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
