RE: Truncated Emax
Dear François,
I do not agree with Jeroen that less than ~1/3 of total data censored is a
guarantee for that these observations can be ignored without substantial
bias. I think this is highly dependent on the nature of the model (system),
the limit of quantification in relationship to Emax etc. To make a statement
on what percentage of censored data (out of the total) that will result in
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 substantial
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 out
of the total. But importantly you do not need to take anyones word for
this since you can test it you self with simulation based diagnostics and/or
simulation and re-estimation with the applied censoring.
The way that I would go about this issue is that I would take into account
also the censored observations. The below code is just a slight alteration
of the M3 method suggested by S. Beal for the handling of observations below
the limit o detection (BQL)[1]. More detail on how this is best implemented
in NONMEM is given in a paper by Anh et.al [2]. Me and others have also
several times discussed how to best diagnose models in the presence of
censored observations (see NMusers archive).
;;; ---------------------------------------------------------
$ERROR
W = THETA(.) ; Residual error model (in this example simple
additive)
ULOQ = 10 ; Upper limit of detection (10mA)
IPRED = PT ; Individual prediction of perception threshold
according to your desired model
DUM = (IPRED-ULOQ)/SIG
CUMD = PHI(DUM)
; Flag variable CENS in dataset. CENS=1 => observation >ULOQ
IF(CENS.EQ.0) THEN ; <ULOQ
F_FLAG = 0
Y = IPRED+SIG*ERR(1)
ENDIF
IF(ALQ.EQ.1) THEN ; >ULOQ
F_FLAG = 1
Y = CUMD
ENDIF
;;; ---------------------------------------------------------
Obs. When applying this code the SIGMA variance is fixed to 1 ($SIGMA 1 FIX)
and the Lapalcian estimation option needs to be utilized (or possibly SAEM
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 quantification
limit. J Pharmacokinet Pharmacodyn. 2001 Oct;28(5):481-504.
[2] Ahn JE, Karlsson MO, Dunne A, Ludden TM. Likelihood based approaches to
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
[email protected]
Visiting scientist:
Mahidol-Oxford Tropical Medicine Research Unit,
Bangkok, Thailand
Phone: +66 8 9796 7611
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Elassaiss - Schaap, J. (Jeroen)
Sent: Tuesday, December 20, 2011 4:12 AM
To: Francois Gaudreault; [email protected]
Subject: RE: [NMusers] Truncated Emax
Hi Francois,
For pain measurements it is not uncommon to analyze data with a upper limit
of quantitation. You can follow the literature on BQL, only reversing from a
lower limit to an upper limIt. In my experience just deleting censored data
works fine, certainly as a first attempt, as long as censoring stays below
~1/3 of total data.
Best regards,
Jeroen
J. Elassaiss-Schaap
Scientist PK/PD
MSD
PO Box 20, 5340 BH Oss, Netherlands
Phone: + 31 412 66 9320
Fax: + 31 412 66 2506
e-mail: [email protected]
_____
From: [email protected] [mailto:[email protected]] On
Behalf Of Francois Gaudreault
Sent: Monday, December 19, 2011 21:40
To: [email protected]
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 the
perioperative period in patients using a quantitative pharmacodynamic
endpoint, i.e, the current perception threshold (CPT) REF: Can. J. Anesth,
57 (S1) 2010). Briefly, CPT is evaluated before and after the administration
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 truncated
Emax ?
Thanks in advance
--
François Gaudreault, Ph.D. Candidate
Pharmacométrie / Pharmacometrics
Charger de cours / Lecturer
Faculté de pharmacie / Faculty of Pharmacy
Université de Montréal