# RE: Calculating shrinkage when some etas are zero

From: Eleveld, DJ <d.j.eleveld>
Date: Fri, 21 Aug 2009 14:57:04 +0200

Hi Pyry and Jacob,

If you exclude zero etas then what happens to infomative individuals who just happen to have the population typical values?
This approch would exclude these individuals when trying to indicate how informative an estimation is about a parameter.
I know this is unlikely, but it is possible.

The etas just tell what value is estimated, its not the whole story about how infomative an estimation is. I dont think you can do
this without considering how 'certian' you are of each of those eta values.

Douglas Eleveld

________________________________

Van: owner-nmusers Jakob
Verzonden: vr 21-8-2009 12:26
Aan: Pyry VĂ¤litalo; nmusers
Onderwerp: RE: [NMusers] Calculating shrinkage when some etas are zero

Hi Pyry,

Yes, when calculating shrinkage or looking at eta-diagnostic plots it is often better to exclude etas from subjects that has no information on that parameter at all. For a PK model we would not include subjects that were only administered placebo (if PK is exogenous compound). In the same manner placebo subjects are not informative on the drug-effects parameters of a (PK-)PD model. These subjects have informative etas for the placebo-part of the PD model, but not on the drug-effects (etas on Emax, ED50, etc.). For any eta-diagnostics you can removed these etas based on design (placebo subject, IV dosing, et c) or the empirical-Bayes estimate of eta being zero.

Cheers

Jakob

________________________________

From: owner-nmusers
Sent: 21 August 2009 10:45
To: nmusers
Subject: [NMusers] Calculating shrinkage when some etas are zero

Hi all,

I saw this snippet of information on PsN-general mailing list.

Kajsa Harling wrote in PsN-general:
"I talked to the experts here about shrinkage. Apparently, sometimes an
individual's eta may be exactly 0 (no effect, placebo, you probably
understand this better than I do). These zeros should not be included in
the shrinkage calculation, but now they are (erroneously) in PsN."

This led me to wonder about the calculation of shrinkage. I decided to post here on nmusers, because my question mainly relates to NONMEM. I could not find previous discussions about this topic exactly.

As I understand, if a parameter with BSV is not used by some individuals, the etas for these individuals will be set to zero. An example would be a dataset with IV and oral dosing data. If oral absorption rate constant KA with BSV is estimated for this data, then all eta(KA) values for IV dosing group will be zero.

The shrinkage of etas is calculated as
1-sd(etas)/omega
If the etas that equal exactly zero would have to be removed from this equation then it would mean that NONMEM estimates the omega based on only those individuals who need it for the parameter in question, e.g. the omega(KA) would be estimated only based on the oral dosing group. Is this a correct interpretation for the rationale to leave out zero etas?

I guess the inclusion of zero etas into shrinkage calculations significantly increases the estimate of shrinkage because the zero etas always reduce the sd(etas). As a practical example, suppose a dataset of 20 patients with oral and 20 patients with IV administration. Suppose NONMEM estimates an omega of 0.4 for BSV of KA. Suppose the sd(etas) for oral group is 0.3 and thus sd(etas) for all patients is 0.3/sqrt(2) since the etas in IV group for KA are zero.
Thus, as far as I know, PsN would currently calculate a shrinkage of 1-(0.3/sqrt(2))/0.4=0.47.
Would it be more appropriate to manually calculate a shrinkage of 1-0.3/0.4=0.25 instead?

Kind regards,
Pyry

Kajsa Harling wrote:

Dear Ethan,

I have also been away for a while, thank you for your patience.

I talked to the experts here about shrinkage. Apparently, sometimes an
individual's eta may be exactly 0 (no effect, placebo, you probably
understand this better than I do). These zeros should not be included in
the shrinkage calculation, but now they are (erroneously) in PsN.

Does this explain the discrepancy?

Then, the heading shrinkage_wres is incorrect, it should say
shrinkage_iwres (or eps) they say.

Comments are fine as long as they do not have commas in them. But this
is fixed in the latest release.

Best regards,
Kajsa

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Received on Fri Aug 21 2009 - 08:57:04 EDT

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