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RE: Truncated Emax

From: Matt Hutmacher <matt.hutmacher>
Date: Thu, 22 Dec 2011 15:36:51 -0500

Hello all,


My apologies for responding to this thread late. I agree with using the =
method when data are censored to a certain value due to assay or =
restrictions. What I am not clear about is the actual suitability of =
approach for this case. I am not sure I understand the data; my =
from François’ which started the thread is that the measurement =
device has
an upper limit of 10 mA. So in the equation 100*(obs-base)/(max-base), =
seems max (max observed presumable but not sure if within or between
subjects) and for that matter obs and base are capped at 10? That is, it
would seem the censoring occurs on the original scale and not on the
%normalized scale. If so, then I am not sure that applying the BQL
methodology directly as specified in the references below is appropriate
unless one models the original scale (mA scale). The %normalized scale =
have the censoring implicit in the scale, but how it manifests will be
somewhat individual dependent and not the same as with the mA scale. =
So, I
would suggest to model the mA scale and then predict the %normalized =
If you do not want to or cannot model the mA scale, then to account for =
10 mA maximum in a principled way when modeling the %normalized data =
require a bit more thought, and may require some additional assumptions.
Another reason to model the mA scale is the difficult distribution that
%normalized scale will likely have due to subtracting and dividing
subtracted observations.


Best regards and happy holidays to all,


PS I deleted some of the thread below with the intent only to help =
this message would not hit the maximum line count and not be =


From: owner-nmusers
Behalf Of Elassaiss - Schaap, J. (Jeroen)
Sent: Tuesday, December 20, 2011 3:23 AM
To: Martin Bergstrand; 'Francois Gaudreault'; nmusers
Cc: 'Waqas Sadiq'
Subject: RE: [NMusers] Truncated Emax


Hi Martin,


Thank you for pointing this out. I actually do agree with you! I =
did not imply that deleting censored data is a guarantee for unbiased


But please keep in mind that especially with pain censoring is not
arbitrary. It is actually a meaningful border, for example unbearable =
or perhaps safety of currents in this case. And as I referred to, I have
compared models for pain with deletion or with M3 but could not find any
difference in results even with a high amount of censoring. My finding
surprised me at first, but when I discussed this with our residential =
statistician he told me that this, unbiased results after deleting of
censored data, was common experience.


I would be curious about experience from others on this list! Please do
share in if you have seen results one way or the other.


Best regards,




From: Martin Bergstrand [mailto:martin.bergstrand
Sent: Tuesday, December 20, 2011 08:27
To: 'Francois Gaudreault'; nmusers
Cc: 'Waqas Sadiq'; Elassaiss - Schaap, J. (Jeroen)
Subject: RE: [NMusers] Truncated Emax

Dear François,


I do not agree with Jeroen that less than ~1/3 of total data censored is =
guarantee for that these observations can be ignored without substantial
bias. I think this is highly dependent on the nature of the model =
the limit of quantification in relationship to Emax etc. To make a =
on what percentage of censored data (out of the total) that will result =
negligible bias is never a good idea since it might be that only a small
portion of the total data speaks to a specific parameter. If a =
amount of that small portion of data is censored it can have important
implications while it is still just a minor percentage that is missing =
of the total. But importantly you do not need to take anyone’s word =
this since you can test it you self with simulation based diagnostics =
simulation and re-estimation with the applied censoring.


The way that I would go about this issue is that I would take into =
also the censored observations. The below code is just a slight =
of the M3 method suggested by S. Beal for the handling of observations =
the limit o detection (BQL)[1]. More detail on how this is best =
in NONMEM is given in a paper by Anh [2]. Me and others have also
several times discussed how to best diagnose models in the presence of
censored observations (see NMusers archive).


Obs. When applying this code the SIGMA variance is fixed to 1 ($SIGMA 1 =
and the Lapalcian estimation option needs to be utilized (or possibly =
etc.) [2].



This type of coding have previously been successfully applied by my
colleague Waqas Sadiq. A manuscript on this project is currently in
preparation and might be referenced once published (look out).


[1] Beal SL. Ways to fit a PK model with some data below the =
limit. J Pharmacokinet Pharmacodyn. 2001 Oct;28(5):481-504.


[2] Ahn JE, Karlsson MO, Dunne A, Ludden TM. Likelihood based approaches =
handling data below the quantification limit using NONMEM VI. J
Pharmacokinet Pharmacodyn. 2008 Aug 7.



Kind regards,


Martin Bergstrand, PhD

Pharmacometrics Research Group

Dept of Pharmaceutical Biosciences

Uppsala University, Sweden



Visiting scientist:

Mahidol-Oxford Tropical Medicine Research Unit,

Bangkok, Thailand

Phone: +66 8 9796 7611




From: owner-nmusers
Behalf Of Francois Gaudreault
Sent: Monday, December 19, 2011 21:40
To: nmusers
Subject: [NMusers] Truncated Emax

Dear NM users


I am currently developing a PK PD model for local anesthetics using a
sequential approach with ADVAN6. The PD model is a sigmoid Emax with an
effect compartment (Ce).


The intensity and duration of nerve blockade are monitored throughout =
perioperative period in patients using a quantitative pharmacodynamic
endpoint, i.e, the current perception threshold (CPT) REF: Can. J. =
57 (S1) 2010). Briefly, CPT is evaluated before and after the =
of the local anesthectic. Data are normalized by baseline using the
following equation :

(observed-baseline) / (max-baseline) *100 (%)


Here is the problem. The device only goes to a maximum of 10 mA. In some
patients, the real Emax is much higher. Any ideas on how handle a =
Emax ?


Thanks in advance



François Gaudreault, Ph.D. Candidate
Pharmacométrie / Pharmacometrics
Charger de cours / Lecturer

Faculté de pharmacie / Faculty of Pharmacy
Université de Montréal


Received on Thu Dec 22 2011 - 15:36:51 EST

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