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Dear all,
I am now working on a Pop PK analysis. After I have a base model built and evaluating the
covariates, I found something very intriguing. In evaluating the first covariate, OFV was decreased
compared to the base model. However, when adding the second covariate, OFV actually increased. I
tried different mathematical relation (EXP, power), but the same problem still exists. I am
thinking, if this is common in the Pop PK analysis, as I am relatively new to Pop PK and NONMEM.
Could any tell me, where is the problem?
The model I am using is a ADVAN4, TRANS4 model. Below is the control file I am using. Thanks in
advance.
$PROBLEM METFORMIN 2013-JUL-06
$DATA metformin_LMF_all.csv IGNORE=#
$INPUT STUD=DROP ID PERN PKCO=DROP DRUG DOSE ELPT DV AGE SEX RCE ETH HGHT BW TIME AMT
$SUBROUTINE ADVAN4 TRANS4
$PK
TVCL=THETA(1)
CL=TVCL*EXP(ETA(1))
TVV2=THETA(2)
V2=TVV2*EXP(ETA(2))
TVKA=THETA(3)
KA=TVKA*EXP(ETA(3))
TVQ=THETA(4)
Q=TVQ*EXP(ETA(4))
TVV3=THETA(5)
V3=TVV3*EXP(ETA(5))
S2=V2/1000
$ERROR
IPRE=F
Y=F*(EPS(1)+EXP(EPS(2))
$THETA
(0.1, ,10); TVCL
(1, 500); TVV2
(0.1, 0.7); TVKA
(0.01, 2);TVQ
(1, 350);TVV3
$OMEGA
0.04
$SIGMA
0.04; ERR
0.06
$ESTIMATION METH=1 MAXEVAL=9999 POSTHOC INTERACTION PRINT=5
$COVARIANCE
$TABLE ID TIME DV PRED IPRE RCE SEX ETH HGHT BW FILE=STDAB
--
Xinting
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Hi Xinting,
It would be better if you can post the covariate model that you tried. Few other things that I
noted, you might want to scale V3 and double check the residual error model. Y = F*(1+EPS(1)) +
EPS(2) or Y = F*EXP(EPS(1)) + EPS(2), in case if you are trying the combined proportional plus
additive error.
Best
Mukul Minocha
CTM
University of Maryland Baltimore
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Xinting,
You wrote:
"In evaluating the first covariate, OFV was decreased compared to the base model. However, when
adding the second covariate, OFV actually increased. "
You seem to have sent the base model code but not the covariate models associated with OFV changes.
This makes it really hard to give a specific answer to your question.
I will make a guess at what you might have done. The first model might have been the effect of SEX
on clearance e.g.
POPCL=THETA(1)
IF (SEX.EQ.0) THEN
FCLFEM=THETA(2) ; women
ELSE
FCLFEM=1 ; men
ENDIF
CL=FCLFEM*POPCL
If smaller people had smaller clearances then this might have shown a decrease in OFV because women
are typically smaller than men.
The second model might have been
CL=POPCL*(TBW/70)**0.75 ; allometric scaled total body weight
Note that this model is not a nested model compared with the base model. I have sometimes found that
the OFV increases when using this model that simply uses total body weight (TBW).
However, when I use normal fat mass (Anderson & Holford 2009) to account for differences in body
composition then I usually find the OFV decreases compared with the base model.
CL=POPCL*(NFM/70)**0.75 ; allometric scaled normal fat mass
The model is still not nested but it shows that accounting for body composition as well as weight
can improve the fit.
The SEX and NFM models can be combined:
CL=FCLFEM*POPCL*(NFM/70)**0.75 ; allometric scaled weight
You can then test if the SEX effect was in fact due to a difference in size and body composition
using a nested model. So far I have never seen an effect of SEX on clearance after accounting for
size and body composition.
Nick
Anderson BJ, Holford NHG. Mechanistic basis of using body size and maturation to predict clearance
in humans. Drug Metab Pharmacokinet. 2009;24(1):25-36.
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Xinting
There is a nmusers group list devoted to pop PK and nonmem
nmusers
As to your problem, try to start from the solution of the
problem with the lowest objective function: you will see your OF
decrease (or stay the same) when you add covariates.
Also, your error model is very strange, was it intentional? If not, use
Y=F*(1+EPS(1)) + EPS(2)
Thanks
Leonid
--
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
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Dear Xinting,
This may sometimes happen simply if your model is not stable and not at global minimum. Try
different initial estimates and see if the model terminates successfully at some other point.
Thanks
Mita
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Dear all,
Thanks very much for your reply. I would revise the error model, adding
scale to V3, and try different set of initial values to see if the current
estimation is a local minimum. Thanks.
As some of you have mentioned, I need to put the covariate model here to
have a better look. The covariates in the first step is listed below (to
name a few):
CL = TVCL * EXP(BW/66*THETA(6)) * ETA(1) (I also investigated the effect of
BW on V2, V3)
CL= TVCL * EXP(AGE/25*THETA(6)) * ETA(1) (Also, AGE on V2, V3, KA)
CL= TVCL * EXP(SEX*THETA(6))*ETA(1) (Also, SEX on V2, V3)
The first step identified that AGE could reduce the OFV by 505, which is
the most significant effect. Most other effect also showed a decrease of
OFV. However, after this, when I was building the second step based on the
first one, OFV actually increased (in most cases). That's what confuses me.
Best Regards
Xinting Wang
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Hi Xinting,
As Age, gender and WT are correlated, It will make much more sense to explain between subject
variability for CL and V with body weight as a covariate first. Once you have taken into account the
body weight then you can try adding age (if still you see a trend in IIVCL vs AGE plots) or gender
as a covariate.
Also, for body weight, a well know model is the power model, not sure the one that you posted is
coded correctly
CL = TVCL*(WT/Median WT)**THETA(1) *EXP(ETA(1)) ; Here THETA(1) is the shape factor that determines
the curvi-linear relationship between WT and CL
V = TVV *(WT/Median WT) *EXP(ETA(2));
You can either estimate THETA(1), the shape factor or fix it to 0.75 as it has been well studied.
Best
Mukul Minocha
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Dear Mukul,
Thanks very much for your great advice.
I tried a different error model, and found that however I change the
initial estimates the model would always converge to an OFV of 114728. So
for now I am assuming that the mode works fine. Then I tried adding
different covariates, but sometimes the model failed to converge (in the
covariance step). Under such circumstances, is it OK if I change the
initial estimates of error? Would this lead to a bias to the OFV, as in the
base model it used different initial estimates.
Another question is regarding the BW first rule you mentioned in your
email. Previously I thought that selecting the first covariate is based on
the one that lead to most reduction of OFV. Which one do you usually use?
Many thanks in advance.
Regards
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Xinting,
Minor changes to initial estimates should not influence your final convergence - if they do it
suggests your parameterization is unstable. I would suggest checking your gradients to make sure you
don't have some parameters hitting or bouncing around a boundary if you are seeing that.
As for covariate selection, when choosing between correlated covariates it can be helpful to choose
based on clinical relevance. In most cases, out of age, weight, and gender, weight provides the
better surrogate for organ/body size and function - thus why it can explain differences in clearance
and volume often. That said, if there are clinical reasons behind age it can be preferential for
covariate choice as well. For example, if you have a diverse age range, possibly including geriatric
or pediatrics, age could more adequately describe clearance due to changes in organ function with
age.
While objective function does describe how well the model explains the data, don't forget to keep
the purpose of the model in mind. If your goal is extrapolation vs interpolation covariate selection
can be driven by the final purpose of the model as well.
Devin
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Dear All:
What is the means by which the likelihood is computed? Is it FOCE or a similar approximation?
If so, it might be wise to use a method which computes the likelihood exactly. Many of these are
available now, such as S-Adapt, and of course the nonparametric approach in the NPAG software in
Pmetrics. This might get around the problem for good.
Very best regards,
Roger Jelliffe
Roger W. Jelliffe, M.D., F.C.P., F.A.A.P.S.
Professor of Medicine,
Founder and Co-Director, Laboratory of Applied Pharmacokinetics
www.lapk.org
USC Keck School of Medicine
2250 Alcazar St, Room 134-B
Los Angeles CA 90033
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Xinting,
A couple of comments on your covariate models.
1. First of all you should change the random effect model to
"*EXP(ETA(1))" instead of "*ETA(1)" in all cases. ETA is sampled from a
normal distribution so if you use "* ETA(1)" then half the CL values
will be zero or negative and half will be positive. That does not make
any sense. So use "*EXP(ETA(1))" which will always return a log normal
distribution of non-negative values.
2. Biology vs empiricism
"CL = TVCL * EXP(BW/66*THETA(6)) * ETA(1) (I also investigated the effect of
BW on V2, V3)"
This is an empirical model for weight that ignores biological knowledge
about the known relationship between weight and PK parameters. Testing
the hypothesis that THETA(6) is different from 0 is just a test of the
adequacy of the design of the study to detect something that must exist.
Very often PK studies are too small to detect a weight effect. It is
foolish to conclude there is no effect of weight (as is often done) when
this is obviously incorrect from a biological perspective.
A biological model would include weight on all size varying parameters
at the same time (CL, V2, Q and V3 in the case of a 2 cpt model).
e.g.
FSIZEV=TBW/70
FIZECL=(TBW/70)**0.75
CL=TVCL*FSIZECL*EXP(ETA(1))
V2=TVV2*FSIZEV*EXP(ETA(2))
Q=TVQ*FSIZECL*EXP(ETA(3))
V3=TVV3*FSIZEV*EXP(ETA(4))
"CL= TVCL * EXP(AGE/25*THETA(6)) * ETA(1) (Also, AGE on V2, V3, KA)"
This empirical model might be appropriate for an age range with a small
(30%) difference in parameter values and decreasing CL with AGE. It will
have very poor extrapolation properties if you apply it to infants and
children when CL will typically increase with AGE. Note that dividing
AGE by 25 does not change the estimation in any way. It just scales the
estimate of THETA(6).
See Anderson & Holford (2008) for a discussion of age models. Age models
for parameters that are known to vary with size should only ever be
tested with a model for size as well. Most changes in clearance with age
are due to changes in size. In order to discover any effect of age you
need to make sure you have accounted for the effect of size.
Anderson BJ, Holford NH. Mechanism-based concepts of size and maturity
in pharmacokinetics. Annu Rev Pharmacol Toxicol. 2008;48:303-32.
"CL= TVCL * EXP(SEX*THETA(6))*ETA(1) (Also, SEX on V2, V3)"
If SEX is coded as 0 and 1 then exp(THETA(6)) will reflect the
fractional difference of SEX=1 relative to SEX=0. An alternative method
of coding a fractional difference that will execute more quickly and
give you a more easily interpretable estimate of THETA(6) is:
IF (SEX.EQ.0) THEN
FSEX=1
ELSE
FSEX=THETA(6)
ENDIF
CL=TVCL*FSEX*ETA(1)
Best wishes,
Nick
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