RE: Baseline as a covariate
Dear Dr. Bonate,
Could you kindly elaborate on the structural model that is being used to
characterize your PD system? In my limited experience, I have seen the
behavior that you describe under 2 circumstances:
a) Simple inhibitory Emax PD model with a baseline: Here patients with a
higher baseline (worse disease state) displayed a more pronounced
effect. There is greater margin/room for improvement for a patient
starting out at a higher baseline and hence shows a better response (vs.
another patient that starts out a lower baseline). I was able to model
this behavior by putting an omega block between Emax and the baseline
parameter Eo. It is then very easy to adjudicate the impact of Eo on the
magnitude of effect in simulation mode.
b) Indirect Response Model: Sun and Jusko [J Pharm Sci 88: 987 (1999)]
have shown that "The baseline value may play an important role in
affecting the extent of the response if its PD relationship can be
described by a turnover Model. When other factors remain constant (e.g.
Smax, SC50, kout), R0 controls the magnitude of the response." Is it
possible that you're getting a spurious baseline covariate effect
because of the choice of your structural model?
I am also quite interested in hearing the general thoughts on the use of
the baseline as a covariate from this forum. In fact I have seen yet
another approach to this problem where the change from baseline was
modeled as the PD endpoint. With this method the baseline is no longer a
parameter in the model and observed baseline can then be used as a
covariate. Does this method offer any benefit or do the statistical
concerns around data transformation negate the benefits of this method.
Thank-you,
Mahesh
Quoted reply history
-----Original Message-----
From: [email protected] [mailto:[email protected]]
On Behalf Of Ken Kowalski
Sent: Wednesday, August 11, 2010 12:12 PM
To: 'Peter Bonate'; [email protected]
Subject: RE: [NMusers] Baseline as a covariate
Hi Pete,
In this setting I generally try to first model the baseline response and
perhaps pursue alternative structural model forms. For example, I may
consider a multiplicative relationship rather than an additive
relationship
between baseline and placebo/drug effects. However, if the distribution
of
the baseline response is quite complex and not easy to model with a
normal
eta on baseline, and I'm concerned that I might be getting a biased
estimate
of the baseline response then I may consider treating the observed
baseline
as a covariate as a fall-back position.
This question is similar to whether one uses observed or predicted
concentrations when developing a PK/PD model. We generally prefer using
predicted concentrations rather than observed concentrations to smooth
out
the measurement error (among other reasons as well). However, if we
have a
lot of lack-of-fit in developing a PK model then it may be preferable to
use
the observed concentrations. There is a tradeoff as to whether more
bias is
introduced due to lack-of-fit (e.g., poor estimation of the baseline
response) or due to measurement error in using the observed baseline
measurements as a covariate. If the residual variability due to
lack-of-fit
is considerably larger than measurement error, and you can't resolve the
lack-of-fit, then you might consider using the observed baseline
response as
a covariate.
Kind regards,
Ken
Kenneth G. Kowalski
President & CEO
A2PG - Ann Arbor Pharmacometrics Group, Inc.
110 E. Miller Ave., Garden Suite
Ann Arbor, MI 48104
Work: 734-274-8255
Cell: 248-207-5082
Fax: 734-913-0230
[email protected]
-----Original Message-----
From: [email protected] [mailto:[email protected]]
On
Behalf Of Peter Bonate
Sent: Wednesday, August 11, 2010 11:22 AM
To: '[email protected]'
Subject: [NMusers] Baseline as a covariate
I'd like to get the group's opinion on something. I have a
pharmacodynamic
model and the baseline was shown to be a covariate on one of the model
parameters. I was hoping to get general thoughts on the use of the
baseline
as a covariate. Is there a preference for using the observed baseline
vs.
NONMEM predicted baseline? And does your opinion change if you have a
large
residual error?
Thanks
Pete bonate
Peter L. Bonate, PhD, FCP, FAAPS
GlaxoSmithKline
Clinical Pharmacology, Modeling, and Simulation
5 Moore Drive, 17.2259
Research Triangle Park, NC 27709
phone: 919-483-7534
fax: 919-483-8948
email: [email protected]
This is a long one but worth it...
Scientists will never make as much money as business executives. There
is
now mathematical proof for this statement.
Postulate 1: Knowledge is power
postulate 2: Time is money
According to the laws of physics,
Work
-------- = Power (Eq. 1)
Time
Since, from the 2 postulates above,
Knowledge = Power and
Time = Money,
we can substitute into the equation 1 and come up with
Work
-------- = Knowledge
Money
Solving for money,
Work
------------ = Money
Knowledge
Hence, there are 2 ways to make money. If we slug our guts out working,
we
can improve our money situation. This is the normal scientific
approach.
However the suits usually opt for the easier solution, i.e., the less
you
know, the more you'll make, regardless of the amount of work done.
-----Original Message-----
From: [email protected] [mailto:[email protected]]
On
Behalf Of Leonid Gibiansky
Sent: Wednesday, August 11, 2010 9:01 AM
To: Ann Rigby-Jones
Cc: '[email protected]'
Subject: Re: [NMusers] Rounding errors with TRANSIT model
Ann
Try ADVAN6 or ADVAN8 or ADVAN13 .
Also, TOL=3 is too small. Increase it to 6-7 or even 9, and also change
to NSIG=3 SIGL=9 ($EST step, as recommended in the guide).
Also, at least initially, I would remove ETAs from the third compartment
and from one of the parameters (Q2 or V2) of the second compartment. Do
you really need both ALAG and transit compartment? They serve the same
goal, to delay the input, so could be strongly correlated; you may see
it on the POSTHOC plot of ETA7-ETA8 versus ETA9. I would try to remove
ETAs from ALAG or KTR to check whether they are needed.
If nothing helps, use UNCONDITIONAL on the $COV to get standard errors,
and if they are reasonable, ignore the error, it may disappear on the
next steps of the modeling process
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
On 8/11/2010 5:57 AM, Ann Rigby-Jones wrote:
> Dear All
>
> I'm trying to evaluate a transit model approach in an attempt to
better
> describe early drug concentrations following intravenous injection (1
> minute and 10 minute infusions) of a sedative-hypnotic drug. However,
> every minimisation attempt is terminated due to rounding errors
(E=134).
> I've tried the usual strategies to overcome this e.g using final
> estimates of a terminated run as initial estimates for the next,
> changing number of sig dig requested, changing from a diagonal omega
to
> a block omega, but nothing has been successful.
>
> I'd be very grateful for any suggestions of what I might try next J
> Standard 3-comp and 4-comp mamillary models minise successful with
these
> data, but so far no luck with any of the transit models, I have tried
> model with 1 to 6 transit compartments. An example control stream is
> shown below. I'm using NONMEM 7 with Intel Fortran.
>
> With thanks and all best wishes
>
> Ann
>
> $PROBLEM 3comp 2 transit
>
> $INPUT ID DOSE AMT RATE DUR TIME ORI DV EVID ART AGE WGT
>
> $DATA PKcen12LN.csv IGNORE=#
>
> $SUBROUTINES ADVAN9 TOL=3
>
> $MODEL
>
> ;NCOMPS=9
>
> COMP(CENTRAL, DEFOBS) ;1
>
> COMP(PERIPH1) ;2
>
> COMP(PERIPH2) ;3
>
> COMP(TRANS1, DEFDOSE) ;4
>
> COMP(TRANS2) ;5
>
> ;COMP(TRANS3) ;6
>
> ;COMP(TRANS4) ;7
>
> ;COMP(TRANS5) ;8
>
> ;COMP(TRANS6) ;9
>
> $PK
>
> CL=THETA(1)*EXP(ETA(1))
>
> Q2=THETA(2)*EXP(ETA(2))
>
> Q3=THETA(3)*EXP(ETA(3))
>
> V1=THETA(4)*EXP(ETA(4))
>
> V2=THETA(5)*EXP(ETA(5))
>
> V3=THETA(6)*EXP(ETA(6))
>
> K10=CL/V1
>
> K12=Q2/V1
>
> K13=Q3/V1
>
> K21=Q2/V2
>
> K31=Q3/V3
>
> S1=V1
>
> IF (DUR.EQ.10) THEN
>
> ALAG4=THETA(7)*EXP(ETA(7))
>
> ELSE
>
> ALAG4=THETA(8)*EXP(ETA(8))
>
> ENDIF
>
> KTR=THETA(9)*EXP(ETA(9))
>
> $DES
>
> ;DADT(1)=A(2)*K21 + A(3)*K31 - A(1)*(K10+K12+K13)
>
> ;DADT(2)=A(1)*K12 - A(2)*K21
>
> ;DADT(3)=A(1)*K13 - A(3)*K31
>
> DADT(1)=A(5)*KTR + A(2)*K21 + A(3)*K31 - A(1)*(K10+K12+K13)
>
> DADT(2)=A(1)*K12 - A(2)*K21
>
> DADT(3)=A(1)*K13 - A(3)*K31
>
> DADT(4)=-A(4)*KTR
>
> DADT(5)=A(4)*KTR - A(5)*KTR
>
> ;DADT(6)=A(5)*KTR - A(6)*KTR
>
> ;DADT(7)=A(6)*KTR - A(7)*KTR
>
> ;DADT(8)=A(7)*KTR - A(8)*KTR
>
> ;DADT(9)=A(8)*KTR - A(9)*KTR
>
> $ERROR
>
> W=1
>
> IPRED= -2
>
> IF (F.GT.0) IPRED=LOG(F)
>
> Y=IPRED + ERR(1)
>
> IRES=DV-IPRED
>
> IWRES=IRES/W
>
> $THETA (0, 725) ;CL
>
> $THETA (0, 238) ;Q2
>
> $THETA (0, 2920) ;Q3
>
> $THETA (0, 311) ;V1
>
> $THETA (0, 38700) ;V2
>
> $THETA (0, 39500) ;V3
>
> $THETA (0.2167, 0.522,1) ;ALAG 10MIN
>
> $THETA (0.00833, 0.122, 1) ;ALAG 1MIN
>
> $THETA (0, 0.720) ;KTR
>
> $OMEGA BLOCK(6)
>
> 0.0959 ; ETA CL
>
> 0.00804 0.0211 ; ETA Q2
>
> 0.00631 0.00143 0.166 ; ETA Q3
>
> -0.00506 0.00121 -0.0635 0.0491 ; ETA V1
>
> 0.00293 -0.00746 0.00708 -0.00315 0.0328 ; ETA V2
>
> 0.00836 0.00688 0.00144 -0.00497 0.00741 0.153 ; ETA V3
>
> $OMEGA 0.217 ; ETA ALAG 10
>
> $OMEGA 0.4 ; ETA ALAG 1
>
> $OMEGA 0.0171 ; ETA KTR
>
> ;$OMEGA (0.0686) ; ETA CL
>
> ;$OMEGA (0.01) ; ETA Q2
>
> ;$OMEGA (0.0251) ; ETA Q3
>
> ;$OMEGA (0 FIX) ; ETA V1
>
> ;$OMEGA (0.0328) ; ETA V2
>
> ;$OMEGA (0 FIX) ; ETA V3
>
> ;$OMEGA (0.170) ; ETA ALAG10
>
> ;$OMEGA (1.37) ; ETA ALAG1
>
> ;$OMEGA (0.00409) ; ETA KTR
>
> $SIGMA (0.0944)
>
> $ESTIMATION METHOD=1 PRINT=1 MAX=9999 NOABORT SIG=3 ;POSTHOC INTER
>
> MSFO=msfo.outputfile
>
> ;$COVA
>
> $TABLE ID EVID AMT TIME IPRED IRES
>
> NOPRINT FILE=AllRecords.txt
>
> $TABLE ID
>
> CL Q2 Q3 V1 V2 V3
>
> ETA1 ETA2 ETA3 ETA4 ETA5 ETA6 ETA7 ;ETA8
>
> FIRSTONLY NOPRINT NOAPPEND FILE=FirstRecords.txt
>
> Ann
>
>
_______________________________________________________________________
>
> *Ann Rigby-Jones PhD MRSC*
> Research Fellow in Pharmacokinetics & Pharmacodynamics
>
> Peninsula College of Medicine & Dentistry
>
> N31, ITTC Phase 1
> Tamar Science Park
> 1 Davy Road
> Derriford
> Plymouth
> PL6 8BX
>
> Tel: +44 (0) 1752 432014
>
_______________________________________________________________________
>