Re: Observed (yaxis) vs Predicted (xaxis) Diagnostic Plot - Scientific basis.
Hi Joga,
Fully agree on this, unfortunately it is still often shown the other way
around which is at least confusing.
There is a publication on this very topic here
https://www.sciencedirect.com/science/article/abs/pii/S0304380008002305 that
arrives at the same conclusion and can be helpful.
Best,
Wilbert
Op do 17 aug 2023 om 19:47 schreef Gobburu, Joga <[email protected]
>:
> Dear James – how have you been?
>
>
>
> Yes, you said it most eloquently. Its not about plotting per se but “the
> problem is really that the loess line is fitting noise in the wrong
> direction if the observed is actually on the x-axis”. Thank you…J
>
>
>
> *From: *James G Wright <[email protected]>
> *Date: *Thursday, August 17, 2023 at 7:16 AM
> *To: *Gobburu, Joga <[email protected]>, [email protected] <
> [email protected]>
> *Subject: *Re: [NMusers] Observed (yaxis) vs Predicted (xaxis) Diagnostic
> Plot - Scientific basis.
>
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>
> So whichever axis the observed data is plotted on is parallel to the
> direction of noise (random residual error). When you fit the loess line, I
> think it will generally assume noise is vertical i.e. parallel to the
> y-axis. So the problem is really that the loess line is fitting noise in
> the wrong direction if the observed is actually on the x-axis ... which
> means you are right, the observed needs to go on the y-axis and deviations
> need to be interpreted parallel to the y-axis.
>
>
>
> Kind regards, James
>
>
>
> https://product.popypkpd.com/
>
>
>
> PS Of course, if you were to fit a loess line with horizontal noise and
> observed data on the x-axis, you should reach identical conclusions to the
> conventional vertical noise and observed data on the y-axis.
>
>
>
Quoted reply history
> On 17/08/2023 11:35, Gobburu, Joga 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
>
>
>
> --
>
> James G Wright PhD,
>
> Scientist, Wright Dose Ltd
>
> Tel: UK (0)772 5636914
>
>