RE: [NMusers] Visual predictive check!

Nick,

Yes, I'm making the assumption that a measured concentration cannot be
negative. Educate me about chemical assays. Can you get troughs rather
than peaks in a chromatogram such that the area below zero is integrated and
reported as a negative concentration? If so, what would happen if you
assayed a bunch of pre-dose samples (before drug is administered) where the
true mean concentration is zero? Would we get measured concentrations
symmetrically distributed about zero (with about 50% of the measured
concentrations reported as negative and 50% positive)? If so, then a normal
residual error model may indeed be appropriate.

Ken

-----Original Message-----
From: owner-nmusers_at_globomaxnm.com [mailto:owner-nmusers_at_globomaxnm.com] On
Behalf Of Nick Holford
Sent: Friday, May 23, 2008 10:40 AM
To: nmusers_at_globomaxnm.com
Subject: Re: [NMusers] Visual predictive check!

Ken,

You wrote among other things:
"The combined residual error model cannot be the correct model at very
low concentrations since the normal distribution will put non-zero
probability mass at concentrations less than zero if the mean is low
relative to its SD."

I think you are making the assumption that *measured* concentrations
have to be non-negative. In a real world measurement system there will
be random measurement noise around true zero. Thus a real world
measurement system would return both negative and positive measurements
for a true zero. Additive residual error models in theory describe this
behaviour. Simulations of *measurements* will then quite reasonably
include negative values.

In the truncated real world of chemical analysis real measurements of
true zero seem to be always reported as non-negative. Its a pity
chemical analysts don't seem to understand that this truncation always
causes measurement bias (whether the LLOQ is 0 or greater).

Best wishes,

Nick

Ken Kowalski wrote:
>
> Andreas,
>
> Your simulations highlight a limitation with the combined (additive +
> proportional or slope-intercept) residual error model. The combined
> residual error model cannot be the correct model at very low
> concentrations since the normal distribution will put non-zero
> probability mass at concentrations less than zero if the mean is low
> relative to its SD. The purist in me says don't truncate as that will
> lead to bias in your simulations although it may be minimal if few
> observations are simulated with negative concentrations. A better
> approach would be to consider an alternative residual error model that
> bounds the concentrations to be positive such as the log-normal
> residual error model (log-transform both sides approach) or fit a
> model that takes into account the censored BQL data ( see Beal, Ways
> to Fit a PK Model with Some Data Below the Quantification Limit. JPP
> 2001;28:481-504).
>
> Ken
>
> Kenneth G. Kowalski
>
> President & CEO
>
> A2PG - Ann Arbor Pharmacometrics Group
>
> 110 E. Miller Ave., Garden Suite
>
> Ann Arbor, MI 48104
>
> Work: 734-274-8255
>
> Cell: 248-207-5082
>
> ken.kowalski_at_a2pg.com
>
> *From:* owner-nmusers_at_globomaxnm.com
> [mailto:owner-nmusers_at_globomaxnm.com] *On Behalf Of *andreas lindauer
> *Sent:* Friday, May 23, 2008 6:23 AM
> *To:* nmusers_at_globomaxnm.com
> *Subject:* [NMusers] Visual predictive check!
>
> Dear NMusers,
>
> I have a question regarding simulations for a VPC. When a combined
> residual error is used it happens that for low concentrations negative
> values are simulated. While this is statistically correct, I wonder if
> it is correct to use these results for the VPC because the
> distribution of the observed low concentrations is truncated by the
> LLOQ. So the VPC might suggest model misspecification for lower
> concentrations. Further, when one wants to use the model for clinical
> trial simulation should then the negative (BQL) values be omitted
> because they would never appear in reality?
>
> I would like to know how the more experienced NMusers handle this.
>
> Thanks in advance, Andreas.
>
> ____________________________
>
> Andreas Lindauer
>
> University of Bonn
>
> Department of Clinical Pharmacy
>
> An der Immenburg 4
>
> D-53121 Bonn
>
> phone:+49 228 73 5781
>
> fax: +49 228 73 9757
>

--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
n.holford_at_auckland.ac.nz tel:+64(9)373-7599x86730 fax:+64(9)373-7090
www.health.auckland.ac.nz/pharmacology/staff/nholford



Received on Fri May 23 2008 - 11:22:19 EDT