Re: Visual predictive check!
Nick, Ken
I don't think it's a matter of an integrated area being negative. This is
of course possible but suggests the area dips down below the baseline
rather than rising above it.
I think the problem is much simpler. When analysts create a standard
curve, from which areas are associated with concentrations, then it is
generally assumed:
a) that the curve is linear (a straight line in this case)
b) that you estimate the intercept
The intercept of course is not required to go through zero - and can be
positive or negative. A non-zero intercept provides bias which analysts
(from my take) appear to be concerned about and hence truncate at a higher
value (LLOQ) from which any bias will be minimal. Note the definition of
LLOQ is all about variance not bias. But I do think it's bias that causes
the LLOQ war not variance (there is no case that variance should cause
such heated feelings on PharmPK). The confidence interval around the
slope will reveal a band of random uncertainty of the assay.
So - to clarify.
For me, a true concentration can never be observed and if it could it
would never be negative. An observed concentration predicted from an
assay can certainly be observed and be negative. A model predicted
concentration should therefore also be allowed to be negative, even though
negative concentrations are often perceived as inconvenient! Confusion may
arise regarding the non-equality of true concentration, observed
concentration and predicted concentration. And observed concentration
perhaps should be termed "assay predicted concentration" while predicted
concentration should be "PK model predicted concentration", but this is a
bit of a mouthful.
Regards
Steve
--
Professor Stephen Duffull
School of Pharmacy
University of Otago
PO Box 913
Dunedin
P 03 479 5044
F 03 479 7034
Quoting Nick Holford <[EMAIL PROTECTED]>:
> 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-----
Quoted reply history
> > From: [EMAIL PROTECTED]
> [mailto:[EMAIL PROTECTED] On
> > Behalf Of Nick Holford
> > Sent: Friday, May 23, 2008 10:40 AM
> > To: [email protected]
> > 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
> >>
> >> [EMAIL PROTECTED]
> >>
> >> *From:* [EMAIL PROTECTED]
> >> [mailto:[EMAIL PROTECTED] *On Behalf Of *andreas
> lindauer
> >> *Sent:* Friday, May 23, 2008 6:23 AM
> >> *To:* [email protected]
> >> *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
> [EMAIL PROTECTED] tel:+64(9)373-7599x86730 fax:+64(9)373-7090
> www.health.auckland.ac.nz/pharmacology/staff/nholford
>
>
>
--
Professor Stephen Duffull
School of Pharmacy
University of Otago
PO Box 913
Dunedin
P 03 479 5044
F 03 479 7034