Error models and weighting
From: "David Nix, Pharm D." <nix@pharmacy.arizona.edu>
Subject: Error models and weighting
Date: Wed, 23 May 2001 15:28:37 -0700
I'm seeking input about error models. Given the assay and PK characteristics, a constant + proportional error model makes the most sense to use. The following model is suggested in the manual for Xpose 2.0.
$ERROR
DEL=0
IF(F.EQ.0) DEL=1
IPRED=F
W=(F**2+THETA(.)**2)**0.5 ; constant + proportional
W=W+DEL
IRES=DV-IPRED
IWRES=IRES/W
Y=IPRED+W*EPS(1)
Niclas Johhson cautioned me about the following:
"You will have to be careful here, though, so that 0 isn't a valid value of F. Are you sure your problems with the first model is not due to a non-fixed SIGMA?"
It was my understanding that THETA(.) in the line
W=(F**2+THETA(.)**2)**0.5
would provide the standard deviation (proportional part). The Sigma would be the variance for the constant CV portion. I did not use a fixed Sigma. If I do fix Sigma, would I add another Theta value to include the constant CV part.
i.e. W=(((F**2)+THETA(.)**2)**0.5 + THETA(..) ????
The simplist control file will run without errors if the Sigma is fixed at 1.
In my case, I have 1-7 zero concentrations prior to the first detectable concentrations. The average Tlag was about 2 hours, although there were a few subjects without any apparent Tlag. I took note of the mixture model discussed recently; however, the presence or absense of Tlag is not determined by any known event. Tlag estimate is 0.622 which appears to be short.
In a previous message via nmusers, Leonid Gibiansky suggested that I use a simplier model - e.g. Y = F*(1+EPS(1))+EPS(2). If this model is used, I do not know how to get IWRES for using Xpose.
Clearly, there are DV values that need to be handled as true 0's. Is it possible to increase weighting for 0 concentrations so that the model can use this data to estimate the lag time better. Obviously, I would not want to influence the fits in a bad way. I can get out all concentrations equal to 0 except those that occur between the dose time and the time of the first detectable concentration. Also, I can get rid of the 0 just prior to the first detectable concentration since this may be below the detection limit but still > 0.
Any suggestions would be appreciated.