Splitting the residual error

Dear all, I would like to share with you and get people's opinions on a recent issue I had. 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: $ERROR GRAD = KA*A(2) - K20*A(3) IF (GRAD.LT.0) GRAD = -1*GRAD C_1 = A(3)/V ; Concentration in the central compartment IPRED = C_1 SD = SQRT(EPROP*C_1**2) ; Standard deviation of predicted concentration Y=IPRED+SD*(1+val*GRAD)*EPS(1) 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? Thanks, Jon Jon Moss, PhD Modeller BAST Inc Limited Loughborough Innovation Centre Charnwood Wing Holywell Park Ashby Road Loughborough, LE11 3AQ, UK Tel: +44 (0)1509 222908