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Splitting the residual error

From: Jonathan Moss <jjmoss>
Date: Fri, 13 May 2016 10:36:40 +0100

Dear all,


I would like to share with you and get people's opinions on a recent issue I

I have a data set of 46 patients, orally dosed, with very dense sampling
during absorption (0.25h, 0.5h, 0.75h, 1h, 1.5h, 2h, 3h, 4h, 6h, 8h, 12h,
24h, 36h), Cmax at around 4 hours.

During modelling, I found that the residual error was not evenly
distributed. Plotting CWRES against time after dose, the result looked like
an "hourglass" shape. I.e. A wide spread during absorption, narrower near
Cmax time, then wider at later time points.

My thinking was as follows: Residual error contains both the assay / model
spec. error, and the error in recorded observation time. When the gradient
of the PK curve is large, any error in recorded observation time equals a
large error in the recorded concentration, whereas if the gradient is small
then the recorded concentration error will be small.

I "split" the residual error into its assay/model spec and time-error parts
in the $ERROR block:



GRAD = KA*A(2) - K20*A(3)




C_1 = A(3)/V ; Concentration in the
central compartment


SD = SQRT(EPROP*C_1**2) ; Standard deviation of
predicted concentration




Note: Sigma is fixed to one and EPROP is estimated as a theta. Here, GRAD is
the right hand side of the differential equation for A(3), in order to
recover the gradient. Val is estimated by NONMEM.


This approach vastly improved the model fit (OFV drop of around 350!). All
GOF plots, VPCs, NPCs, NPDEs, individual fits looked good. This got me
thinking, and I tried this approach on some of my other popPK models. I
found for the simpler models, the result was nearly always a significant
improvement in the model fit. For the more complicated models, NONMEM had
trouble finishing the runs.


I struggled to find any approach like this in the literature, which leads me
to believe that there is something wrong, as it is a relatively simple
concept. Please, what are peoples thoughts on this?





Jon Moss, PhD


BAST Inc Limited

Loughborough Innovation Centre

Charnwood Wing

Holywell Park

Ashby Road

Loughborough, LE11 3AQ, UK

Tel: +44 (0)1509 222908


Received on Fri May 13 2016 - 05:36:40 EDT

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