# RE: inclusion of covariates with \$PRIOR

From: Mats Karlsson <Mats.Karlsson>
Date: Thu, 16 May 2019 12:22:12 +0000

Hi Anna,

That you want to explore covariate relationships on a parameter suggests that you believe your data contain plenty of information about the parameter. Therefore do you really need to use a prior on the parameter(s) in question? A little more info around what your “base” model is and why you use a prior could help answering.

You write “"OBJECTIVE FUNCTION VALUE WITHOUT CONSTANT" (without PRIOR penalty). ”, but the CONSTANT mentioned is not related to the prior, but rather the term of the OFV that is related to the number of observations only (Nobs*LN(2*PI)).
For obtaining a reference distribution for the likelihood ratio test a randomization (permutation) test is often useful as it uses the real data as opposed to simulated data. PsN functionality for this is “randtest”.

Best regards,
Mats
From: owner-nmusers obomaxnm.com <owner-nmusers
Sent: den 16 maj 2019 10:46
To: nmusers
Subject: [NMusers] inclusion of covariates with \$PRIOR

Dear NMusers

I am wondering about the inclusion of covariates with the \$PRIOR subroutine.

The article "Use of Prior Information to Stabilize a Population Data Analysis" (Gisleskog, Karlsson, Beal 2002) states that Stepwise Covariate Modelling (SCM) is possible on a parameter estimated with prior information, under conditions :

1) Population parameters have to be centered around the prior geometric mean (often the median) of the covariate (for example, if the power function is used: (COV/medianCOV)**THETA(COV), medianCOV is the median in the prior dataset)
Is it correct to use functions like linear function (1+THETA(COV)*(COV-medianCOV) or exponential function (exp(THETA(COV)*(COV-medianCOV) ?

2) the SUM of the objective function and the PRIOR penalty should be used to perform hypothesis tests.
Could you confirm I have properly understood this condition??
I am in doubt because automated SCM with \$PRIOR in PsN (https://uupharmacometrics.github.io/PsN/docs.html<https://urlproxy.sunet.se/canit/urlproxy.php?_q=aHR0cHM6Ly91dXBoYXJtYWNvbWV0cmljcy5naXRodWIuaW8vUHNOL2RvY3MuaHRtbA%3D%3D&_s=bWF0cy5rYXJsc3NvbkBmYXJtYmlvLnV1LnNl&_c=ef5b1054&_r=dXUtc2U%3D>) compares the "OBJECTIVE FUNCTION VALUE WITHOUT CONSTANT" (without PRIOR penalty).

3) hypothesis tests such as the Likelihood Ratio Test needs to be performed with the ACTUAL significance level
Is there a way to determine the actual significance level faster than Stochastic Simulation and Estimation?

4) the prior omega of the parameter on which the covariate impacts should be decreased by the product of THETA(COV)² and the prior population variance of log(COV).
Does that mean we should manually adjust the \$OMEGAP value of a parameter on which we test the covariate ? OMEGAP(adjusted) = OMEGAP - (THETA(COV))²*var
with OMEGAP = prior OMEGA estimate of the parameter on which the covariate is added ; var = prior population variance of log COV

Thank you very much for your understanding,

Sincerely yours,

Anna Chan Kwong
PhD sudent in Pharmacometrics, Marseille University.

När du har kontakt med oss på Uppsala universitet med e-post så innebär det att vi behandlar dina personuppgifter. För att läsa mer om hur vi gör det kan du läsa här: http://www.uu.se/om-uu/dataskydd-personuppgifter/