- On 12 Jul 2013 at 23:31:18, Xinting Wang sent the message

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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 - On 13 Jul 2013 at 08:33:23, Mukul Minocha sent the message

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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 - On 13 Jul 2013 at 08:36:23, Nick Holford sent the message

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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. - On 13 Jul 2013 at 08:43:13, Leonid Gibiansky sent the message

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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 - On 13 Jul 2013 at 09:02:55, Mita sent the message

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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 - On 13 Jul 2013 at 22:44:25, Xinting Wang sent the message

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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 - On 14 Jul 2013 at 08:23:30, Mukul Minocha sent the message

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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 - On 14 Jul 2013 at 18:08:13, Xinting Wang sent the message

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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 - On 15 Jul 2013 at 12:06:34, Devin Pastoor sent the message

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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 - On 15 Jul 2013 at 12:07:24, Roger W. Jelliffe sent the message

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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 - On 15 Jul 2013 at 12:08:20, Nick Holford sent the message

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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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