Parameter Uncertainty and Covariate effects
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, asymptotic)
distribution of the estimator (i.e. normal with mean THETA and covariance
according to the NONMEMs $COR output for the THETAs).
This approach may in some cases (particularly, when there are a lot of
covariate effects estimated) lead to very broad parameter distributions, even
assigning some quite high probability of unphysiological values if one didn’t
have good quality data, strong priors or a very careful parametrization of the
model (e.g. transforming/bounding parameters, which requires/introduces 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 parameter
uncertainty, the female population will have a more variable (uncertain) PK,
not just different one. If we phrase the problem differently, using
CL = TVCL * SEX_EFF**(1-SEX) , (Eq. 2)
The conclusion would be the other way around (i.e. male PK is more uncertain).
One approach to deal with the second problem could be this:
In order to remove this (usually unjustified) assumption (the female population
having a less certain PK compared to the male), one could try to model 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 parameters used in
Eq.1).
With this approach, both sub-populations, male and female get “some part” of
the uncertainty effect.
Of course it would be even nicer to let the data decide which sub-population
gets how much uncertainty exactly instead of evenly splitting it.
How do you deal with uncertainty in the estimates of covariate effects when it
comes to simulations/predictions?
Kind Regards,
________________________________________________________________________________________________________________________
SVEN STODTMANN, PHD
Pharmacometrician
AbbVie Deutschland GmbH & Co KG
Clinical Pharmacology and Pharmacometrics
Knollstrasse 50
67065 Ludwigshafen am Rhein, Germany
OFFICE +49 621-589-1940
EMAIL [email protected]
abbvie.com
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