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
