Re: [NMusers] Visual predictive check!

Ken,

First of all -- I have almost no real world experience of modern
analytical laboratory methods. But I have seen chromatograms from HPLC
machines which have baseline noise. One way to quantitate the sample is
to integrate over an interval at the expected retention time after a
true zero specimen had passed through the system then the resulting area
could be either positive or negative. Another method would be to search
for a positive peak around the expected retention time and center the
integration around that peak -- this would of course lead to a positive
bias.

So if the first (potentially unnbiased) method is used for a series of
pre-dose concs then the resulting distribution should have both negative
and positive values. Whether it was symmetrical or even normal would
depend on the factors that cause the baseline noise.

I suspect that commonly used methods today rely on software that will
have a truncation bias built into it (e.g. using the second method) even
before the LLOQ bias is added.

I have even less experience of mass spectroscopy methods - my naive
understanding is that the mass lines are measured within one atomic
weight unit of resolution so it is unlikely even for true zero samples
that a negative mass would be obtained. So for mass spec assays the
assumption that measurements are non-negative may be true.

Best wishes,

Nick

Ken Kowalski wrote:
> 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 - 11:47:19 EDT