Bioequivalence and Bioavailability Forum

Helmut
★★★

Vienna, Austria,
2012-10-11 19:29
(4070 d 06:27 ago)

Posting: # 9393
Views: 7,704

Precision of CVwr in replicate designs [General Statistics]

Dear all,

I’m wondering what we can say about the precision of estimated CV_WR in different replicate designs. One full replicate (TRTR|RTRT) and the partial replicate (TRR|RTR|RRT) are mentioned by both the FDA and the EMA. An alternative full replicate, but requiring only three periods was used by the Lászlós in 2009 and is also mentioned in the new Russian draft GL, namely TRT|RTR. On the contrary to the partial replicate we could also derive CV_WT. For CV 30%, T/R 95%, 80% target power I get n=20 for the 4-period design and n=30 for both 3-period designs with power of 82.02% in all designs. So far so good. What about the precision of the estimated CV_WR? Let’s look from how many subjects the value is estimated:

TRTR|RTRT:   20 (100%)

TRR|RTR|RRT: 30 (100%)

TRT|RTR:     15 (50%)

Heretic question: From TRT|RTR the estimate will be less precise (only half of the subjects used), but we get additional information about the test. Less chance of outliers? Duno.

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

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Science Quotes

jag009 ★★★ NJ, 2012-10-12 18:52 (4069 d 07:04 ago) @ Helmut Posting: # 9407 Views: 6,501	Precision of CVwr in replicate designs Post reply
	Hi Helmut, ❝ An alternative full replicate, but requiring only three periods was used by the Lászlós in 2009 and is also mentioned in the new Russian draft GL, namely TRT\|RTR. Could you provide the reference for the Laszlos paper? Thanks John

Helmut
★★★

Vienna, Austria,
2012-10-12 19:37
(4069 d 06:19 ago)

@ jag009
Posting: # 9408
Views: 6,815

Tóthfalusi et al. (2009)

Post reply

Hi John!

❝ Could you provide the reference for the Laszlos paper?

Tóthfalusi L, Endrényi L, García Arieta A. Evaluation of Bioequivalence for Highly Variable Drugs with Scaled Average Bioequivalence. Clin Pharmacokinet. 2009;48(11):725–43. doi:10.2165/11318040-000000000-00000

These simulations (GMR restriction 0.8–1.25, CV 35, 45, 55%; each data point representing 10 000 studies) are based on a TRT|RTR design in 36 subjects. Circles: unscaled, squares: EMA’s method (without the 50% cap – paper published before the BE-GL), triangles: FDA’s method. Studies passing = empiric power.

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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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d_labes
★★★

Berlin, Germany,
2012-10-17 12:40
(4064 d 13:16 ago)

@ Helmut
Posting: # 9427
Views: 6,783

Precision of CVwr in replicate designs

Post reply

Dear Helmut,

❝ I’m wondering what we can say about the precision of estimated CV_WR in different replicate designs. [...] Let’s look from how many subjects the value is estimated:

❝ TRTR|RTRT: 20 (100%)

❝ TRR|RTR|RRT: 30 (100%)

❝ TRT|RTR: 15 (50%)

❝ Heretic question: From TRT|RTR the estimate will be less precise (only half of the subjects used) ...

The 50% is only valid if you talk EMA :-D

.
Otherwise all the data are used for the fit of a (mixed) model.

Why not use the confidence intervals of the covariance parameter estimates from the fit of a mixed model as precision? Ok, this leaves out the partial replicate design because we are not aware if the σ²_WR is valid from fitting the mixed model, at least in the form of FDA code.

At least we can think in terms of intra-subject contrasts to estimate σ²_WR via an ANOVA with sequence group as the solely effect (as implemented in the FDA progesterone guidance in the framework of scaled ABE). The df for this analysis are n-seq where n is the number of intra-subject contrasts evaluable (=subject/2 in case of design TRT|RTR i.e. the 50% above are again correct).

Thus take formulas given by your own in the early days of this forum :cool:

for obtaining a confidence interval for σ²_WR and then transformed to CV to obtain a measure of the precision of estimated CV_WR.

Lets go with the numbers of subjects given by you and assume that the estimated CV is obtained always as 20% (statistically only with vanishing probability :-D

# R function upper confidence limit of CV - as one liner

CVUCL <- function(alpha=0.05, CV, df){

  sqrt(exp(log(1.0 + CV^2)*df/qchisq(alpha,df))-1)

}

gives

design         n   df  upper CL

TRTR|RTRT     20   18   27.94%

TRR|RTR|RRT   30   27   26.03%

TRT|RTR       15   13   30.07%

BTW: May it be that there is an error in this post in calculating SS-intra from MS-intra? The final result is again correct :cool:

. That remains me on my old school days: Bad school grade (5) if final result correct but intermediate steps with errors :-D

—
Regards,

Detlew

Helmut
★★★

Vienna, Austria,
2012-10-17 17:28
(4064 d 08:28 ago)

@ d_labes
Posting: # 9428
Views: 6,365

Great post!

Post reply

Dear Detlew,

you made my day!

❝ Lets go with the numbers of subjects given by you and assume that the estimated CV is obtained always as 20% (statistically only with vanishing probability :-D ):

❝ # R function upper confidence limit of CV - as one liner

❝ CVUCL <- function(alpha=0.05, CV, df){

❝ sqrt(exp(log(1.0 + CV^2)*df/qchisq(alpha,df))-1)

❝ }

❝ gives

❝ design n df upper CL

❝ TRTR|RTRT 20 18 27.94%

❝ TRR|RTR|RRT 30 27 26.03%

❝ TRT|RTR 15 13 30.07%

Interesting that the CV from the partial replicate is (although slightly) more precise than the 4-period 2-sequence full replicate. I didn’t expect that. Which design is the ‘best’? Pros & cons:

TRTR|RTRT
Pro: CV_WR and CV_WT estimable, model code from EMA and FDA available (not specified for CV_WT, but trivial), ~33% fewer subjects than in the 3-period designs, sample size tables available.
Con: Four periods (blood samples, drop-outs), CV slightly less precise than from the partial replicate.
TRR|RTR|RRT
Pro: Only three periods, code available, most precise estimate of CV_WR, sample size tables available.
Con: No estimate of CV_WT, ~50% more subjects than in the 4-period replicate (might require slightly more than +50%, sequences multiple of three).
TRT|RTR
Pro: CV_WR and CV_WT estimable, sample size – marginally – smaller than partial replicate.
Con: Less precise estimate than from the other designs, no official code, no sample size tables (simulations required).

❝ BTW: May it be that there is an error in this post in calculating SS-intra from MS-intra?

Blast! Will correct it.

❝ The final result is again correct :cool: . That remains me on my old school days: Bad school grade (5) if final result correct but intermediate steps with errors :-D .

Happened to me regularly. Especially if the final result came from my neighbor – who was much better in maths than I ever was. :lol3:

—
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, 2012-10-17 18:39 (4064 d 07:17 ago) @ Helmut Posting: # 9429 Views: 6,410	Nice to know? Post reply
	Dear Helmut, ❝ you made my day! My pleasure! Being pleased to do it again. ❝ Which design is the ‘best’? Pros & cons: [...] May be that the precision of CV_wR is different between these designs if powered to the same value of stating BE. But in no guidance I know the precision of CV_wR is an criterion. And we don't use it in any decision. So what? Nice to know? — Regards, Detlew

Helmut
★★★

Vienna, Austria,
2012-10-17 21:11
(4064 d 04:45 ago)

@ d_labes
Posting: # 9430
Views: 6,410

Nice to know!

Post reply

Dear Detlew!

❝ ❝ Which design is the ‘best’? Pros & cons: [...]

❝

❝ May be that the precision of CV_wR is different between these designs if powered to the same value of stating BE.

❝ But in no guidance I know the precision of CV_wR is an criterion. And we don't use it in any decision.

Yessir!

❝ So what? Nice to know?

Exactly – in the spirit of Bio-International ’94, where “Need to know vs. nice to know” was the unofficial slogan. Primarily I was interested whether it is worthwhile to go with TRT|RTR instead of the partial replicate because you get the bonus of CV_WT. Some sponsors are interested how their formulation performs but the 4-period replicate has its drawbacks.

—
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

Precision of CVwr in replicate designs [General Sta­tis­tics]

Precision of CVwr in replicate designs

Tóthfalusi et al. (2009)

Precision of CVwr in replicate designs

Great post!

Nice to know?

Nice to know!

Precision of CVwr in replicate designs [General Statistics]