From: "Agoram, Balaji"
Subject: [NMusers] Covariate analysis
Date:Fri, 25 Apr 2003 16:20:50 -0700
I have a novice question on how to select covariates during a popPKPD
analysis using NONMEM.
Specifically I am interested in the following scenarios:
1. While using an indirect response model (stimulation of generation of
response) and the case where my Kin and Kout are known apriori and therefore
are not fitted, I find that my fitted EC50s are correlated with Kins. Can I
use Kin as a covariate for EC50?
2. Same as (1), but in this case, I am fitting Kin also.
3. For this drug, the CL decreases with each dose. Can I use the total dose
administered as a covariate for the CL?
In general, what rules do you all follow to select covariates. Feel free to
point out any valuable references regarding this subject.
Regards,
Balaji Agoram
Research Scientist I, PKDM
Phone 805 447 4035
Fax 805 375 6416
Covariate analysis
From:Nick Holford
Subject:Re: [NMusers] Covariate analysis
Date:Sun, 27 Apr 2003 12:28:08 +1200
Agoram,
It is unusual to be in a situation where you would know Kin and Kout a priori. Kin can of
course be re-parameterized in terms of the baseline value of the response and Kout so I
can see how you might fix Kin based on the value of the observed baseline response and an
estimate of Kout. Nevertheless I would prefer to estimate this parameter. The value of
Kout can only be obtained by perturbing the response system. Perhaps if you use a
different procedure to perturb it (e.g. another drug) then you can learn the value of
Kout a priori. I would like to know why you think you know Kin and Kout a priori.
> 2. Same as (1), but in this case, I am fitting Kin also.
If you estimate Kin (and preferably Kout as well) then there are two ways you might find
a correlation between Kin and EC50.
The first assumes that the covariance step runs successfully. You might then find a high
correlation between Kin and EC50 in the correlation matrix of the estimate. This is a
diagnostic that usually means that the experimental design is inadequate in order to
separately identify Kin and EC50. This could happen if the drug concs (C) are usually
less than EC50 so that the PD model is approximately linear:
The Emax model:
dR
-- = Kin * (1+Emax*C/(EC50+C)) - Kout * R
dt
becomes more like this:
dR
-- = Kin * (1+Emax*C/EC50) - Kout * R
dt
dR
-- = Kin + Kin*Emax*C/EC50) - Kout * R
dt
then Kin and EC50 (and Emax) will all be highly correlated. In this case it would be a
bad idea to use Kin as an covariate predicting EC50. You need a better design in order to
estimate the parameters properly. Clinical trial simulation can be helpful to test
alternative designs and find designs that reduce the estimation correlation.
The second way you might discover a correlation would be by inclusing an off diagonal
element in OMEGA e.g.
$OMEGA BLOCK (2)
.5 ; Kin
.1 .5 ; EC50
The off-diagonal element is the covariance of the random effect for Kin and EC50. It can
be used to calculate the correlation between Kin and EC50:
Corr = OMEGA(1,2)/sqrt(OMEGA(1,1)*OMEGA(2,2))
If the correlation beween individual subject estimates of Kin and EC50 is high then it
suggests there is another independent covariate that determines Kin and EC50. You should
look for other covariates in your data set to try to explain this correlation. If you
cannot find any you could then you might consider using Kin as a covariate for EC50.
You may be able to justify this association based on your knowledge of the particular
biological system you are studying. Suppose the drug you are studying is an
erythropoietin (EPO) like substance which stimulates the production of red blood cells.
If endogenous EPO is similar for all subjects and endogenous RBC production (Kin) is high
in some then it could mean that the EC50 for endogenous EPO is low (and vice versa).
Suppose the correlation between Kin and EC50 of your EPO like drug is negative then this
means that a low EC50 for your EPO like drug would be correlated with a high Kin and
therefore with a low EC50 for endogenous EPO. This might be expected if your EPO like
drug acts on the same receptor as endogenous EPO.
> 3. For this drug, the CL decreases with each dose. Can I use the total dose
> administered as a covariate for the CL?
This is a much easier case to deal with. You should indeed use dose (and probably
concentration) as a covariate for CL. This could be expressed in a mechanistic fashion
using a mixed order model (aka Michaelis-Menten) model for elimination:
C=A(1)/V
CL=Vmax/(Km+C)
dA(1)
----- = Drug_Ratein - CL*C
dt
I think the most important rule for covariate selection is based on biology. If you know
of a biological mechanism that would make the covariate a plausible explanation for
between and/or within subject variability in a parameter then you should include it in
the model.
Covariate associations can be detected by statistical means but should be viewed with
extreme caution if you cannot think of a plausible biological explanation. You should
also be cautious of covariates that decrease the objective function but do not produce an
important decrease in the size of population parameter variability (PPV) (i.e. the OMEGA
estimates). If the covariate does not really change PPV then it is clearly unimportant as
an explanation of between subject variability and is of little value as a predictor of a
parameter.
Nick
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
_______________________________________________________