I am conducting a sequential pharmacokinetic-pharmacodynamic model. The
pharmacokinetic fits look good and I was using an indirect response model.
The PD model is that the drug inhibits clearance of the analyte (PD
response), thus one expects that the response increases with increasing drug
(Model II). There is a baseline measured (=Kfor/Kcl) and a dummy dose=1
unit given. It seems despite trying various permutations of the model, eta1
seems to be very small and no covariance step is conducted. The model and
data for the first 3 subjects are reproducted below. Any assistance would
be appreciated. Note that since conc (COP) are read in, the model only
requires a single differential equation. Any insight would be appreciated.
Nishit
$PROBLEM PD - ADVAN6
$DATA C:\PDDATA.CSV
$INPUT ID TIME DV AMT=DOSE COP MDV
; data are subject ID, Time, DV=PD response, Amt (dummy dose of 1 inserted),
COP=plasma conc which drive PD model, MDV
$SUBROUTINES ADVAN6 TOL=6
$MODEL
COMP=(EFFECT, DEFDOSE, DEFOBS)
$PK
KFOR = THETA(1)
KCL = THETA(2)*EXP(ETA(1))
IC50 = THETA(3)
IMAX = THETA(4)
F1 = KFOR/KCL
COEF = IMAX*COP/(IC50+COP)
$DES
DADT(1) = KFOR-KCL*(1-COEF)*A(1)
$ERROR
W = F
Y = F*EXP(ERR(1))
IPRED = F
IRES = DV-IPRED
IF (W.LE.0.) W=1
IWRES = IRES/W
$THETA (0,0.3)
$THETA (0, 0.003)
$THETA (0,10)
$THETA (0, 0.3, 1)
$OMEGA 0.01
$SIGMA 0.5
$ESTIMATION METHOD=1 MAXEVAL=5000 PRINT=20
$COVR
$TABLE ID TIME PRED IPRED IRES KFOR KCL IC50 IMAX
NOPRINT ONEHEADER
FILE=C:\PD.TAB
1001 0 . 1 0 1
1001 0 98.3 . 0 0
1001 168 90.6 . 122.44 0
1001 840 92.8 . 183.69 0
1002 0 . 1 0 1
1002 0 105.1 . 0 0
1002 840 88.5 . 61.253 0
1002 842 106.7 . 106.8 0
1002 844 122.1 . 116.4 0
1002 1848 129.1 . 121.46 0
1002 1850 160.4 . 212.63 0
1002 1852 157.1 . 231.89 0
1101 0 . 1 0 1
1101 0 68.1 . 0 0
1101 840 88.1 . 0.13884 0
1101 842 105.5 . 0.12987 0
1101 844 108.8 . 0.12147 0
1101 1848 113.3 . 227.79 0
1101 1850 62.6 . 379.54 0
1101 1852 138.7 . 412.18 0
Indirect response model
Dear Nishit,
If I understand correctly, you are using concentration (COP) of
your drug as a time dependent covariate which is then used as
forcing function for your PD model.
As concentrations change over time, you probably need the
CALLFL = 0 option ($PK CALLFL=0) to read in the concentration
at every new time. I would write out COP in $TABLE in order to
check, if COP changes over time as it should.
This should work much better, but it will still give you a piecewise
constant concentration profile. This may cause numerical problems.
Instead, I would include the differential equations for your PK
model. This should give you better numerical stability and more
correct concentration predictions. You could start with reading in
the individual PK parameters (IPP approach, see reference below)
and then go to more complex PKPD analyses.
You might try the MATRIX=S statement in $COV, if you like to get
the covariance step to work.
Hope some of this works.
Best regards
Juergen
Reference:
Zhang, L., S. L. Beal, and L. B. Sheiner. 2003. Simultaneous vs.
sequential analysis for population PK/PD data I: best-case performance.
J Pharmacokinet Pharmacodyn 30:387-404.
-----------------------------------------------
Juergen Bulitta, PhD, Post-doctoral Fellow
Pharmacometrics, University at Buffalo, NY, USA
Phone: +1 716 645 2855 ext. 281, [EMAIL PROTECTED]
-----------------------------------------------
-----Ursprüngliche Nachricht-----
Von: "Modi, Nishit [ALZUS]" <[EMAIL PROTECTED]>
Gesendet: 15.05.07 18:31:57
An: [EMAIL PROTECTED]
CC: [email protected]
Betreff: [NMusers] Indirect response model
I am conducting a sequential pharmacokinetic-pharmacodynamic model. The
pharmacokinetic fits look good and I was using an indirect response model. The
PD model is that the drug inhibits clearance of the analyte (PD response), thus
one expects that the response increases with increasing drug (Model II). There
is a baseline measured (=Kfor/Kcl) and a dummy dose=1 unit given. It seems
despite trying various permutations of the model, eta1 seems to be very small
and no covariance step is conducted. The model and data for the first 3
subjects are reproducted below. Any assistance would be appreciated. Note
that since conc (COP) are read in, the model only requires a single
differential equation. Any insight would be appreciated.
Nishit
$PROBLEM PD - ADVAN6
$DATA C:\PDDATA.CSV
$INPUT ID TIME DV AMT=DOSE COP MDV
; data are subject ID, Time, DV=PD response, Amt (dummy dose of 1 inserted),
COP=plasma conc which drive PD model, MDV
$SUBROUTINES ADVAN6 TOL=6
$MODEL
COMP=(EFFECT, DEFDOSE, DEFOBS)
$PK
KFOR = THETA(1)
KCL = THETA(2)*EXP(ETA(1))
IC50 = THETA(3)
IMAX = THETA(4)
F1 = KFOR/KCL
COEF = IMAX*COP/(IC50+COP)
$DES
DADT(1) = KFOR-KCL*(1-COEF)*A(1)
$ERROR
W = F
Y = F*EXP(ERR(1))
IPRED = F
IRES = DV-IPRED
IF (W.LE.0.) W=1
IWRES = IRES/W
$THETA (0,0.3)
$THETA (0, 0.003)
$THETA (0,10)
$THETA (0, 0.3, 1)
$OMEGA 0.01
$SIGMA 0.5
$ESTIMATION METHOD=1 MAXEVAL=5000 PRINT=20
$COVR
$TABLE ID TIME PRED IPRED IRES KFOR KCL IC50 IMAX
NOPRINT ONEHEADER
FILE=C:\PD.TAB
1001 0 . 1 0 1
1001 0 98.3 . 0 0
1001 168 90.6 . 122.44 0
1001 840 92.8 . 183.69 0
1002 0 . 1 0 1
1002 0 105.1 . 0 0
1002 840 88.5 . 61.253 0
1002 842 106.7 . 106.8 0
1002 844 122.1 . 116.4 0
1002 1848 129.1 . 121.46 0
1002 1850 160.4 . 212.63 0
1002 1852 157.1 . 231.89 0
1101 0 . 1 0 1
1101 0 68.1 . 0 0
1101 840 88.1 . 0.13884 0
1101 842 105.5 . 0.12987 0
1101 844 108.8 . 0.12147 0
1101 1848 113.3 . 227.79 0
1101 1850 62.6 . 379.54 0
1101 1852 138.7 . 412.18 0
Hi Nishit,
Isn't F1 a reserved parameter in the PK block? I would try the
following code.
$PK
KFOR = THETA(1)
KCL = THETA(2)*EXP(ETA(1))
IC50 = THETA(3)
IMAX = THETA(4)
BASE = KFOR/KCL
COEF = IMAX*COP/(IC50+COP)
$DES
DADT(1) = BASE*KCL-KCL*(1-COEF)*A(1)
Regards,
Sunny
Quoted reply history
________________________________
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]
On Behalf Of Modi, Nishit [ALZUS]
Sent: Tuesday, May 15, 2007 12:21 PM
To: [EMAIL PROTECTED]
Cc: [email protected]
Subject: [NMusers] Indirect response model
I am conducting a sequential pharmacokinetic-pharmacodynamic model. The
pharmacokinetic fits look good and I was using an indirect response
model. The PD model is that the drug inhibits clearance of the analyte
(PD response), thus one expects that the response increases with
increasing drug (Model II). There is a baseline measured (=Kfor/Kcl)
and a dummy dose=1 unit given. It seems despite trying various
permutations of the model, eta1 seems to be very small and no covariance
step is conducted. The model and data for the first 3 subjects are
reproducted below. Any assistance would be appreciated. Note that
since conc (COP) are read in, the model only requires a single
differential equation. Any insight would be appreciated.
Nishit
$PROBLEM PD - ADVAN6
$DATA C:\PDDATA.CSV
$INPUT ID TIME DV AMT=DOSE COP MDV
; data are subject ID, Time, DV=PD response, Amt (dummy dose of 1
inserted), COP=plasma conc which drive PD model, MDV
$SUBROUTINES ADVAN6 TOL=6
$MODEL
COMP=(EFFECT, DEFDOSE, DEFOBS)
$PK
KFOR = THETA(1)
KCL = THETA(2)*EXP(ETA(1))
IC50 = THETA(3)
IMAX = THETA(4)
F1 = KFOR/KCL
COEF = IMAX*COP/(IC50+COP)
$DES
DADT(1) = KFOR-KCL*(1-COEF)*A(1)
$ERROR
W = F
Y = F*EXP(ERR(1))
IPRED = F
IRES = DV-IPRED
IF (W.LE.0.) W=1
IWRES = IRES/W
$THETA (0,0.3)
$THETA (0, 0.003)
$THETA (0,10)
$THETA (0, 0.3, 1)
$OMEGA 0.01
$SIGMA 0.5
$ESTIMATION METHOD=1 MAXEVAL=5000 PRINT=20
$COVR
$TABLE ID TIME PRED IPRED IRES KFOR KCL IC50 IMAX
NOPRINT ONEHEADER
FILE=C:\PD.TAB
1001 0 . 1 0 1
1001 0 98.3 . 0 0
1001 168 90.6 . 122.44 0
1001 840 92.8 . 183.69 0
1002 0 . 1 0 1
1002 0 105.1 . 0 0
1002 840 88.5 . 61.253 0
1002 842 106.7 . 106.8 0
1002 844 122.1 . 116.4 0
1002 1848 129.1 . 121.46 0
1002 1850 160.4 . 212.63 0
1002 1852 157.1 . 231.89 0
1101 0 . 1 0 1
1101 0 68.1 . 0 0
1101 840 88.1 . 0.13884 0
1101 842 105.5 . 0.12987 0
1101 844 108.8 . 0.12147 0
1101 1848 113.3 . 227.79 0
1101 1850 62.6 . 379.54 0
1101 1852 138.7 . 412.18 0
----------------------------------------------------------------------
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Dear Nishit,
Jurgen is correct, you are using concentration (COP) as a forcing function.
But, in ID 1101, for example, the COP has a value of 0 from TIME=0 to 840 and
then values around 0.12 until TIME 1848. Unless this is what you had in mind,
I would suggest two steps: 1. Include more time points for COP. These need
not coincide with TIMEs were you have DV values. 2. Create a linear
interpolation of COP to be used in the $DES block.
One way to do this linear interpolation is to add two columns to your data
file: PTME (previous time) and PCOP (previous concentration). Then, compute
SLOPE = (COP-PCOP)/(TIME-PTME) and use a linear interpolation of conc: PCOP +SLOPE*(T-PTME) in place of COP in computing your COEF parameter (must be in $DES block).
I hope this helps,
David Salinger
RFPK, Univ. of Washington
Quoted reply history
On Tue, 15 May 2007, Jurgen Bulitta wrote:
> Dear Nishit,
>
> If I understand correctly, you are using concentration (COP) of
> your drug as a time dependent covariate which is then used as
> forcing function for your PD model.
>
> As concentrations change over time, you probably need the
> CALLFL = 0 option ($PK CALLFL=0) to read in the concentration
> at every new time. I would write out COP in $TABLE in order to
> check, if COP changes over time as it should.
>
> This should work much better, but it will still give you a piecewise
> constant concentration profile. This may cause numerical problems.
> Instead, I would include the differential equations for your PK
> model. This should give you better numerical stability and more
> correct concentration predictions. You could start with reading in
> the individual PK parameters (IPP approach, see reference below)
> and then go to more complex PKPD analyses.
>
> You might try the MATRIX=S statement in $COV, if you like to get
> the covariance step to work.
>
> Hope some of this works.
>
> Best regards
> Juergen
>
> Reference:
> Zhang, L., S. L. Beal, and L. B. Sheiner. 2003. Simultaneous vs.
> sequential analysis for population PK/PD data I: best-case performance.
> J Pharmacokinet Pharmacodyn 30:387-404.
>
> -----------------------------------------------
> Juergen Bulitta, PhD, Post-doctoral Fellow
> Pharmacometrics, University at Buffalo, NY, USA
> Phone: +1 716 645 2855 ext. 281, [EMAIL PROTECTED]
> -----------------------------------------------
>
> -----Ursprüngliche Nachricht-----
> Von: "Modi, Nishit [ALZUS]" <[EMAIL PROTECTED]>
> Gesendet: 15.05.07 18:31:57
> An: [EMAIL PROTECTED]
> CC: [email protected]
> Betreff: [NMusers] Indirect response model
>
> I am conducting a sequential pharmacokinetic-pharmacodynamic model. The
> pharmacokinetic fits look good and I was using an indirect response model. The
> PD model is that the drug inhibits clearance of the analyte (PD response), thus
> one expects that the response increases with increasing drug (Model II). There
> is a baseline measured (=Kfor/Kcl) and a dummy dose=1 unit given. It seems
> despite trying various permutations of the model, eta1 seems to be very small
> and no covariance step is conducted. The model and data for the first 3
> subjects are reproducted below. Any assistance would be appreciated. Note
> that since conc (COP) are read in, the model only requires a single
> differential equation. Any insight would be appreciated.
>
> Nishit
>
> $PROBLEM PD - ADVAN6
>
> $DATA C:\PDDATA.CSV
>
> $INPUT ID TIME DV AMT=DOSE COP MDV
>
> ; data are subject ID, Time, DV=PD response, Amt (dummy dose of 1 inserted),
> COP=plasma conc which drive PD model, MDV
>
> $SUBROUTINES ADVAN6 TOL=6
>
> $MODEL
>
> COMP=(EFFECT, DEFDOSE, DEFOBS)
>
> $PK
>
> KFOR = THETA(1)
>
> KCL = THETA(2)*EXP(ETA(1))
>
> IC50 = THETA(3)
>
> IMAX = THETA(4)
>
> F1 = KFOR/KCL
>
> COEF = IMAX*COP/(IC50+COP)
>
> $DES
>
> DADT(1) = KFOR-KCL*(1-COEF)*A(1)
>
> $ERROR
>
> W = F
>
> Y = F*EXP(ERR(1))
>
> IPRED = F
>
> IRES = DV-IPRED
>
> IF (W.LE.0.) W=1
>
> IWRES = IRES/W
>
> $THETA (0,0.3)
>
> $THETA (0, 0.003)
>
> $THETA (0,10)
>
> $THETA (0, 0.3, 1)
>
> $OMEGA 0.01
>
> $SIGMA 0.5
>
> $ESTIMATION METHOD=1 MAXEVAL=5000 PRINT=20
>
> $COVR
>
> $TABLE ID TIME PRED IPRED IRES KFOR KCL IC50 IMAX
>
> NOPRINT ONEHEADER
>
> FILE=C:\PD.TAB
>
> 1001 0 . 1 0 1
>
> 1001 0 98.3 . 0 0
>
> 1001 168 90.6 . 122.44 0
>
> 1001 840 92.8 . 183.69 0
>
> 1002 0 . 1 0 1
>
> 1002 0 105.1 . 0 0
>
> 1002 840 88.5 . 61.253 0
>
> 1002 842 106.7 . 106.8 0
>
> 1002 844 122.1 . 116.4 0
>
> 1002 1848 129.1 . 121.46 0
>
> 1002 1850 160.4 . 212.63 0
>
> 1002 1852 157.1 . 231.89 0
>
> 1101 0 . 1 0 1
>
> 1101 0 68.1 . 0 0
>
> 1101 840 88.1 . 0.13884 0
>
> 1101 842 105.5 . 0.12987 0
>
> 1101 844 108.8 . 0.12147 0
>
> 1101 1848 113.3 . 227.79 0
>
> 1101 1850 62.6 . 379.54 0
>
> 1101 1852 138.7 . 412.18 0
Dear all,
I agree, implementing the actual PK model (i.e. IPP) or using linear
interpolation to describe the individual PK profiles as suggested by Juergen
and David is necessary in this example.
However, for understanding when input concentrations can be used directly as
a reasonable approximation I have the following question: If the input
concentrations were to be used, as originally presented by Nishit, wouldn't
nonmem use the input concentrations according to last observation carried
BACKWARD, rather than forward? In that case, for ID 1101 (the third
individual in the dataset):
0 < TIME <= 840 -> COP=0.13884
840 < TIME <= 842 -> COP=0.12987
842 < TIME <= 844 -> COP=0.12147
844 < TIME <= 1848 -> COP=227.79
...
I haven't checked myself that nonmem uses LOCB rather than LOCF, but have
been told so by Mats Karlsson which usually makes checking superfluous:>) I
think this could be important in other situations as well: The LOCB-rule
could induce false covariate relations if the drug affects a potential
covariate. For example, disease level/score/stage may falsely appear to
affect the drug clearance if investigated within nonmem. To properly
quantify such a covariate relation a simultaneous fit of the PK-PD model may
be necessary, treating the covariate (biomarker) as an integrated part of
the model. Getting back to this thread:
Nishit, if using nonmem version 6, the dummy dose into compartment 1 is not
needed for initializing the baseline. Dummy-dosing records can be removed
from the datafile and this line in the model file:
F1 = KFOR/KCL
can be replace by
A_0(1) = KFOR/KCL
Lastly, either fit log-transformed DV:s using an additive error model OR add
"INTERACTION" on the $ESTIMATION, to account for the interaction between
ETA1 and EPS1 in the current error model. I would prefer the first
alternative for several reasons.
Kind regards,
Jakob
$INPUT ID TIME DV AMT=DOSE COP MDV
ID 1101 in the dataset:
1101 0 . 1 0 1
1101 0 68.1 . 0 0
1101 840 88.1 . 0.13884 0
1101 842 105.5 . 0.12987 0
1101 844 108.8 . 0.12147 0
1101 1848 113.3 . 227.79 0
1101 1850 62.6 . 379.54 0
1101 1852 138.7 . 412.18 0
Quoted reply history
-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On
Behalf Of David H Salinger
Sent: den 16 maj 2007 18:14
To: Jurgen Bulitta
Cc: Modi, Nishit [ALZUS]; [EMAIL PROTECTED]; [email protected]
Subject: Re: [NMusers] Indirect response model
Dear Nishit,
Jurgen is correct, you are using concentration (COP) as a forcing function.
But, in ID 1101, for example, the COP has a value of 0 from TIME=0 to 840
and then values around 0.12 until TIME 1848. Unless this is what you had
in mind, I would suggest two steps: 1. Include more time points for COP.
These need not coincide with TIMEs were you have DV values. 2. Create a
linear interpolation of COP to be used in the $DES block.
One way to do this linear interpolation is to add two columns to your data
file: PTME (previous time) and PCOP (previous concentration). Then, compute
SLOPE = (COP-PCOP)/(TIME-PTME)
and use a linear interpolation of conc:
PCOP +SLOPE*(T-PTME)
in place of COP in computing your COEF parameter (must be in $DES block).
I hope this helps,
David Salinger
RFPK, Univ. of Washington
This is another recent thread that I would like to comment on.
On the issue of LOCB vs LOCF: The question is discussed at great length
in NONMEM Users Guide VI, PREDPP, in chapter III, section B.2 Time-
Varying Concomitant Variables. The idea is that, prior to advancing the
state vector from time t1 to time t2, the PK routine is called (i.e.,
$PK is evaluated) with the next record (time t2), so that the values
computed by PK for the record with TIME=t2 are used during the advance
from t1 to t2.
This is easily justified. If the values on the record with t1 were
used, the values (other than TIME) recorded on the last record in the
data set would never be seen by PK, and could not enter into the
model. Linear interpolation such as you are discussing could not be
carried out properly. As it is, the first data record is always seen
by PK (because there is always a call to PK with the first data record
of the individual record), and subsequent data records are seen prior
to the advance to that record.
The linear interpolation suggested by Jakob could also be carried out
in $PK without any change to the data set. I think that I recall some
of Lewis' fellows doing similar interpolations in the past.
The following code is a suggestion. I have not tested it!!
$PK
KFOR = THETA(1)
KCL = THETA(2)*EXP(ETA(1))
IC50 = THETA(3)
IMAX = THETA(4)
F1 = KFOR/KCL
IF (TIME.EQ.0) THEN
PCOP=0
PTME=0
SLOPE=0
OCOP=0
ELSE
SLOPE=(COP-PCOP)/(TIME-PTME)
OCOP=PCOP
ENDIF
PCOP=COP
PTME=TIME
$DES
ICOP=OCOP+SLOPE*(T-PTME)
COEF = IMAX*ICOP/(IC50+ICOP)
DADT(1) = KFOR-KCL*(1-COEF)*A(1)
On Thu, 17 May 2007 11:52:54 +0200, "Jakob Ribbing"
<[EMAIL PROTECTED]> said:
> Dear all,
>
> I agree, implementing the actual PK model (i.e. IPP) or using linear
> interpolation to describe the individual PK profiles as suggested by
> Juergen
> and David is necessary in this example.
>
> However, for understanding when input concentrations can be used directly
> as
> a reasonable approximation I have the following question: If the input
> concentrations were to be used, as originally presented by Nishit,
> wouldn't
> nonmem use the input concentrations according to last observation carried
> BACKWARD, rather than forward? In that case, for ID 1101 (the third
> individual in the dataset):
> 0 < TIME <= 840 -> COP=0.13884
> 840 < TIME <= 842 -> COP=0.12987
> 842 < TIME <= 844 -> COP=0.12147
> 844 < TIME <= 1848 -> COP=227.79
> ...
> I haven't checked myself that nonmem uses LOCB rather than LOCF, but have
> been told so by Mats Karlsson which usually makes checking superfluous:>)
> I
> think this could be important in other situations as well: The LOCB-rule
> could induce false covariate relations if the drug affects a potential
> covariate. For example, disease level/score/stage may falsely appear to
> affect the drug clearance if investigated within nonmem. To properly
> quantify such a covariate relation a simultaneous fit of the PK-PD model
> may
> be necessary, treating the covariate (biomarker) as an integrated part of
> the model. Getting back to this thread:
>
> Nishit, if using nonmem version 6, the dummy dose into compartment 1 is
> not
> needed for initializing the baseline. Dummy-dosing records can be removed
> from the datafile and this line in the model file:
> F1 = KFOR/KCL
> can be replace by
> A_0(1) = KFOR/KCL
>
> Lastly, either fit log-transformed DV:s using an additive error model OR
> add
> "INTERACTION" on the $ESTIMATION, to account for the interaction between
> ETA1 and EPS1 in the current error model. I would prefer the first
> alternative for several reasons.
>
> Kind regards,
>
> Jakob
>
> $INPUT ID TIME DV AMT=DOSE COP MDV
> ID 1101 in the dataset:
>
> 1101 0 . 1 0 1
> 1101 0 68.1 . 0 0
> 1101 840 88.1 . 0.13884 0
> 1101 842 105.5 . 0.12987 0
> 1101 844 108.8 . 0.12147 0
> 1101 1848 113.3 . 227.79 0
> 1101 1850 62.6 . 379.54 0
> 1101 1852 138.7 . 412.18 0
>
Quoted reply history
> -----Original Message-----
> From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]
> On
> Behalf Of David H Salinger
> Sent: den 16 maj 2007 18:14
> To: Jurgen Bulitta
> Cc: Modi, Nishit [ALZUS]; [EMAIL PROTECTED]; [email protected]
> Subject: Re: [NMusers] Indirect response model
>
> Dear Nishit,
>
> Jurgen is correct, you are using concentration (COP) as a forcing
> function.
> But, in ID 1101, for example, the COP has a value of 0 from TIME=0 to 840
> and then values around 0.12 until TIME 1848. Unless this is what you
> had
> in mind, I would suggest two steps: 1. Include more time points for
> COP.
> These need not coincide with TIMEs were you have DV values. 2. Create a
> linear interpolation of COP to be used in the $DES block.
>
> One way to do this linear interpolation is to add two columns to your
> data
> file: PTME (previous time) and PCOP (previous concentration). Then,
> compute
> SLOPE = (COP-PCOP)/(TIME-PTME)
> and use a linear interpolation of conc:
> PCOP +SLOPE*(T-PTME)
> in place of COP in computing your COEF parameter (must be in $DES block).
>
> I hope this helps,
>
> David Salinger
> RFPK, Univ. of Washington
>
>
--
Alison Boeckmann
[EMAIL PROTECTED]