# Re: Parameter Uncertainty and Covariate effects

From: Mats Karlsson <Mats.Karlsson>
Date: Tue, 12 Jan 2016 05:02:23 +0000

Dear Sven

If you don't assume the covariance between THETA(1) and THETA(2) to be zero=
but use the estimated covariance value, you do let the data speak. A probl=
em in this respect is that publications never give such values even if it o=
f course is possible. With online access to model code and output (as with =
the DDMoRe repository (repository.ddmore.eu)) it will be more likely to fin=
d the information.

Best regards,
Mats

Skickat från min iPhone

> 11 jan 2016 kl. 14:28 skrev Stodtmann, Sven <sven.stodtmann
>
> Dear All,
>
> In order to account for uncertainty in estimated parameters when running =
a simulation, a natural approach would be running multiple simulations for =
different parameter vectors which are drawn from the (theoretical, asymptot=
ic) distribution of the estimator (i.e. normal with mean THETA and covarian=
ce according to the NONMEMs \$COR output for the THETAs).
> This approach may in some cases (particularly, when there are a lot of co=
assigning some quite high probability of unphysiological values if one did=
n’t have good quality data, strong priors or a very careful parametrizati=
on of the model (e.g. transforming/bounding parameters, which requires/intr=
oduces prior knowledge as well).
>
> Another problem connected with parameter uncertainty on covariate effects=
is the following. Say we model
> TVCL = THETA(1)
> SEX_EFF = THETA(2)
> CL = TVCL * SEX_EFF**SEX, =
(Eq. 1)
> where male is coded as SEX=0, female as SEX=1.
> In this case, when using the above mentioned technique to account for par=
ameter uncertainty, the female population will have a more variable (uncert=
ain) PK, not just different one. If we phrase the problem differently, usin=
g
> CL = TVCL * SEX_EFF**(1-SEX) , (=
Eq. 2)
> The conclusion would be the other way around (i.e. male PK is more uncert=
ain).
>
> One approach to deal with the second problem could be this:
> In order to remove this (usually unjustified) assumption (the female popu=
lation having a less certain PK compared to the male), one could try to mod=
el the same covariate effect as follows:
> TVCL = THETA(1)
> SQRT_SEX_EFF = THETA(2)
> CL = TVCL * SQRT_SEX_EFF**SEX / SQRT_SEX_EFF**(1-SEX)
> In this case TVCL would already include “half” of the effect (on the =
log scale; the “new” TVCL would be TVCL*SQRT(SEX_EFF) in terms of the p=
arameters used in Eq.1).
> With this approach, both sub-populations, male and female get “some par=
t” of the uncertainty effect.
> Of course it would be even nicer to let the data decide which sub-populat=
ion gets how much uncertainty exactly instead of evenly splitting it.
>
> How do you deal with uncertainty in the estimates of covariate effects wh=
en it comes to simulations/predictions?
>
> Kind Regards,
> _________________________________________________________________________=
_______________________________________________
> SVEN STODTMANN, PHD
> Pharmacometrician
>
> AbbVie Deutschland GmbH & Co KG
> Clinical Pharmacology and Pharmacometrics
> Knollstrasse 50
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> OFFICE +49 621-589-1940
> EMAIL sven.stodtmann
>
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Received on Tue Jan 12 2016 - 00:02:23 EST

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