interpretation of WRES of logarithmically transformed data

From: Anthe Zandvliet Apaza@SLZ.NL Subject: [NMusers] interpretation of WRES of logarithmically transformed data Date: 11/21/2003 5:40 AM Dear all, I have fitted the natural logarithms of measured concentrations to a PK model. The error block is given below. $ERROR IF (DV.EQ.0) THEN IPRED=-3 ELSE IPRED=LOG(F) ENDIF Y=IPRED+THETA(10)*EPS(1) W=IPRED IRES=DV-IPRED IWRES=IRES/W EPS(1) is fixed at 1. In order to interpret the output of my runs, I should calculate EXP(DV), EXP(PRED) and EXP(IPRED) of the logarithmic DV's, PRED's and IPRED's to obtain the linear values. However, I can not transform WRES values to their corresponding linear values. Does anyone have suggestions how to interpret the WRES values that are calculated by NONMEM? Thank you! Best regards, Anthe Zandvliet Slotervaart Hospital Dept. Pharmacy and Pharmacology Louwesweg 6 1066 EC AMSTERDAM The Netherlands Telephone +31 20 512 4657 FAX + 31 20 512 4753

From: "Kowalski, Ken" Ken.Kowalski@pfizer.com Subject: RE: [NMusers] interpretation of WRES of logarithmically transformed data Date: 11/21/2003 8:28 AM Anthe, The log-transformed model assumes that the residual errors are additive with a constant variance, in your case, sigma2=THETA(10)2. Thus, to calculate the weighted (standardized) residuals you should divide the IRES by sigma (i.e., W=THETA(10)). If the assumptions of your model are correct, these IWRES should be unimodal and symmetric about zero with constant variance. Moreover, if the errors are normally distributed approximately 99% of the residuals should fall between 3 (within 3 standard deviations). Note, there is no need to transform these residuals back to the untransformed scale. Moreover, in doing so you lose the diagnostic properties (symmetry about zero and uniform variance). The whole point to doing the transformation is to find a scale in which it is reasonable to assume that EPS(1) has a symmetric distribution with constant variance. Untransforming the DVs and predictions (PREDs and IPREDs) to the original concentration scale are fine, however, evaluating the goodness of fit in terms of the deviations from the model fit should be performed in the log-transformed scale IF the assumptions of the log-transformed model are valid. Also, I would avoid arbitrarily fixing the prediction to -3 when DV=0. If your model must predict zero (i.e., F=0), such as when an ALAG parameter is included in the model, there is another parameterization of the log-transformed model that introduces a bias parameter to resolve the log(0) problem (see Beal, JPP 2001;28:481-504). There has also been discussion of the pros/cons of this model on Nmusers awhile ago so you might want to search the archives. Ken

From: VPIOTROV@PRDBE.jnj.com Subject: RE: [NMusers] interpretation of WRES of logarithmically transformed data Date: 11/24/2003 10:26 AM The only need to set IPRED to an arbitrary value (-3 in Anthe's case) is to protect from the run stop due to log domain error since the model may accidentally return F<=0. Certainly F = 0 during the lag time. If the IPRED value selected for those cases deviates substantially from the range of DV for your data, this will serve as a flag helping to locate subjects with "problematic" measurements. Of course actions should be taken to avoid situations when Tlag >= time of the 1st sample with a measurable concentration. In the simulation study that Ken cited, Stuart suggested the following residual error model, which seems to solve the problem of nonzero measurements during the lag-time period (i.e., when the model predicts zero concentration): log(y(t)) = log(f(t)+m) + f(t)*e1(t)/(f(t)+m) + m*e2(t)/(f(t)+m) I wonder if somebody from the list tested this model. I did not test it myself yet as with the absorption model I use routinely long Tlag is almost always avoided. Best regards, Vladimir

From:"Nandy, Partha" Partha.Nandy@pharma.com Subject: RE: [NMusers] interpretation of WRES of logarithmically transformed data Date: 11/24/2003 11:39 AM The attached file did not transmit...may be the "reply" button was used. Can someone FW: the attachment to the group. Thanks Partha

From: VPIOTROV@PRDBE.jnj.com Subject: RE: [NMusers] interpretation of WRES of logarithmically transformed data Date: 11/25/2003 3:48 AM Apparently, the model equation was filtered out somehow. Below I replace the graphical object by the text. log(y(t)) = log(f(t)+m) + f(t)*e1(t)/(f(t)+m) + m*e2(t)/(f(t)+m) Best regards, Vladimir _______________________________________________________