# [NMusers] RE: Parameter Uncertainty and Covariate effects

From: Denney, William S. <William.S.Denney_at_pfizer.com>
Date: Tue, 12 Jan 2016 14:28:43 +0000

Hi Sven,

As Mats said, you need to account for correlation between parameters. Using uncorrelated parameters, you will have all the issues discussed below (high variability on the second population). For model building, you could do the following to minimize that correlation and have the variance of your terms more reasonable (likely approximately proportional to the percent of subjects in your data set who are men and women):

TVCL = THETA(1)*(1-SEX) + THETA(2)*SEX

That would give separate estimates of THETA(1) and THETA(2) for each sex that would be logically uncorrelated. If you have a specific desire to estimate the ratio of clearance, there are several potential ways to estimate it from separate parameters. The best is probably bootstrapping the results and using the empirical distribution from the bootstrap. Taking the ratio of two normally distributed variables unfortunately gives a Cauchy distributed parameter which has no mean or standard deviation (though many people just take the ratio and move on-- it's not far from accurate).

Thanks,

Bill

-----Original Message-----
From: owner-nmusers_at_globomaxnm.com [mailto:owner-nmusers_at_globomaxnm.com] On Behalf Of Stodtmann, Sven
Sent: Monday, January 11, 2016 7:53 AM
To: nmusers_at_globomaxnm.com
Subject: [NMusers] 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 sven.stodtmann_at_Abbvie.com

abbvie.com
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