Dear All,
I'm working on a one-compartment iv model. I have used a model for the IWRES from a discussion from May 2001 (thanks to Mats Karlsson, Niclas Jonsson and Nick Holford), where you use thetas to obtain the sigmas when using a combined residual model:
IPRED=F
IRES=DV-IPRED
IWRES=(DV-IPRED)/SQRT(F*F*THETA(3)*THETA(3)+THETA(4)*THETA(4))
Y=F*(1+THETA(3)*ERR(1))+THETA(4)*ERR(2).
where you then fix the sigmas to 1. I obtained the following results for a particular base model:
ETA = 3.16 28.1 0.0804 0.163
ETASD = 1.23693 1.42478
ERRSD = 1 1
THETA:se% = 23.9 32.0 39.9 23.3
OMEGA:se% = 18.4 33.8
SIGMA:se% = 0.0 0.0
I then ran the same model but using the normal code in the $ERROR section to see if there was any difference in the final estimates:
IPRED=F
IRES=DV-IPRED
Y=F*(1+ERR(1))+ERR(2)
and obtained these results:
THETA = 3.16 28.1
ETASD = 1.23693 1.42478
ERRSD = 0.0803741 0.163095
THETA:se% = 23.5 32.0
OMEGA:se% = 18.5 33.9
SIGMA:se% = 79.3 45.9
Here are few questions: 1.Can anyone tell me why the standard errors for the thetas in model 1 and the standard errors for the sigmas in model 2 differ so significantly? 2.Why does the algorithm used to obtain the standard errors for the sigmas differ so much from that used to obtain standard errors for the thetas, and how? 3.What are the implications when then using INTERACTION? 4....and finally, which model should i use?
Thankyou in advance for any light that can be shed.
Best,
Paul Westwood.
Combined residual model and IWRES.
Paul,
In thetas, SE% refers to SE% of SD while in OMEGAs it refers to variances (SD^2). To make them identical, use
IWRES=(DV-IPRED)/SQRT(F*F*THETA(3)+THETA(4))
Y=F*(1+SQRT(THETA(3))*ERR(1))+SQRT(THETA(4))*ERR(2).
also, if you take the square of SD SE%, you will see that it nearly matches SE% for OMEGAs, as it should
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
Paul Westwood wrote:
> Dear All,
>
> I'm working on a one-compartment iv model. I have used a model for the IWRES from a discussion from May 2001 (thanks to Mats Karlsson, Niclas Jonsson and Nick Holford), where you use thetas to obtain the sigmas when using a combined residual model:
>
> IPRED=F
> IRES=DV-IPRED
> IWRES=(DV-IPRED)/SQRT(F*F*THETA(3)*THETA(3)+THETA(4)*THETA(4))
> Y=F*(1+THETA(3)*ERR(1))+THETA(4)*ERR(2).
>
> where you then fix the sigmas to 1. I obtained the following results for a particular base model:
>
> ETA = 3.16 28.1 0.0804 0.163
> ETASD = 1.23693 1.42478
> ERRSD = 1 1
> THETA:se% = 23.9 32.0 39.9 23.3
> OMEGA:se% = 18.4 33.8
> SIGMA:se% = 0.0 0.0
>
> I then ran the same model but using the normal code in the $ERROR section to see if there was any difference in the final estimates:
>
> IPRED=F
> IRES=DV-IPRED
> Y=F*(1+ERR(1))+ERR(2)
>
> and obtained these results:
>
> THETA = 3.16 28.1
> ETASD = 1.23693 1.42478
> ERRSD = 0.0803741 0.163095
> THETA:se% = 23.5 32.0
> OMEGA:se% = 18.5 33.9
> SIGMA:se% = 79.3 45.9
>
> Here are few questions: 1.Can anyone tell me why the standard errors for the thetas in model 1 and the standard errors for the sigmas in model 2 differ so significantly? 2.Why does the algorithm used to obtain the standard errors for the sigmas differ so much from that used to obtain standard errors for the thetas, and how? 3.What are the implications when then using INTERACTION? 4....and finally, which model should i use?
>
> Thankyou in advance for any light that can be shed.
>
> Best,
>
> Paul Westwood.
Dear Paul,
You can use the delta method to compute the variance and expected value of a
transformation, which is square in your case.
given y=theta^2
E(y)=theta^2
Var(y)=Var(theta)+(2*theta)^2 ; the later portion is square of the first
derivative of y with respect of theta.
In your example theta is the standard deviation whereas error estimate is
variance. I did not follow your values very well, so I ran a model with same
reparameterization and got following results.
theta=2.65, rse=27.2%
err=7.04; rse=54.4%
theta.1<-2.65
rse<-27.2
var.theta.1<-(rse*theta.1/100)^2 ## = 0.51955
err.1<-7.04
rse.err.1<-54.4#%
var.err.1<-(rse.err.1*err.1/100)^2 ## = 14.66
##now from delta method
E(err)=2.65^2 ## 7.025 close to 7.04
var(err)=(2*2.65)^2*0.51955 ## 14.59 close to 14.66
Hope it helps
Varun Goel
PhD Candidate, Pharmacometrics
Experimental and Clinical Pharmacology
University of Minnesota
Paul Westwood <[EMAIL PROTECTED]> wrote: Dear All,
I'm working on a one-compartment iv model. I have used a model for the
IWRES from a discussion from May 2001 (thanks to Mats Karlsson, Niclas
Jonsson and Nick Holford), where you use thetas to obtain the sigmas when
using a combined residual model:
IPRED=F
IRES=DV-IPRED
IWRES=(DV-IPRED)/SQRT(F*F*THETA(3)*THETA(3)+THETA(4)*THETA(4))
Y=F*(1+THETA(3)*ERR(1))+THETA(4)*ERR(2).
where you then fix the sigmas to 1. I obtained the following results for a
particular base model:
ETA = 3.16 28.1 0.0804 0.163
ETASD = 1.23693 1.42478
ERRSD = 1 1
THETA:se% = 23.9 32.0 39.9 23.3
OMEGA:se% = 18.4 33.8
SIGMA:se% = 0.0 0.0
I then ran the same model but using the normal code in the $ERROR section
to see if there was any difference in the final estimates:
IPRED=F
IRES=DV-IPRED
Y=F*(1+ERR(1))+ERR(2)
and obtained these results:
THETA = 3.16 28.1
ETASD = 1.23693 1.42478
ERRSD = 0.0803741 0.163095
THETA:se% = 23.5 32.0
OMEGA:se% = 18.5 33.9
SIGMA:se% = 79.3 45.9
Here are few questions: 1.Can anyone tell me why the standard errors for
the thetas in model 1 and the standard errors for the sigmas in model 2
differ so significantly? 2.Why does the algorithm used to obtain the
standard errors for the sigmas differ so much from that used to obtain
standard errors for the thetas, and how? 3.What are the implications when
then using INTERACTION? 4....and finally, which model should i use?
Thankyou in advance for any light that can be shed.
Best,
Paul Westwood.
---------------------------------
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