Em 18 de ago. de 2023, à(s) 09:27, Nick Holford
<n.holf...@auckland.ac.nz> escreveu:
Thanks Joga for raising the issue of so called diagnostic plots and
Martin’s reminder that they are not reliable as diagnostics.
The gold standard tool for model evaluation, which may also help
diagnose model problems, it the VPC. Martin - it is not a “for
example” method -- it is the primary model evaluation tool.
Comparison of the median observed percentile with the median
predicted percentile is the first step in using a VPC. Unfortunately,
there are still VPCs being produced that show only the observed
percentiles without the corresponding predicted percentiles.
All so called diagnostic plots and VPCs that do not show observed AND
predicted percentiles belong in the bin.
Best wishes,
Nick
--
Nick Holford, Professor Emeritus Clinical Pharmacology, MBChB, FRACP
mobile:NZ+64(21)46 23 53 ; FR+33(6)62 32 46 72
email: n.holf...@auckland.ac.nz <mailto:n.holf...@auckland.ac.nz>
web: http://holford.fmhs.auckland.ac.nz/
<http://holford.fmhs.auckland.ac.nz/>
*From:*owner-nmus...@globomaxnm.com <owner-nmus...@globomaxnm.com>
*On Behalf Of *Martin Bergstrand
*Sent:* Friday, August 18, 2023 9:48 AM
*To:* Gobburu, Joga <jgobb...@rx.umaryland.edu>
*Cc:* nmusers@globomaxnm.com
*Subject:* Re: [NMusers] Observed (yaxis) vs Predicted (xaxis)
Diagnostic Plot - Scientific basis.
Dear Joga and all,
Joga makes a valuable point that all pharmacometricians should be
aware of. Standard methodology for regression assumes that the
x-variable is without error (loess, linear regression etc.). Note
that it is the same for NLME models i.e. we generally assume that our
independent variables e.g. time, covariates etc. are without error.
For DV vs. PRED plots it is common practice, even among those that do
not know why, to plot PRED on the x-axis and DV on the y-axis. A
greater problem with these plots is the commonly held expectation
that for a "good model" a smooth or regression line should align with
the line of unity. Though this seems intuitive it is a flawed
assumption. This issue was clearly pointed out by Mats Karlsson and
Rada Savic in their 2007 paper titled "Diagnosing Model
Diagnostics''. For simple well-behaved examples you will see an
alignment around the line of unity for DV vs. PRED plots. However,
there are several factors that contribute to an expected deviation
from this expectation:
(1) Censoring (e.g. censoring of observations < LLOQ)
- In this case DVs are capped at LLOQ but PRED values are not. This
makes it perfectly expected that there will be a deviation from
alignment around the line of unity in the lower range.
(2) Strong non-linearities
- The more nonlinear the modelled system is, the greater the expected
deviation from the line of unity. Especially in combination with
significant ETA correlations.
(3) High variability
- With higher between/within subject variability (e.g. IIV and RUV)
that isn't normally distributed (e.g. exponential distributions) will
result in an expected deviation from the line of unity. Note: this is
a form of non-linearity so it may fall under the above category.
(4) Adaptive designs (e.g. TDM dosing)
- Listed in the original paper by Karlsson & Savic but I have not
been able to recreate an issue in this case.
I am rather sure that many thousands of hours have been spent on
modeling trying to correct for perceived model misspecifications that
are not really there. This is why I recommend relying primarily on
simulation-based model diagnostics (e.g. VPCs) and as far as possible
account for censoring that affects the original dataset. As pointed
out by Karlsson & Savic a simulation/re-estimation based approach can
also be used to investigate the expected behavior for DV vs. PRED
plots for a particular model and dataset (e.g. mirror plots in
Xpose). Note that to my knowledge there is yet no automated way to
handle censoring in this context (clearly doable if anyone wants to
develop a nifty implementation of that).
If we leave the DV vs. PRED plot case, there are many other instances
where we use scatter plots where it is much less clear what can be
considered the independent variable and yet other cases where the
assumption that the x-variable is without error is violated in a way
that makes the results hard to interpret. One instance of the latter
is when exposure-response is studied by plotting observed PD response
versus observed trough plasma concentrations. This is already a way
too long email so I will not deep dive into that problem as well.
Best regards,
Martin Bergstrand, Ph.D.
Principal Consultant
Pharmetheus AB
martin.bergstr...@pharmetheus.com
www.pharmetheus.com <http://www.pharmetheus.com>
On Thu, Aug 17, 2023 at 12:44 PM Gobburu, Joga
<jgobb...@rx.umaryland.edu> wrote:
Dear Friends – Observations versus population predicted is
considered a standard diagnostic plot in our field. I used to
place observations on the x-axis and predictions on the yaxis.
Then I was pointed to a publication from ISOP
(https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5321813/figure/psp412161-fig-0001/)
which recommended plotting predictions on the xaxis and
observations on the yaxis. To the best of my knowledge, there was
no justification provided. It did question my decades old
practice, so I did some thinking and digging. Thought to share it
here so others might benefit from it. If this is obvious to you
all, then I can say I am caught up!
1. We write our models as observed = predicted + random error;
which can be interpreted to be in the form: y = f(x) + random
error. It is technically not though. Hence predicted goes on
the xaxis, as it is free of random error. It is considered a
correlation plot, which makes plotting either way acceptable.
This is not so critical as the next one.
2. However, there is a statistical reason why it is important to
keep predictions on the xaxis. Invariably we always add a
loess trend line for these diagnostic plots. To demonstrate
the impact, I took a simple iv bolus single dose dataset and
compared both approaches. The results are available at this
link:
https://github.com/jgobburu/public_didactic/blob/main/iv_sd.html.pdf.
I used Pumas software, but the scientific underpinning is
agnostic to software. See the two plots on Pages 5 and 6. The
interpretation of the bias between the two approaches is
different. This is the statistical reason why it matters to
plot predictions on the xaxis.
Joga Gobburu
University of Maryland
/This communication is confidential and is only intended for the use
of the individual or entity to which it is directed. It may contain
information that is privileged and exempt from disclosure under
applicable law. If you are not the intended recipient please notify
us immediately. Please do not copy it or disclose its contents to any
other person./
/Any personal data will be processed in accordance with Pharmetheus'
privacy notice, available here
<https://pharmetheus.com/privacy-policy/>./
