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 <jgobb...@rx.umaryland.edu >: > 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 <ja...@wright-dose.com> > *Date: *Thursday, August 17, 2023 at 7:16 AM > *To: *Gobburu, Joga <jgobb...@rx.umaryland.edu>, nmusers@globomaxnm.com < > nmusers@globomaxnm.com> > *Subject: *Re: [NMusers] Observed (yaxis) vs Predicted (xaxis) Diagnostic > Plot - Scientific basis. > > You don't often get email from ja...@wright-dose.com. Learn why this is > important <https://aka.ms/LearnAboutSenderIdentification> > > *CAUTION: *This message originated from a non-UMB email system. Hover > over any links before clicking and use caution opening attachments. > > 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. > > > > 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 > >
