Leonid,
I accept that the unit volume parameterization of VM is quite reasonable
if you think that all elimination occurs in the same volume as the
distribution volume. This is the usual test tube model that gives rise
to the unit volume belief system. It is not a realistic view of
elimination from the human body
I would also accept that if all elimination occurs in some blood cell
distribution volume (e.g.white cells) then this will be highly
correlated with the drug distribution volume and the unit volume
parameterization will appear to work fine but will fail if there is some
covariate that determines blood cell volume distribution differently
from drug distribution volume.
However, I don't accept that the elimination of a biological can be
independent of weight if we refer to the actual mass eliminated per unit
time. The first order part of the model for elimination which uses
clearance is certainly not independent of weight so why would you
imagine that the mixed order elimination process would be independent of
weight?
Note that the oldest example of a mixed order elimination process is for
ethanol (Widmark essentially invented the science of pharmacokinetics
with a mixed order elimination model). Ethanol elimination largely
occurs in the liver while it distributes in total body water. Liver
metabolism scales allometrically in a different way from total body
water so I do not believe that the mixed order elimination of ethanol
should be described with the unit volume belief system. I much prefer
the unit body belief system.
Sorry - I was confused by your residual error model which at first sight
seemed to be a transform both sides model. However, the model you use
restricts all residual errors to be non-negative which is not a
realistic description of any non-censored residual error process. All
real world uncensored measurement errors should have an error
distribution on both sides of zero when the true value is zero.
Nick
Leonid Gibiansky wrote:
Hi Nick
This form of equations can be derived from the target-mediated drug
disposition equations. In that, VM=Kint*Rmax, where Kint is the
internalization rate and Rmax is the concentration of the target
(receptor). Target-mediated clearance is believed to be carried out in
the central volume (in that particular form of the equations), and
thus, VM is coming from the enzyme theory equations (maximum reaction
rate). In my experience, if you follow parametrization that I use, VM
is independent on weight (and thus, random effect on volume does not
correlate with the random effect on VM - if the one is needed- unlike
the parameterization that you propose). For biologics, if we believe
that the mechanism of non-linear clearance is TMDD, it is more
mechanistic to use parameterization suggested in my e-mail.
Alternatively, the same MM equation can be derived from TMDD using
slightly different assumptions. In that form, VM=ksyn, where ksyn is
the target production rate per unit volume. Both forms (Vm=ksyn or
VM=Kint*Rmax) interpret MM constants in terms of mechanistic
parameters of the TMDD system.
As to the error model, I used non-transformed variables but borrowed
the error model from the log-transformed case. I like it because it
would not deliver negative results on simulations.
While the log-transformation may or may not provide much benefits, it
is the only way to implement true exponential (rather than
proportional) error model in nonmem. This is purely technical
(mathematical-statistical-numerical method-related) problem, no
biology behind this transformation, so I cannot see much sense to
argue for or against using this trick.
Any way, the question was about MM part, not the error model. We can
supplement MM model with any more conventional error model of personal
choice (hopefully supported by the data and confirmed by the VPC).
Best !
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
Nick Holford wrote:
Leonid,
Thanks for the code example which illustrates one side of a religious
debate which took place a few weeks ago on PharmPK. The essence of
this debate was should one normalize PK parameters to a unit volume
or to a unit body.
The unit volume believers feel that the rate constant is the
'natural' way to describe pharmacokinetics while the unit body
believers feel that clearance is more 'natural'. Both groups agree
that the two systems are just reparameterizations and make identical
numerical predictions.
Your coding of Vmax for the mixed order elimination process has the
implicit units of mass/time per unit volume e.g. mg/h/L. This is the
unit volume belief system.
I am a unit body believer so I would code this system differently
with a very simple change- substituting A(1) with C1 to multiply the
mixed order expression. I have also changed VM to VMUB to indicate
that the dimensions of the Vmax parameter are per unit body i.e. mg/h
per body.
DADT(1) = -K10*A(1)-C1*VMUB/(KM+C1)-K12*A(1)+K21*A(2)
It could also be written like this to emphasize that the mixed order
process has the same units as CL (for unit body believers) when C1
tends to 0:
DADT(1) = -C1*(CL+VMUB/(KM+C1) - K12*A(1)+K21*A(2)
I note also that your residual error model implies that the DV has
been log transformed. This reflects yet another belief system which I
think you have shown has little, if any, practical merit. I prefer to
keep the DV in the original units.
Best wishes,
Nick
Leonid Gibiansky wrote:
ADVAN6 ADVAN8 or (nm7) ADVAN13
The code is below
Leonid
-------------------
$SUBROUTINE ADVAN6 TOL=9
$MODEL
NCOMP = 2
COMP = (CENTRAL) ;1
COMP = (PERIPH) ;2
$PK
CL= THETA(1)*EXP(ETA(1))
V1= THETA(2)*EXP(ETA(2))
Q = THETA(3)*EXP(ETA(3))
V2= THETA(4)*EXP(ETA(4))
VM= THETA(5)*EXP(ETA(5))
KM= THETA(6)
K10 = CL/V1
K12 = Q/V1
K21 = Q/V2
S1 = V1
S2 = V2
$DES
C1 = A(1)/S1
DADT(1) = -K10*A(1)-A(1)*VM/(KM+C1)-K12*A(1)+K21*A(2)
DADT(2) = K12*A(1)-K21*A(2)
$ERROR
TY = A(1)/V1
IPRED=TY
W = SQRT(THETA(7)**2/TY**2+THETA(8)**2)
Y = IPRED*EXP(W*ERR(1))
$THETA
.....
$OMEGA
.....
$SIGMA
1 FIX ; ~ERR
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
[email protected] wrote:
Dear All,
I am working with a Biologic and would like to have a PK model with
parallel first order and Michaelis-Menten elimination. Any
suggestion about which subroutine I am supposed to use? If you can
share an example for the control stream, that will be a great help.
Thanks,
Yuhong
--
Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology
University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
tel:+64(9)923-6730 fax:+64(9)373-7090 mobile:+64(21)46 23 53
email: [email protected]
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
--
Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology
University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
tel:+64(9)923-6730 fax:+64(9)373-7090 mobile:+64(21)46 23 53
email: [email protected]
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
