# [NMusers] Additive plus proportional error model for log-transform data

Date: Thu, 2 Jun 2016 02:27:29 +0000

Dear NMusers,

I am developing a PK model using log-transformed single-dose oral data. My =
question relates to using combined error model for log-transform data.

I have read few previous discussions on NMusers regarding this, which were =
really helpful, and I came across two suggested formulas (below) that I tes=
ted in my PK models. Both formulas had similar model fits in terms of OFV =
(OFV using Formula 2 was one unit less than OFV using Formula1) with slight=
ly changed PK parameter estimates. My issue with these formulas is that the=
model simulates very extreme concentrations (e.g. upon generating VPCs) at=
the early time points (when drug concentrations are low) and at later time=
points when the concentrations are troughs. These simulated extreme concen=
trations are not representative of the model but a result of the residual e=
rror model structure.

My questions:

1. Is there a way to solve this problem for the indicated formulas?

2. Are the two formulas below equally valid?

3. Is there an alternative formula that I can use which does not have=
this numerical problem?

4. Any reference paper that discusses this subject?

Here are the two formulas:

1. Formula 1: suggested by Mats Karlsson with fixing SIGMA to 1:

W=SQRT(THETA(16)**2+THETA(17)**2/EXP(IPRE)**2)

2. Formula 2: suggested by Leonid Gibiansky with fixing SIGMA to 1:

W = SQRT(THETA(16)+ (THETA(17)/EXP(IPRE))**2 )

The way I apply it in my model is this:

FLAG=0 ;TO AVOID ANY CALCULATIONS OF LOG (0)
IF (F.EQ.0) FLAG=1
IPRE=LOG(F+FLAG)

W=SQRT(THETA(16)**2+THETA(17)**2/EXP(IPRE)**2) ;FORMULA 1

IRES=DV-IPRE
IWRES=IRES/W
Y=(1-FLAG)*IPRE + W*EPS(1)

\$SIGMA
1. FIX

Best regards,