Dear nmusers,
I have a drug with clearance autoinduction. I have sparse data(three
observations on day 1, two between day 7 and 14, and one on day 28). I am
trying to run a time-dependent clearance model. I tried FO and FOCEI, but I
always got unreasonable estimate for the initial clearance (CLI) which is about
0.15 L/h (from knowledge of previous studies, the reasonable initial clearance
should be around 20 L/h and maximum induction occurs around day 7). Could
someone give me some advice about my model and my data? Thank you.
Xiaofeng
The CTL file:
$PROB
$INPUT C ID TIME AMT DV MDV EVID ADDL II CMT
$DATA C:/ IGNORE=C
$SUBROUTINES ADVAN6 TOL=6
$MODEL NCOMPARTMENTS=3
COMP=(DEPOT,DEFDOSE)
COMP=(CENTRAL,DEFOBS)
COMP=(PERIP)
$PK
CLI=THETA(1)*EXP(ETA(1))
CLSS=THETA(2)*EXP(ETA(2))
KIN=THETA(3)*EXP(ETA(3))
V2= THETA(4)*EXP(ETA(4))
Q= THETA(5)*EXP(ETA(5))
V3= THETA(6)*EXP(ETA(6))
KA= THETA(7)*EXP(ETA(7))
S2=V2
K23=Q/V2
K32=Q/V3
$DES
CL=CLSS-(CLSS-CLI)*EXP(-KIN*T)
K20=CL/V2
DADT(1)=-KA*A(1)
DADT(2)=KA*A(1)+K32*A(3)-K23*A(2)-K20*A(2)
DADT(3)=K23*A(2)-K32*A(3)
$ERROR
IPRE=LOG(1)
IF(F.GT.0) IPRE=LOG(F)
Y = IPRE+EPS(1)
$EST METHOD=0 POSTHOC PRINT=10 MAX=9999 SIG=2 NOABORT MSFO=050.MSF
$THETA
(0, 20);[CLI]
(0, 65);[CLSS]
(0, 0.02) ;[KIN]
(0, 45);[V2]
(0, 5);[Q]
(0, 58);[V3]
(0, 0.2);[KA]
$OMEGA .25 .25 .25 .25 .25 .25 .25
$SIGMA .2
$COV PRINT=E
$TABLE ID TIME DV CLI CLSS KIN V2 Q V3 KA IPRE CWRES ONEHEADER NOPRINT
FILE=050.TAB
$TABLE ID TIME CLI CLSS KIN V2 Q V3 KA FIRSTONLY NOAPPEND NOPRINT FILE=050.PAR
$TABLE ID ETA1 ETA2 ETA3 ETA4 ETA5 ETA6 ETA7 FIRSTONLY NOAPPEND NOPRINT
FILE=050.ETA
$TABLE ID TIME CLI CLSS KIN V2 Q V3 KA FIRSTONLY NOAPPEND NOPRINT FILE=PATAB050
time-dependent clearance model
Hi Jeet,
Thanks for the advice. I got the initial guess of KIN from previous studies
which believe that the maximum induction occurs at day 7. So I let clearance at
168 hrs be equal to 98% of steady stage clearance (CLSS) and by using initial
guesses of CLI and CLSS, the initial guess of KIN was calculated as 0.02. The
clearance is induced. It increases with time instead of decreasing. How should
I determine if my model is over-parameterized?
Thank you.
Best,
Xiaofeng
Quoted reply history
________________________________
From: Isingh716 [[email protected]]
Sent: Sunday, March 04, 2012 7:22 PM
To: Wang, Xiaofeng
Subject: Re: [NMusers] time-dependent clearance model
How do you know the initial guess of KIN ? Right now it is 0.02 which will mean
~40-50hr for CL half life (so to imagine) you think it's reasonable for CL to
drop by that much in 50hrs ? You can possibly try different initial guesses for
KIN and see how does system react to ? Look for correlation and see if you are
not over parametrizing the model.
Best
Jeet
Sent from my iPhone
On Mar 4, 2012, at 4:33 PM, "Wang, Xiaofeng"
<[email protected]<mailto:[email protected]>> wrote:
Dear nmusers,
I have a drug with clearance autoinduction. I have sparse data(three
observations on day 1, two between day 7 and 14, and one on day 28). I am
trying to run a time-dependent clearance model. I tried FO and FOCEI, but I
always got unreasonable estimate for the initial clearance (CLI) which is about
0.15 L/h (from knowledge of previous studies, the reasonable initial clearance
should be around 20 L/h and maximum induction occurs around day 7). Could
someone give me some advice about my model and my data? Thank you.
Xiaofeng
The CTL file:
$PROB
$INPUT C ID TIME AMT DV MDV EVID ADDL II CMT
$DATA C:/ IGNORE=C
$SUBROUTINES ADVAN6 TOL=6
$MODEL NCOMPARTMENTS=3
COMP=(DEPOT,DEFDOSE)
COMP=(CENTRAL,DEFOBS)
COMP=(PERIP)
$PK
CLI=THETA(1)*EXP(ETA(1))
CLSS=THETA(2)*EXP(ETA(2))
KIN=THETA(3)*EXP(ETA(3))
V2= THETA(4)*EXP(ETA(4))
Q= THETA(5)*EXP(ETA(5))
V3= THETA(6)*EXP(ETA(6))
KA= THETA(7)*EXP(ETA(7))
S2=V2
K23=Q/V2
K32=Q/V3
$DES
CL=CLSS-(CLSS-CLI)*EXP(-KIN*T)
K20=CL/V2
DADT(1)=-KA*A(1)
DADT(2)=KA*A(1)+K32*A(3)-K23*A(2)-K20*A(2)
DADT(3)=K23*A(2)-K32*A(3)
$ERROR
IPRE=LOG(1)
IF(F.GT.0) IPRE=LOG(F)
Y = IPRE+EPS(1)
$EST METHOD=0 POSTHOC PRINT=10 MAX=9999 SIG=2 NOABORT MSFO=050.MSF
$THETA
(0, 20);[CLI]
(0, 65);[CLSS]
(0, 0.02) ;[KIN]
(0, 45);[V2]
(0, 5);[Q]
(0, 58);[V3]
(0, 0.2);[KA]
$OMEGA .25 .25 .25 .25 .25 .25 .25
$SIGMA .2
$COV PRINT=E
$TABLE ID TIME DV CLI CLSS KIN V2 Q V3 KA IPRE CWRES ONEHEADER NOPRINT
FILE=050.TAB
$TABLE ID TIME CLI CLSS KIN V2 Q V3 KA FIRSTONLY NOAPPEND NOPRINT FILE=050.PAR
$TABLE ID ETA1 ETA2 ETA3 ETA4 ETA5 ETA6 ETA7 FIRSTONLY NOAPPEND NOPRINT
FILE=050.ETA
$TABLE ID TIME CLI CLSS KIN V2 Q V3 KA FIRSTONLY NOAPPEND NOPRINT FILE=PATAB050
Xiaofeng,
Such a large difference suggests you may have a problem with units:
check AMT, DV, and the parameter S2 for consistency.
A couple of other points:
- If the full induction is expected by day 7, and you only have data
on day 1 and after day 7, you may not be able to estimate KIN. You
may be better off with the model where there is CLI on day 1 and
CLSS on days >1 (And you will not need $DES for that model).
- You have 6 observations per subject and you have 7 ETAs, it is too
many, your model should be overparameterized (Check whether relative
standard errors are large).
Regards,
Katya
Ekaterina Gibiansky, Ph.D.
CEO&CSO, QuantPharm LLC
Web: www.quantpharm.com
Email: EGibiansky at quantpharm.com
On 3/4/2012 5:33 PM, Wang, Xiaofeng wrote:
Dear nmusers,
I have a drug with clearance autoinduction.
I have sparse data(three observations on day 1, two between
day 7 and 14, and one on day 28). I am trying to run a
time-dependent clearance model. I tried FO and FOCEI, but I
always got unreasonable estimate for the initial clearance
(CLI) which is about 0.15 L/h (from knowledge of previous
studies, the reasonable initial clearance should be around 20
L/h and maximum induction occurs around day 7). Could someone
give me some advice about my model and my data? Thank you.
Xiaofeng
The CTL file:
$PROB
$INPUT C ID TIME AMT DV MDV EVID ADDL II
CMT
$DATA C:/ IGNORE=C
$SUBROUTINES ADVAN6 TOL=6
$MODEL NCOMPARTMENTS=3
COMP=(DEPOT,DEFDOSE)
COMP=(CENTRAL,DEFOBS)
COMP=(PERIP)
$PK
CLI=THETA(1)*EXP(ETA(1))
CLSS=THETA(2)*EXP(ETA(2))
KIN=THETA(3)*EXP(ETA(3))
V2= THETA(4)*EXP(ETA(4))
Q= THETA(5)*EXP(ETA(5))
V3= THETA(6)*EXP(ETA(6))
KA= THETA(7)*EXP(ETA(7))
S2=V2
K23=Q/V2
K32=Q/V3
$DES
CL=CLSS-(CLSS-CLI)*EXP(-KIN*T)
K20=CL/V2
DADT(1)=-KA*A(1)
DADT(2)=KA*A(1)+K32*A(3)-K23*A(2)-K20*A(2)
DADT(3)=K23*A(2)-K32*A(3)
$ERROR
IPRE=LOG(1)
IF(F.GT.0) IPRE=LOG(F)
Y = IPRE+EPS(1)
$EST METHOD=0 POSTHOC PRINT=10 MAX=9999
SIG=2 NOABORT MSFO=050.MSF
$THETA
(0, 20);[CLI]
(0, 65);[CLSS]
(0, 0.02) ;[KIN]
(0, 45);[V2]
(0, 5);[Q]
(0, 58);[V3]
(0, 0.2);[KA]
$OMEGA .25 .25 .25 .25 .25 .25 .25
$SIGMA .2
$COV PRINT=E
$TABLE ID TIME DV CLI CLSS KIN V2 Q V3 KA
IPRE CWRES ONEHEADER NOPRINT FILE=050.TAB
$TABLE ID TIME CLI CLSS KIN V2 Q V3 KA
FIRSTONLY NOAPPEND NOPRINT FILE=050.PAR
$TABLE ID ETA1 ETA2 ETA3 ETA4 ETA5 ETA6
ETA7 FIRSTONLY NOAPPEND NOPRINT FILE=050.ETA
$TABLE ID TIME CLI CLSS KIN V2 Q V3 KA
FIRSTONLY NOAPPEND NOPRINT FILE=PATAB050
Xiaofeng,
It always amazes me how many parameters we try to estimate based on the
limited amount of data available. This is specially the case when a rather
complex event is taking place, such as autoinduction in this case, and that
based on sparse samples. In your case, there are a total of 15 parameters to
be estimated, which, as Katya points out seems to be way too many.
I would suggest that you start with the simplest model and then make it more
complex once you have the structural (i.e., your PK) model in place. Since
you have data only at pre- and post-induction, I think it is a good idea to
estimate different CL values for the two occasions. This way, you can use
the built-in library, with explicit solutions, which is normally faster than
trying to solve the equations in the $DES. Why not start with this and 1-2
ETAs on the CLs on days 1 and 7? If this simple model works, you can always
move ahead and add ETAs.
Toufigh
Quoted reply history
On 3/4/12 8:51 PM, "Wang, Xiaofeng" <[email protected]> wrote:
> Hi Katya,
>
> Thank you. I double checked the units. mcg for AMT, ng/mL for DV, and L for
> CL. I think there is no problem with the units. Since I am using
> log-transformed data, does that influence the units?
>
> I will try kicking in CLSS after day 1. For 6 observations per patients, what
> is the reasonable number of ETAs?
>
> Best,
> Xiaofeng
>
> From: [email protected] [[email protected]] on behalf of
> Ekaterina Gibiansky [[email protected]]
> Sent: Sunday, March 04, 2012 8:53 PM
> To: '[email protected]'
> Subject: Re: [NMusers] time-dependent clearance model
>
> Xiaofeng,
>
> Such a large difference suggests you may have a problem with units: check AMT,
> DV, and the parameter S2 for consistency.
> A couple of other points:
> - If the full induction is expected by day 7, and you only have data on day 1
> and after day 7, you may not be able to estimate KIN. You may be better off
> with the model where there is CLI on day 1 and CLSS on days >1 (And you will
> not need $DES for that model).
> - You have 6 observations per subject and you have 7 ETAs, it is too many,
> your model should be overparameterized (Check whether relative standard errors
> are large).
>
> Regards,
> Katya
> Ekaterina Gibiansky, Ph.D.
> CEO&CSO, QuantPharm LLC
> Web: www.quantpharm.com http://www.quantpharm.com
> Email: EGibiansky at quantpharm.com
>
>
> On 3/4/2012 5:33 PM, Wang, Xiaofeng wrote:
>> Dear nmusers,
>>
>> I have a drug with clearance autoinduction. I have sparse data(three
>> observations on day 1, two between day 7 and 14, and one on day 28). I am
>> trying to run a time-dependent clearance model. I tried FO and FOCEI, but I
>> always got unreasonable estimate for the initial clearance (CLI) which is
>> about 0.15 L/h (from knowledge of previous studies, the reasonable initial
>> clearance should be around 20 L/h and maximum induction occurs around day 7).
>> Could someone give me some advice about my model and my data? Thank you.
>>
>> Xiaofeng
>>
>> The CTL file:
>> $PROB
>> $INPUT C ID TIME AMT DV MDV EVID ADDL II CMT
>> $DATA C:/ IGNORE=C
>> $SUBROUTINES ADVAN6 TOL=6
>> $MODEL NCOMPARTMENTS=3
>> COMP=(DEPOT,DEFDOSE)
>> COMP=(CENTRAL,DEFOBS)
>> COMP=(PERIP)
>> $PK
>> CLI=THETA(1)*EXP(ETA(1))
>> CLSS=THETA(2)*EXP(ETA(2))
>> KIN=THETA(3)*EXP(ETA(3))
>> V2= THETA(4)*EXP(ETA(4))
>> Q= THETA(5)*EXP(ETA(5))
>> V3= THETA(6)*EXP(ETA(6))
>> KA= THETA(7)*EXP(ETA(7))
>> S2=V2
>> K23=Q/V2
>> K32=Q/V3
>>
>> $DES
>> CL=CLSS-(CLSS-CLI)*EXP(-KIN*T)
>> K20=CL/V2
>> DADT(1)=-KA*A(1)
>> DADT(2)=KA*A(1)+K32*A(3)-K23*A(2)-K20*A(2)
>> DADT(3)=K23*A(2)-K32*A(3)
>> $ERROR
>> IPRE=LOG(1)
>> IF(F.GT.0) IPRE=LOG(F)
>> Y = IPRE+EPS(1)
>> $EST METHOD=0 POSTHOC PRINT=10 MAX=9999 SIG=2 NOABORT MSFO=050.MSF
>> $THETA
>> (0, 20);[CLI]
>> (0, 65);[CLSS]
>> (0, 0.02) ;[KIN]
>> (0, 45);[V2]
>> (0, 5);[Q]
>> (0, 58);[V3]
>> (0, 0.2);[KA]
>>
>> $OMEGA .25 .25 .25 .25 .25 .25 .25
>> $SIGMA .2
>> $COV PRINT=E
>> $TABLE ID TIME DV CLI CLSS KIN V2 Q V3 KA IPRE CWRES ONEHEADER NOPRINT
>> FILE=050.TAB
>> $TABLE ID TIME CLI CLSS KIN V2 Q V3 KA FIRSTONLY NOAPPEND NOPRINT
>> FILE=050.PAR
>> $TABLE ID ETA1 ETA2 ETA3 ETA4 ETA5 ETA6 ETA7 FIRSTONLY NOAPPEND NOPRINT
>> FILE=050.ETA
>> $TABLE ID TIME CLI CLSS KIN V2 Q V3 KA FIRSTONLY NOAPPEND NOPRINT
>> FILE=PATAB050
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>
Dear Xiaofeng,
Presumably the CL at the start and at SS are correlated. If you in the model
assumed a lack of correlation, that may well be the cause of a variance
driven to zero.
I agree with Toufigh that starting simple is usually a good idea. Given your
data sparsity, I would start very simple. Why not apply a one-compartment
model without CL induction. You can then extend to a model that has 2
compartments and separately one that has a CL changing with time (or even
better one that changes with concentration as was discussed recently on
nmusers). If both are models better than your simple starting model, you can
try combining the two.
Best regards,
Mats
Mats Karlsson, PhD
Professor of Pharmacometrics
Dept of Pharmaceutical Biosciences
Faculty of Pharmacy
Uppsala University
Box 591
75124 Uppsala
Phone: +46 18 4714105
Fax + 46 18 4714003
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Toufigh Gordi
Sent: 05 March 2012 22:45
To: Wang, Xiaofeng; '[email protected]'
Subject: Re: [NMusers] time-dependent clearance model
Whenever I start a modeling process, my first objective is to get the
structural model, i.e., your PK model in this case, well defined and in
place. If you start from there and you are pretty confident that you have
the right model, finding what parameters differ between subjects should not
be difficult. In your case with the very low ETA on CL1, how confident are
you about the model estimates, i.e., V3 or Q? Are they stay the same from
days 1 to ss? I can't really give any specific advice since I haven't seen
the results and know very little about the model and the fits.
Toufigh
On 3/5/12 1:30 PM, "Wang, Xiaofeng" <[email protected]> wrote:
Hi Toufigh,
Thank you for the suggestion. I tried the simplest model with 2 ETAs on the
pre- and post-induction clearance. The result gave very small omega estimate
for the pre-induction clearance (2.50e-005). But I don't believe that there
is no between subject variability for the pre-induction clearance. Could you
please give me some suggestion about this? Thank you.
Best,
Xiaofeng
_____
From: Toufigh Gordi [[email protected]]
Sent: Monday, March 05, 2012 2:30 AM
To: Wang, Xiaofeng; '[email protected]'
Subject: Re: [NMusers] time-dependent clearance model
Xiaofeng,
It always amazes me how many parameters we try to estimate based on the
limited amount of data available. This is specially the case when a rather
complex event is taking place, such as autoinduction in this case, and that
based on sparse samples. In your case, there are a total of 15 parameters to
be estimated, which, as Katya points out seems to be way too many.
I would suggest that you start with the simplest model and then make it more
complex once you have the structural (i.e., your PK) model in place. Since
you have data only at pre- and post-induction, I think it is a good idea to
estimate different CL values for the two occasions. This way, you can use
the built-in library, with explicit solutions, which is normally faster than
trying to solve the equations in the $DES. Why not start with this and 1-2
ETAs on the CLs on days 1 and 7? If this simple model works, you can always
move ahead and add ETAs.
Toufigh
On 3/4/12 8:51 PM, "Wang, Xiaofeng" <[email protected]
<UrlBlockedError.aspx> > wrote:
Hi Katya,
Thank you. I double checked the units. mcg for AMT, ng/mL for DV, and L for
CL. I think there is no problem with the units. Since I am using
log-transformed data, does that influence the units?
I will try kicking in CLSS after day 1. For 6 observations per patients,
what is the reasonable number of ETAs?
Best,
Xiaofeng
_____
From: [email protected] <UrlBlockedError.aspx>
[[email protected] <UrlBlockedError.aspx> ] on behalf of
Ekaterina Gibiansky [[email protected] <UrlBlockedError.aspx> ]
Sent: Sunday, March 04, 2012 8:53 PM
To: '[email protected] <UrlBlockedError.aspx> '
Subject: Re: [NMusers] time-dependent clearance model
Xiaofeng,
Such a large difference suggests you may have a problem with units: check
AMT, DV, and the parameter S2 for consistency.
A couple of other points:
- If the full induction is expected by day 7, and you only have data on day
1 and after day 7, you may not be able to estimate KIN. You may be better
off with the model where there is CLI on day 1 and CLSS on days >1 (And you
will not need $DES for that model).
- You have 6 observations per subject and you have 7 ETAs, it is too many,
your model should be overparameterized (Check whether relative standard
errors are large).
Regards,
Katya
Ekaterina Gibiansky, Ph.D.
CEO&CSO, QuantPharm LLC
Web: www.quantpharm.com http://www.quantpharm.com
Email: EGibiansky at quantpharm.com
On 3/4/2012 5:33 PM, Wang, Xiaofeng wrote:
Dear nmusers,
I have a drug with clearance autoinduction. I have sparse data(three
observations on day 1, two between day 7 and 14, and one on day 28). I am
trying to run a time-dependent clearance model. I tried FO and FOCEI, but I
always got unreasonable estimate for the initial clearance (CLI) which is
about 0.15 L/h (from knowledge of previous studies, the reasonable initial
clearance should be around 20 L/h and maximum induction occurs around day
7). Could someone give me some advice about my model and my data? Thank you.
Xiaofeng
The CTL file:
$PROB
$INPUT C ID TIME AMT DV MDV EVID ADDL II CMT
$DATA C:/ IGNORE=C
$SUBROUTINES ADVAN6 TOL=6
$MODEL NCOMPARTMENTS=3
COMP=(DEPOT,DEFDOSE)
COMP=(CENTRAL,DEFOBS)
COMP=(PERIP)
$PK
CLI=THETA(1)*EXP(ETA(1))
CLSS=THETA(2)*EXP(ETA(2))
KIN=THETA(3)*EXP(ETA(3))
V2= THETA(4)*EXP(ETA(4))
Q= THETA(5)*EXP(ETA(5))
V3= THETA(6)*EXP(ETA(6))
KA= THETA(7)*EXP(ETA(7))
S2=V2
K23=Q/V2
K32=Q/V3
$DES
CL=CLSS-(CLSS-CLI)*EXP(-KIN*T)
K20=CL/V2
DADT(1)=-KA*A(1)
DADT(2)=KA*A(1)+K32*A(3)-K23*A(2)-K20*A(2)
DADT(3)=K23*A(2)-K32*A(3)
$ERROR
IPRE=LOG(1)
IF(F.GT.0) IPRE=LOG(F)
Y = IPRE+EPS(1)
$EST METHOD=0 POSTHOC PRINT=10 MAX=9999 SIG=2 NOABORT MSFO=050.MSF
$THETA
(0, 20);[CLI]
(0, 65);[CLSS]
(0, 0.02) ;[KIN]
(0, 45);[V2]
(0, 5);[Q]
(0, 58);[V3]
(0, 0.2);[KA]
$OMEGA .25 .25 .25 .25 .25 .25 .25
$SIGMA .2
$COV PRINT=E
$TABLE ID TIME DV CLI CLSS KIN V2 Q V3 KA IPRE CWRES ONEHEADER NOPRINT
FILE=050.TAB
$TABLE ID TIME CLI CLSS KIN V2 Q V3 KA FIRSTONLY NOAPPEND NOPRINT
FILE=050.PAR
$TABLE ID ETA1 ETA2 ETA3 ETA4 ETA5 ETA6 ETA7 FIRSTONLY NOAPPEND NOPRINT
FILE=050.ETA
$TABLE ID TIME CLI CLSS KIN V2 Q V3 KA FIRSTONLY NOAPPEND NOPRINT
FILE=PATAB050