From: Toufigh Gordi 
Subject:[NMusers] Covariate effect
Date: Fri, 07 Mar 2003 14:47:15 -0500

Dear all,

I have a general question with regard to incorporation of covariate(s) into 
the model. If I understand it correctly, a covariate can partly explain the 
variability of a particular model parameter, meaning that upon insertion of 
the covariate effect the inter-individual variability normally decreases. A 
significant decrease in objective function value is also another indication 
that the presence of the covariate in the model has improved the general 
fit.

What if the incorporation of a covariate results in a large decrease of the 
OFV but very small or no change in the ETA of the particular parameter? Am 
I correct to conclude that the decrease in OFV is probably the result of 
having an extra parameter rather than having the correct reason for the 
observed variability? Would a simpler model be as good as the more complete 
(with covariate effect built into it)? Put another way, which model is 
preffered: one without a covariate or one with a covariate with 
significantly lower OFV but no change in ETA?

Toufigh Gordi 
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From: "Serge Guzy" 
Subject:RE: [NMusers] Covariate effect
Date: Fri, 7 Mar 2003 13:58:23 -0800

Without entering into mathematical details, my impression is that an influential covariate should
lead to a better objective function (ignoring the degree of freedom effect) and at the same time
decrease the ETA.  The use of a covariate separates to some extent the whole population into
subset of populations, each of them characterized by different population means. Suppose the 1
compt model, bolus injection and V lognormal 
V=Vfixed*exp(Vrandom): Suppose Vfixed=exp(a+b*weight(i)) and the covariate weight is really
significant(i for individual i).
If I am coming back to each individual and plug their corresponding weight into the Vfixed term, I
see that Vfixed will be different for every individual. If the covariate is influential, it will
decrease the residual part for every individual(V random).Consequently, the eta will decrease.

Serge Guzy
President POP-PHARM(510 453 7443)
Head of Pharmacometrics and Preclinical Statistics
Xoma: tel(510) 2047476
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From: "Gobburu, Jogarao V" 
Subject:RE: [NMusers] Covariate effect
Date:Fri, 7 Mar 2003 18:17:50 -0500

The case you describe is not unusual. I am assuming there is not much prior
information about this covariate. If there is no drop in the unexplained
variability, inspite of having a significant drop in OFV, the full model
might not be of practical use (for example dose adjustment). But certainly
it might be a signal to probe more into influential individuals/data points
(Mats Karlsson performed some work on these lines). Another source of this
happening could be that it is false-positive finding. 

Regards,
 Joga Gobburu
 Pharmacometrics
 CDER, FDA
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From:"Kowalski, Ken" 
Subject: RE: [NMusers] Covariate effect
Date:Mon, 10 Mar 2003 10:04:01 -0500

Toufigh,

It is likely that you have substantial power to detect relatively small
differences in the covariate effect.  This occurs quite frequently with
continuous covariates like body weight when you have a lot of subjects and a
wide range of values.  Since the change in OFV is the yardstick we use to
determine statistical significance of the covariate effects, I wouldn't
discard it and exclude the covariate effect from the model simply because it
doesn't appear to be clinically relevant.  I would use clinical relevance
only to intrepet the parameters for the final model and their impact on
dosing.  I would not use a clinical relevance assessment to guide model
building as this can be very subjective (based on one's assessment of what
is clinically relevant for each covariate effect).

Ken
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