# Calculating shrinkage when some etas are zero

From: Pyry Välitalo <pyry.valitalo>
Date: Fri, 21 Aug 2009 12:45:03 +0300

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

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

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
>
>
>

Received on Fri Aug 21 2009 - 05:45:03 EDT

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