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
