thread of the publication ... of course, I'm interested in any opinion. My deepest apologies to everyone.

Parallel‽

I had a miscomprehension of the statistical analysis, i read again and they used an ANOVA included the following factors: sequence (SEQ), subject nested within sequence (SUBJECT [SEQ]), period (PHASE), and treatment (TREAT). I though that they maked a paired comparation, one at time.

But in this case: https://accp1.onlinelibrary.wiley.com/doi/abs/10.1177/009127009903901108?sid=nlm%3Apubmed

The study had an open-label, single-dose, three-way crossover design. Subjects were randomly assigned to receive one of three treatments per period

Design: 3x2 N= 17

A vs B ----> IC (84.9-106)
A vs C ----> IC (169-211)
B vs C ----> IC (178-222)

How to calculate %CV Intra-individual???

100*CVfromCI(lower=0.849, upper=1.06, n=17, design='2x2x3', alpha=0.05)

it's that correct???
Helmut
★★★

Vienna, Austria,
2019-02-20 17:14
(1436 d 05:48 ago)

@ Rosy
Posting: # 19941
Views: 8,930

## type known.designs() in PowerTOST

Hi Rosy,

❝ The study had an open-label, single-dose, three-way crossover design. Subjects were randomly assigned to receive one of three treatments per period

Was it a Latin Square (ABC|BCA|CAB) or a Williams’s design (ABC|ACB|BAC|BCA|CAB|CBA)? Not mentioned anywhere in the paper. But this part is strange:

Seventeen healthy [] were enrolled.

Enrolled, how comes? It is OK to have dropouts but to start a study with incomplete sequences is bizarre. The sample size has to be a multiple of the number of sequences.

❝ A vs B ----> IC (84.9-106)

❝ A vs C ----> IC (169-211)

❝ B vs C ----> IC (178-222)

❝ 100*CVfromCI(lower=0.849, upper=1.06, n=17, design='2x2x3', alpha=0.05)

❝ it's that correct???

No, it isn’t. "2x2x3" is for the two-treatment two-sequence three-period full replicate design (TRT|RTR).
For the Latin Square use "3x3" and for the Williams’ design "3x6x3". BTW, in all functions of PowerTOST the default is alpha=0.05. As long as you deal with the 100(1–2×0.05) = 90% confidence interval you can simply leave it out.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
Rosy
☆

Mexico,
2019-02-20 18:14
(1436 d 04:47 ago)

@ Helmut
Posting: # 19942
Views: 8,931

## type known.designs() in PowerTOST

Hi Helmut :)

A vs B ----> IC (84.9-106) ----> 19.16
A vs C ----> IC (169-211) -----> 19.16
B vs C ----> IC (178-222) -----> 19.07

If i assume a 3x3 design, i will have a %CV of each comparation after calculation (100*CVfromCI(lower=1.69, upper=2.11, n=17, design='3x3), that is almost the same in each case, that is consider the intra-individual variability of the drug to calculate a sample size for a 2x2 study?