Re: Log transformation of both sides
Norman,
I think both variants are not correct. If you worry only about VPC, you can use your current model output, and just replace negative values with zeros. If you would like to change the model using transformation from both sides, you need to work in the log-transformed domain, with DV=log(concentration). If you denote the model prediction as TY, then the error model can be presented as
Y = LOG(TY) + EPS(1) ; exponential model
or
W = SQRT(THETA()/TY**2+THETA()) ; something like combined model
Y = LOG(TY) + W*EPS(1) ;
$SIGMA
1 FIXED
If there is a chance that TY=0 (e.g., on the first dosing record or if you use the lag time), you may put some protection
W = 1
LOGTY=0 ; or some other number, e.g., LOG(LLOQ/2)
IF(TY.GT.0) LOGTY = LOG(TY)
IF(TY.GT.0) W = SQRT(THETA()/TY**2+THETA() ; similar to combined model
Y = LOGTY + W*EPS(1)
Sometimes this error model inflates variance too strongly (at low TY values). Then something like EMAX error model in logs can help:
W = THETA() - THETA()*TY/(THETA()+TY)
Y = LOG(TY) + W*EPS(1) ;
$SIGMA
1 FIXED
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
Quoted reply history
On 6/27/2012 5:25 PM, Norman Z wrote:
> Dear NMusers,
>
> I am working on a one compartment model with additive and proportional
> error model.
> Y = F*(1+EPROP*EPS(1))+EADDS*EPS(2)
>
> When I performed VPC, I found some 2.5% percentile of the concentration
> CI is negative. I guess it may be due to the concentration is very low
> after several t1/2, and the additive error on top of the low DV values
> causes the negative values.
> So I'd like to take "log transformation both sides" approach to avoid
> the issue. I wonder if any one can comment on the differences of the
> following methods:
> 1. Generate a ln(DV) column in the dataset, and use
> Y =LOG(F*(1+EPROP*EPS(1))+EADDS*EPS(2))
> in the $ERROR block.
>
> 2. Use DV in the model, and code the $ERROR block
> Y1=LOG(F*(1+EPROP*EPS(1))+EADDS*EPS(2))
> Y=EXP(Y1)
>
> Are these two methods equivalent to achieve log transformation of both
> sides, or they are different?
>
> Thanks for your help.
>
> Norman
>
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