Sasi
☆

2008-06-10 10:44
(edited by Jaime_R on 2008-06-10 11:48)

Posting: # 1933
Views: 21,575

Calculation of AUC0-72 [NCA / SHAM]

Dear all

in BA/BE study i need to calculate AUC0-72 instead of AUClast and AUCinf how can i calculate this value by using winnonlin.

How many minimum concentrations requried for calculation of t1/2 and Kel.

Thanks and regards
sasi

--
Edit: Category changed. [Jaime]
Jaime_R
★★

Barcelona,
2008-06-10 12:18

@ Sasi
Posting: # 1934
Views: 19,333

Calculation of AUC0-72

Hi Sasi!

» ... i need to calculate AUC0-72 instead of AUClast and AUCinf how can i calculate this value by using winnonlin.

I'm not sure whether I understand your question.
• If your study was planned to be evaluated with AUC0-72 as the primary target parameter, I would expect that your last sampling time point was 72 hours - therefore AUC0-72 = AUClast.
• If you have sampled for a longer time period and later on changed your mind (why?), you have to exclude these time points from calculations:
Assuming your sampling times are contained in a column named 'time' > click this column once > Data > Exclude > Criteria >
Write '72' in the field 'Find'
In the 'Search Area' select the second option 'Column: time'
In the 'Operation' field select '>'
Check [x] the box 'Exclude Row Matching Criteria'
Click 'Exclude'
Then proceed as usual in th BE-wiz.

» How many minimum concentrations requried for calculation of t1/2 and Kel.

For the estimation of kel 3, for the calculation of t½ zero. SCNR

Regards, Jaime
Ohlbe
★★★

France,
2008-06-10 17:28

@ Jaime_R
Posting: # 1935
Views: 19,392

Calculation of AUC0-72

Dear all,

» » How many minimum concentrations requried for calculation of t1/2 and Kel.
»
» For the estimation of kel 3, for the calculation of t1/2 zero. SCNR

What is the point in calculating kel and t½, if you are using truncated AUC ?

If you are truncating your AUC at 72 h, it probably means that you have a drug with a long terminal half-life. The points you have till 72 hours may not be sufficient and adequate to provide a reliable estimate of kel.

Regards
Ohlbe
Jaime_R
★★

Barcelona,
2008-06-10 18:45

@ Ohlbe
Posting: # 1936
Views: 19,200

Calculation of AUC0-72

Dear Ohlbe!

» What is the point in calculating kel and t1/2, if you are using truncated AUC ?

Of course you are right; estimating kel in a truncated setting doesn't make any sense! I answered too quickly (minimum 3 points...) and forgot the post's subject line. Sorry.

Regards, Jaime
d_labes
★★★

Berlin, Germany,
2009-06-18 09:26

@ Jaime_R
Posting: # 3872
Views: 18,214

Regulators truncated

Dear Ohlbe, dear Jaime, dear all,

let me share some experience with regulators in the EMEA. In a recent submission of a BE study with a long half-life product (t1/2 from literature about 50-70 h) we submitted an evaluation with AUC(0-72h), Cmax and tmax as metrics, the typical truncated area setting.

Regulators response:
The French asked for lamdaZ (kel) and t1/2!

Hopefully they will not ask for residual area <20% .

Regards,

Detlew
Ohlbe
★★★

France,
2009-06-18 10:37

@ d_labes
Posting: # 3874
Views: 18,105

Regulators truncated

Dear D. Labes,

» Regulators response:
» The Germans asked for AUC(0-inf)!
» The French asked for lamdaZ (kel) and t1/2!
»
» Hopefully they will not ask for residual area <20% .

I hesitate between and

Regards
Ohlbe

Regards
Ohlbe
Helmut
★★★

Vienna, Austria,
2009-06-18 14:49

@ d_labes
Posting: # 3875
Views: 18,156

Regulators truncated

Dear D. Labes,

To be honest, which kind of 'truncation' are you dreaming of?
(a)(b) (c)

Cheers,
Helmut Schütz

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

Berlin, Germany,
2009-06-18 15:26

@ Helmut
Posting: # 3877
Views: 18,142

Regulators truncated

Dear Helmut,

after long thinking I would go for (a) + (b) + (c) and additionally for keelhauling under the command of ElMaestro.

I have a suggestion: What about holding your fine lectures especially for regulators? Eventually the great EMEA pays a good price.

Now leaving for Salzburg to visit your fine country and the birthplace of "Wolferl" Mozart. I hope to forget for a while ...

Regards,

Detlew
Helmut
★★★

Vienna, Austria,
2009-06-18 15:44

@ d_labes
Posting: # 3878
Views: 18,229

Regulators truncated

Dear D. Labes,

» keelhauling under the command of ElMaestro.

Must be fun!

» I have a suggestion: What about holding your fine lectures especially for regulators?

Oh, some of them are regularily listening to my lectures with great disgust.

» Eventually the great EMEA pays a good price.

Great idea. Normally I’m not paid to give presentations. The Austrian Agency asked me back in 2000, but were shocked by the quotation.
The only regulatory authority asking me recently was the Saudi FDA . Since I don’t wear suits (don't even own one) I asked about dresscode being told that jeans/jacket would be OK.

» Now leaving for Salzburg to visit your fine country and the birthplace of "Wolferl" Mozart.

If possible avoid the Getreidegasse!

Cheers,
Helmut Schütz

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

Belgium?,
2009-06-19 22:16

@ Helmut
Posting: # 3883
Views: 18,153

Regulators truncated

Oh,
did the Saudi FDA also try to get you to do the one-week tuition?
How was it? I would have loved to go, but couldn't for a number of reasons. But then again, Belgian sailors ain't of much use in the desert.

EM.
Helmut
★★★

Vienna, Austria,
2009-06-19 22:35

@ ElMaestro
Posting: # 3884
Views: 18,215

Regulators truncated

Ahoy!

» did the Saudi FDA also try to get you to do the one-week tuition?

They asked for a workshop – whateverthatmeans.

» How was it?

Wrong tempus. They asked me already two years ago, and nothing happened – last month again. I’m not the type of guy doing client acquisition. If they really want me to go, they will come up again; if not – not.

» But then again, Belgian sailors ain't of much use in the desert.

Yeah, but SA has a quite lengthy shoreline with some nice harbors.

Cheers,
Helmut Schütz

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

Belgium?,
2009-06-18 14:50

@ d_labes
Posting: # 3876
Views: 18,245

Luke 23:34

"Forgive them, for they know not what they do."

EM.
d_labes
★★★

Berlin, Germany,
2008-09-05 15:00

@ Ohlbe
Posting: # 2323
Views: 19,101

Calculation of AUC0-72

Dear Ohlbe, dear Jaime, dear all,

I would like to discuss this a bit further.
How do you act in a truncated setting if the last sample is missing? Or if some subject has conc. <LOQ due to faster kinetics?

Omit this subject from the analysis? Or try to extrapolate to t=72h?

If extrapolation is an option for you: how?
Using an estimate of lamdaZ or by the last preceding 2 points?

Regards,

Detlew
Helmut
★★★

Vienna, Austria,
2009-01-26 16:24

@ d_labes
Posting: # 3123
Views: 18,911

Calculation of AUC0-72

Dear D. Labes,

sorry for the late response – I was driven by discussions about the drafted European BE-Guideline.

» I would like to discuss this a bit further.
» How do you act in a truncated setting if the last sample is missing? Or if some subject has conc. <LOQ due to faster kinetics?
»
» Omit this subject from the analysis?

I have heard of CROs omitting subjects if AUC72 was stated as the primary parameter and the sample at 72 h (or earlier) was ≤LOQ. In the strict sense I would consider this correct.
But: with the current trend of moving from seening BE as a surrogate of clinical safety/efficacy to a measure of pharmaceutical performance in vivo I would go with Kamal Midha’s Mantra and accept AUCs where the absorption is completed (Clast ≥2–4 times tmax). See Example 2 in this thread. If we truncate AUCs of subjects with Clast<72 (for any treatment) at the last time point where C>LOQ (for all treatments), it should be possible to get an unbiased estimate of the T/R-ratio.* Unfortunately this method is not available in commercial software (at least not in the current versions of WinNonlin, Kinetica, EquivTest/PK).

I wouldn’t start trying to get an estimate of C72.

Edit (years later)
• Fisher D, Kramer W, Burmeister Getz E. Evaluation of a Scenario in Which Estimates of Bioequivalence Are Biased and a Proposed Solution: tlast (Common). J Clin Pharm. 2016;56(7):794–800. doi:10.1002/jcph.663. free resource.

Cheers,
Helmut Schütz

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

Berlin, Germany,
2009-01-26 16:57

@ Helmut
Posting: # 3125
Views: 18,553

Calculation of AUC0-72

Dear Helmut,

» sorry for the late response – I was driven by discussions about the drafted European BE-Guideline.

"Late is not too late".

I am with you if the values in the last part of the concentration time course are <LOQ. But I think it's different with missing values (vial broken or so) especially in case of long half life drugs.

Because time points are spread occasionally with 24h in the last part, there may be a considerable portion of AUC missing.

» I wouldn’t start trying to get an estimate of C72.

Is this sentence then furthermore your opinion?

Regards,

Detlew
Helmut
★★★

Vienna, Austria,
2009-01-26 17:20

@ d_labes
Posting: # 3126
Views: 18,570

Calculation of AUC0-72

Dear D. Labes,

» I am with you if the values in the last part of the concentration time course are <LOQ. But I think it's different with missing values (vial broken or so) especially in case of long half life drugs.

If a value is missing – or even came up as <LOQ in repeated analyses – and is included within values which are clearly (!) above LOQ I routinely substitute such a value by a (log)interpolated estimate. I have such a procedure since decades (oh, I’m getting old) in my protocols, and never got any problems.

» Because time points are spread occasionally with 24h in the last part, there may be a considerable portion of AUC missing.

This wouldn’t bother me as long as Clast ≥2–4 times tmax.

» » I wouldn’t start trying to get an estimate of C72.
»
» Is this sentence then furthermore your opinion?

Yes.

Cheers,
Helmut Schütz

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

Berlin, Germany,
2009-01-27 11:48

@ Helmut
Posting: # 3137
Views: 18,655

The missing 72h

Dear Helmut,

» ... I have such a procedure since decades (oh, I’m getting old) in my protocols ...

Don't lose heart! Getting old is not for sissies (Bette Davis) !

I have the vague suspicion that I have not explained my point precise enough.

So let me give an example (real data):
        time      Conc. ----------------------------------  1     0.0        0.00  2     0.5        0.00  3     1.0        2.55  4     2.0        9.79  5     3.0       13.23  6     4.0       14.43  7     5.0       12.49  8     6.0       12.78  9     7.0       10.96 10     8.0       12.40 11    10.0       11.68 12    12.0       11.26        * 13    24.0        8.36        * 14    48.0        7.53        * 15    72.0        4.78 (missing) ----------------------------------

Half live for this curve with no missings is 53.6 h (using points 12-72 h).
AUC(0-72)=584.93 (linear trapezoidal rule for sake of simplicity).

If now the conc. value at 72h is missing unfortunately (vial broken or so), what to do?
AUC(0-48h) is 437.21, considerably lower than AUC(0-72), only 75%.
1. Option: Exclude subject
2. Option: Use AUC(0-48)
3. Option: Extrapolate to 72h (C(calc.)=5.69 using log-lin regression with * points) and calculate then AUC (result=595.85).
Other users also a position?

Regards,

Detlew
Ohlbe
★★★

France,
2009-01-28 00:00

@ d_labes
Posting: # 3148
Views: 18,595

The missing 72h

Dear D. Labes,

» 1. Option: Exclude subject
» 2. Option: Use AUC(0-48)
» 3. Option: Extrapolate to 72h (C(calc.)=5.69 using log-lin regression with * points) and calculate then AUC (result =595.85).

Whichever option you select, you can be sure there will be an Agency to say it was the wrong one... (At least the French Agency, I guess )

» 1. Option: Exclude subject
They will hate that... They will be afraid that you may pretend to have broken a tube in order to remove a subject with "annoying" results...

» 2. Option: Use AUC(0-48)
I suppose you would do that for both treatments. In a way you would introduce a bias by using an under-estimated AUC... And you might be suspected again of playing with the data.

» 3. Option: Extrapolate to 72h (C(calc.)=5.69 using log-lin regression with * points) and calculate then AUC (result=595.85).
Introducing another bias. The question will be, how reliable is your estimate ? It will depend on the PK of the drug (mono- or multicompartmental), sampling times, etc. (Basically, if you remove the last sample, will the calculated half-life still be the terminal half-life ?). Probably closer to the truth than Option 2, but they may refer to the current EU guideline: "The exclusive use of compartmental based estimates are not recommended", and forget about "exclusive".

I'm not even sure my opinion would be worth twopence here, but... write in your protocol what you would do in such a situation, do it this way, and keep you fingers crossed, hoping for your file to be reviewed by an assessor with not more than 30 or 60 minutes on his hands (ElMaestro would say you have good chances).

Regards
Ohlbe
martin
★★

Austria,
2009-01-28 08:26

@ Ohlbe
Posting: # 3150
Views: 18,443

sensitivity analyses ?

dear ohlbe !

what do you think about a sensitivity analysis?

best regards

martin

Ps.: in my opinion the best way to handle this issue is to perform a blinded review and specify the method how you will handle this issue (may be motivated by sensitivity analyses in combination with monte carlo methods)
d_labes
★★★

Berlin, Germany,
2009-01-28 09:54

@ Ohlbe
Posting: # 3151
Views: 18,394

Regulators ways are inscrutable

Dear Ohlbe,

» Whichever option you select, you can be sure there will be an Agency to say it was the wrong one... (At least the French Agency, I guess )

Is it that evil with your experience with regulators?

» [...] I'm not even sure my opinion would be worth twopence here [...]

I would pay 4 cents (Euro cents of course) .

Regards,

Detlew
Ohlbe
★★★

France,
2009-01-28 10:16

@ d_labes
Posting: # 3152
Views: 18,419

Regulators ways are inscrutable (at least the French)

Dear D. Labes,

» » Whichever option you select, you can be sure there will be an Agency to say it was the wrong one... (At least the French Agency, I guess )
»
» Is it that evil with your experience with regulators?

Andrew Leary wrote that 'The English are a strange bunch who take pleasure in disagreeing with everyone else'. In France this is not a pleasure, but a very serious and full-time job .

Best regards
Ohlbe
ElMaestro
★★★

Belgium?,
2009-01-28 14:32

@ d_labes
Posting: # 3155
Views: 18,689

The missing 72h

» 1. Option: Exclude subject
» 2. Option: Use AUC(0-48)
» 3. Option: Extrapolate to 72h (C(calc.)=5.69 using log-lin regression with * points) and calculate then AUC (result=595.85).

Hi,

I'd go for option 3 (after all we are used to extrapolations when it comes to AUCinf and nobody has a problem with that. If you can extrapolate something to inf then why not to 72 hrs. as well?!).

Excluding a subject is a possibility if something went wrong (vial broken, a UFO landed and the chromatograph melted, etc).
The CHMP has been working a lot on aspects of missing values etc, and they have come up with all sorts of strange concepts that have very little relevance for this situation.

Finally, depending on the combo of RMS and CMSs it might not make a difference at all what you choose. Of course, if you advertise in a very clear manner that something is fishy in the dataset then you might be able to force the assessor to look into it, but why not just leave it as it is and mention it on page 3848 and hope for the best.

Martin: 'Sensitivity analyses' (them being a lot of things) are probly a good idea. But it has absolutely no focus for PK assessors at the moment. But in a centralised procedure with survival curves the CHMP will sing with loud and clear voice "oh yeah, gimme gimme gimme sensitivity analyses"

EM.
d_labes
★★★

Berlin, Germany,
2009-01-28 14:51

@ ElMaestro
Posting: # 3156
Views: 18,535

Page 3848 of 221

Dear ElMaestro,

» [...] to force the assessor to look into it, but why not just leave it as it is and mention it on page 3848 and hope for the best.

Very good idea! I will add always a page 3848 to my 221 (or so) pages PK report in the future!

All jokes aside. Thanks for your points. I agree with you.

Regards,

Detlew
Astea
★

Russia,
2017-03-11 20:14

@ d_labes
Posting: # 17149
Views: 9,788

Partial AUC calculation

Dear all!
Sorry for reviving the battered topic but for validation purposes I need to understand the methods of calculating partial areas in some nasty cases. I have a premonition that it would be hard to understand my question so I’ll try to use more illustrations…

Suppose we have to calculate AUC0-72. The biggest problem is to decide: to extrapolate or nor to extrapolate. Let us follow the first scene. Suppose that the protocol states to use a simple linear trapezoid method to calculate AUC. How to calculate AUC0-72 in the following situations?
1. There were time deviations in the first point (that is instead of t0=0, we have, for example, t0=1 hour)
2. There were time deviations in the last sample point (that is instead of tlast=72 h we have tlast=71 h or tlast=73 h). Additionally what if we have concentrations below LLOQ in the several last points (agree it is strange for drugs with long half-life but who knows..)?
3. There were abscent samples (NA) at the last time point 72 h
As Phoenix WinNonLin® presents itself as a golden standard of NCA, I tried to understand what methods does it use in the uppermentioned cases.

To compare different methods I used the following concentration-time table:

 time      Conc.  ---------------------------------- 0    0 (NA) 1   3 2   17 3   55 4   87 5   190 6   250 7   315 8   330 10   230 12   185 16   115 18   100 24   125 48   100 72(71,73)    77 (NA)  ----------------------------------

1. Let us start with the first case: as it is intuitevily simple we just use a linear approximation to zero point. It is hard to invent an alternative approach because it is difficult to approximate by a known function the absorbtion part of the curve. Only if there was a non-zero concentration in the first sample (not enough wash-out or some unsufficient endogenous calculation) the results would differ.
AUClast=AUCall=AUC0-72=8391

2. To calculate AUC0-72 (AUC truncated) for the cases with tlast>72 h we can just truncate (cut down) at the time t=72 h (see the upper picture).
For tlast=73: AUClast=AUCall=8479.5; AUC0-72=8402.0

But when we deal with tlast<72 h there appear different opportunities to get the value at t=72 h:
a). rude linear approximation (over the two last values or over the elimination period)
For tlast=71: C72=76
b). log-linear interpolation (over the elimination period)
For tlast=71: C72=76.84
( AUClast=AUCall=8302.5);
After assessing the concentration at 72 h we have to calculate the area under the last curve.
It can be done via:
- linear trapezoid method
1+C2)/2*(t2-t1)
AUC0-72=8379.0
- log trapezoid method
1-C2)/(ln С1-lnC2)*(t2-t1)
AUC0-72=8376.9
I can’t imagine what else there could be done. What method does WinNonLin use if it gets a value 8379.421 (very close to linear interpolation but not equal to it)

3. If there were no samples at t=72 h, the last point can be approximated by linear or log-linear interpolation and area can be calculated via linear or log trapezoid as in the previous case.
Comparing the results of the calculation I conclude that in this case WinNonLin use:
- Log-linear interpolation and log trapezoid method to calculate AUC0-72.
AUClast=AUCall=6267; AUC0-72=7983.3
The question arises: is it not strange to calculate the last part by log trapezoid method while the whole curve is calculated via untransformed trapezoid? Of course log interpolation is more preferable for the elimination part of the curve but we initially stated to use untransformed method.
Why does the situations 2) and 3) have different solution methods?

"Being in minority, even a minority of one, did not make you mad"
mittyri
★★

Russia,
2017-03-16 19:46

@ Astea
Posting: # 17159
Views: 9,697

Partial AUC calculation

Dear Astea,

» 1. There were time deviations in the first point (that is instead of t0=0, we have, for example, t0=1 hour)
I didn't get this. Does that mean the deviation in dosing time or what?

» 2. There were time deviations in the last sample point (that is instead of tlast=72 h we have tlast=71 h or tlast=73 h). Additionally what if we have concentrations below LLOQ in the several last points (agree it is strange for drugs with long half-life but who knows..)?
» 3. There were abscent samples (NA) at the last time point 72 h

I think all options are described in WNL Guide:
• If a start or end time falls within the range of the data but does not coincide with an observed data point, then a linear or logarithmic interpolation is done to estimate the corresponding Y, according to the AUC Calculation method selected in the NCA Options. (See “NCA Options tab” on page 42.) Note that logarithmic interpolation is overridden by linear interpolation in the case of a non-positive endpoint.
• If a start or end time occurs after the last numeric observation (i.e., not “missing” or “BQL”) and λz is estimable, λz is used to estimate the corresponding Y:

Y = exp(alpha – λz * t)
= exp(alpha – λz * tlast) * exp(–λz * (t-tlast))
= (predicted concentration at tlast) * exp(–λz * (t-tlast))

The values alpha and λz are those values found during the regression for λz The value for alpha is not given in the normal output, but can be obtained by selecting the Intermediate Output checkbox on the Options tab, and finding the alpha in the Core Output. Note that a last observation of zero will be used for linear interpolation, i.e., this rule does not apply prior to a last observation of zero.
• If a start or end time falls after the last numeric observation and λz is not estimable, the partial area will not be calculated.
• If both the start and end time for a partial area fall at or after the last positive observation, then the log trapezoidal rule will be used. However, if any intervals used in computing the partial area have non-positive endpoints or equal endpoints (for example, there is an observation of zero that is used in computing the partial area), then the linear trapezoidal rule will override the log trapezoidal rule.

» The question arises: is it not strange to calculate the last part by log trapezoid method while the whole curve is calculated via untransformed trapezoid? Of course log interpolation is more preferable for the elimination part of the curve but we initially stated to use untransformed method.

Then we need to use another lambda for 'linear regression', right? How to calculate it? Should we use some rules for it? How many points do we need?
So many questions as you see...
Think about WNL Partial Areas rules as about huge combination of compromises.
You're free to create your own rules in WNL or in R or other data management/plotting tool.

» Why does the situations 2) and 3) have different solution methods?

Different ClastPreds, different Lambdas, different solutions

Kind regards,
Mittyri