Babe_Ruth
☆

USA,
2018-07-13 21:36
(1241 d 03:57 ago)

(edited by Babe_Ruth on 2018-07-13 22:19)
Posting: # 19053
Views: 6,429

## WNL Calculation of partial areas > tlast with BQL= 0 rule [Software]

I noticed something peculiar with how WNL (currently using v 6.3) calculates partial areas where BQL is imputed with 0 for samples after Tlast.

Let's say my partial area to be calculated is AUC 0-24hr. Tlast is 12h, and every sample taken after 12h was BQL (16, 24, 48, 72 hr).

I've noticed that in the 0-24hr partial area calculation, there are differences between imputing BQL with 0 and setting it as no value.

When I set BQL to "no value," then it uses the rules stated in documentation: WNL rules for partial areas are stated here. Most notably: "If ... end time falls after the last numeric observation and λz is not estimable, the partial area will not be calculated." Requiring λz suggests that WNL does not default to another calculation method in case log-linear isn't available.

However, when I set BQL to 0, it uses a linear-trapezoidal rule: (Clast + 0)*(T16 - Tlast)

Nowhere in the documentation does it say that this was the plan.

In summary, when I set BQL to 0, calculation method for partial area changes and the values slightly differ. Is this intended? Is this normal practice? In general, the differences between the two methods of calculation is less than 1%

ElMaestro
★★★

Denmark,
2018-07-13 22:25
(1241 d 03:08 ago)

@ Babe_Ruth
Posting: # 19054
Views: 5,826

## WNL Calculation of partial areas > tlast with BQL= 0 rule

Hi Babe_Ruth,

» When I set BQL to "no value," then it (blah)
»
» However, when I set BQL to 0, it uses a linear-trapezoidal rule: (Clast + 0)*(T16 - Tlast)
» Nowhere in the documentation does it say that this was the plan.

Do you mean it uses AUCpartial=0.5*(Clast + 0)*(T16 - Tlast) ?

If yes, then this is expected behaviour: Remember that you distinguish between BLQ, missing and a zero.
If you set it to zero then it means you tell WNL to believe that the value is really zero in contrast to not measured. Thus, it was quantifiable so now the last quantifiable value is no longer at t=12 but at t=16. The residual area will naturally also be zero, so the extrapolated area is zero percent. I'd say you are within expectations and specifications.

Pass or fail!
ElMaestro
Helmut
★★★

Vienna, Austria,
2018-07-13 23:28
(1241 d 02:05 ago)

@ Babe_Ruth
Posting: # 19058
Views: 5,857

## BQL = 0: bad rule

Hi Babe_Ruth,

» […] WNL (currently using v 6.3) …

Your version is four releases behind the current one (v8.1). High time to update.

» I've noticed that in the 0-24hr partial area calculation, there are differences between imputing BQL with 0 and setting it as no value.

As expected.

» When I set BQL to "no value," then it uses the rules stated in documentation: WNL rules for partial areas are stated here. Most notably: "If ... end time falls after the last numeric observation and λz is not estimable, the partial area will not be calculated." Requiring λz suggests that WNL does not default to another calculation method in case log-linear isn't available.

Correct (note that this post referred to v7.0 of 2016).

» However, when I set BQL to 0, it uses a linear-trapezoidal rule: (Clast + 0)*(T16 - Tlast)

Also correct.

» Nowhere in the documentation does it say that this was the plan.

See the last bullet point of the linked post:
• […] if […] 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.
You will not find this in the documentation of v6.3; too lazy to check its behavior.

» In summary, when I set BQL to 0, calculation method for partial area changes and the values slightly differ. Is this intended?

As designed and explained by ElMaestro above.

» Is this normal practice?

Bad practice to force BQLs after tmax to zero. I have seen many “rules” (e.g., first BQL to BQL/√2 or BQL/2, keep subsequent ones at BQL, whatsoever…). IMHO, that’s all crap. AFAIK, Martin Wolfsegger and Alexander Bauer are working on a NCA-method dealing with terminal BQLs. In the meantime I suggest to keep BQLs as they are.

Dif-tor heh smusma 🖖
Helmut Schütz

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

USA,
2018-07-16 15:02
(1238 d 10:31 ago)

(edited by Babe_Ruth on 2018-07-16 15:12)
@ Helmut
Posting: # 19066
Views: 5,681

## BQL = 0: bad rule

Thank you Helmut! and everybody else.

You are correct, I just double-checked; the documentation in v6.3 is missing the clarification for usage of linear trapezoidal rule if BQL imputed with "0" after Tlast. This is what sparked my initial question of whether this was an intended behavior within WNL or not.

» Bad practice to force BQLs after tmax to zero

What about for sparse sampling methods? If there are 3 samples/time point, wouldn't we want to use 3 values for the calculation of the mean concentration? In which case imputing BQL concentrations with a value of 0 or close to 0 would be more favorable than not including the value altogether?

Sorry if my questions seem trivial! I went to Pharmacy school, and there was only 1-2 classes on PK, nothing in-depth. I've just started in this industry. Right now I'm writing TK reports and Phase I/II stuff and I'm interested in learning more about what I'm doing.

Browsing these forums in my spare time really helps me see where others are in environment of the Ba/Be world :) Searching old topics have answered most of the questions I have had, which is super helpful.
Helmut
★★★

Vienna, Austria,
2018-07-16 16:02
(1238 d 09:31 ago)

@ Babe_Ruth
Posting: # 19067
Views: 5,929

## BQL = 0: bad rule

Hi Babe_Ruth,

» » Bad practice to force BQLs after tmax to zero
»
» What about for sparse sampling methods?

Sparse sampling is another cup of tea. Sounds trivial but actually isn’t.

» If there are 3 samples/time point, wouldn't we want to use 3 values for the calculation of the mean concentration? In which case imputing BQL concentrations with a value of 0 or close to 0 would be more favorable than not including the value altogether?

Some ideas:
• Phoenix/WinNonlin supports only the linear trapezoidal rule for spare sampling. Hence, anything is possible.
• Imputing 0 for post dose BQLs goes against the grain for me. Most commonly used is LLOQ/2. But why the heck divide by two? What I would do: Try to get an idea of the PK (well, difficult in the first TK-study of a drug). Perform simulations and based on the LLOQ & sampling schedule come up with a reasonable ratio.
• Try also the R-package PK* which contains more methods for sparse sampling designs than PHX/WNL.
Both authors are members of the forum. I’ll notify them; maybe they can jump into the discussion.

» […] I'm interested in learning more about what I'm doing.

Basic research is what I’m doing
when I don’t know what I’m doing.
Wernher von Braun

» Browsing these forums in my spare time really helps me see where others are in environment of the Ba/Be world :) Searching old topics have answered most of the questions I have had, which is super helpful.

Maybe you can convince your employer to browse the forum in your payed time…

• Jaki T, Wolfsegger MJ. Estimation of pharmacokinetic parameters with the R package PK. Pharm Stat. 2011;10(3):284–8. doi:10.1002/pst.449.

Dif-tor heh smusma 🖖
Helmut Schütz

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

Austria,
2018-07-16 20:03
(1238 d 05:29 ago)

@ Helmut
Posting: # 19071
Views: 5,686

## BQL = 0: bad rule

Dear all,

I am happy to share my thoughts regarding handling of values BLQ in sparse sampling design:

1) In such cases I would recommend using a modeling approach using M3 method of Beal for handling values BLQ.

a. For serial sampling designs (i.e. only one sample per subject): this is just a straightforward modeling exercise (i.e. no random effects) including model selection techniques / approaches

b. For a batch design (more than one sample per subject): this would require a NLME modeling approach where it’s tricky to include Beal’s M3 but possible (I think Alex did this also in SAS )

2) If you have to stick with NCA the following heuristic approach may be useful. Lets’ assume there are n time points: t1 < t2 < t3 < ti < … < tn. At each time point there are k samples where the first value BLQ is observed at time point tj < tn

a. At time point tj: set all individual values BLQ to zero and calculate the mean at this time Point tj

i. If mean <BLQ omit this and all subsequent time points

ii. If mean > BLQ find adequate imputations for individual BLQ values

iii. Adequate imputations for individual values BLQ can be for example derived by fitting a log-linear regression on previous sample time points (e.g. based on time points tj-3, tj-2, tj-1 < tj) and use the corresponding predictions at time point tj. This requires some thoughts regarding adequate selection of time points and likely a linear mixed model in case of batch design. Please note also that this Approach is valid only on the premise of linear PK (e.g. no concentration dependent clearance). Handling of values BLQ at the next time point tj+1 could be derived subsequently on a similar approach.

Please be aware that in case of more than one value BLQ at time point tj, the above imputation impacts the total variability of concentration at this time point and likely adding some variability on the individual predicted values should be advantages (e.g. as sensitivity analysis).

Best regards & hope this helps

Martin
martin
★★

Austria,
2018-07-16 20:43
(1238 d 04:49 ago)

@ Helmut
Posting: # 19072
Views: 5,647

## BQL = 0: bad rule

Dear Helmut,

» […] IMHO, that’s all crap. AFAIK, Martin Wolfsegger and Alexander Bauer are working on a NCA-method dealing with terminal BQLs […]

Yes this is correct and we have already all the maths available. However, due to some lack of resources/time this project has slowed down. However, if some forum members would have some interest in generating a corresponding manuscript they may contact me. We would just need some simulation illustrating the performance in reasonable settings where generation corresponding scenarios turned out beeing rather complex (we thought about using Beals' M3 as competitor)

best regards

Martin
mittyri
★★

Russia,
2018-07-13 23:31
(1241 d 02:02 ago)

@ Babe_Ruth
Posting: # 19059
Views: 5,743

## is zero positive?

Hi Babe_Ruth,

» However, when I set BQL to 0, it uses a linear-trapezoidal rule: (Clast + 0)*(T16 - Tlast)
well... let me try to cite it again
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.
A question:
is 0 a positive endpoint?

PS: nice to see you are using good oldie 6.3 (decennary next year)

Kind regards,
Mittyri
Helmut
★★★

Vienna, Austria,
2018-07-13 23:58
(1241 d 01:35 ago)

@ mittyri
Posting: # 19060
Views: 5,789

## sgn(0) = 0

Hi mittyri,

» A question:
» is 0 a positive endpoint?

Nope. 0 is by definition neither positive nor negative.*

sgn(x < 0) = –1
sgn(x = 0) =   0
sgn(x > 0) = +1

Also

x = sgn(x)·|x|

Logarithms are defined only for >0.

Dif-tor heh smusma 🖖
Helmut Schütz

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

USA,
2018-07-16 14:49
(1238 d 10:44 ago)

@ mittyri
Posting: # 19064
Views: 5,679

## is zero positive?

» Note that logarithmic interpolation is overridden by linear interpolation in the case of a non-positive endpoint.
» A question:
» is 0 a [non-]positive endpoint?

0 is non-positive, but the original BQLs after Tlast is probably positive. Seems like I shouldn't be substituting BQL as 0 then.

» PS: nice to see you are using good oldie 6.3 (decennary next year)

We're in the process of upgrading to 8.1, haha. Many new fancy functions! A lot more expensive licensure too... I'll miss the floating license discount :P
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