model for OMEGA and SIGMA

From: "Luciane Velasque" Subject: [NMusers] model for OMEGA and SIGMA Date:Fri, 7 Feb 2003 14:45:31 -0200 Dear Users, Can I have an additive model for interindividual error : CL = TVCL+ETA(n) and a proportional structure for intraindividual error : Y=F*(1+EPS(1))? Which is it the implication of that ? How do I calculate the OMEGA and SIGMA CV ? Thanks in advance Luciane

From: "Bachman, William" Subject:RE: [NMusers] model for OMEGA and SIGMA Date: Fri, 7 Feb 2003 13:25:38 -0500 Luciane, Basically you can code anything you want (you're not limited to additive, proportional, exponential, etc.). But, the idea is that your error structure reflect your data! So, typically we use a proportional or exponetial inter-individual error model because PK parameters like V & CL are often log-normally distributed. By the same token, if you know something about the residual error distribution, e.g. from the characteristics of your assay, etc, you can make some assumptions about what the residual error model should be. As an example, you might have an assay where the error is proportional over most of the range of concentrations but constant near the limits of detection. In that case, and additive plus proportional residual error model might be an appropriate choice: Y = F + F*ERR(1) + ERR(2) Finally, fit your model to your data and test your assumptions. Bill

From:VPIOTROV@PRDBE.jnj.com Subject: RE: [NMusers] model for OMEGA and SIGMA Date: Fri, 7 Feb 2003 21:59:08 +0100 Luciane, Bill is right saying that the error structure should reflect somehow your data. All PK parameters are positive, and by coding interindividual variability like CL=THETA(.)*EXP(ETA(.) and by using FOCE method we constrain CL to be positive. Similarly, concentration is positive, and the way to constrain it could be Y=F*EXP(EPS(1)). However, due to model linearization, NONMEM will treat this as Y=F*(1+EPS(1)). In order to properly constrain the model prediction you have to apply a so-called tranform-both-side approach by taking the logarithm of measured concentrations (DV variable in your data set) and of model prediction. In the log domain the exponential residual error becomes additive. The $ERROR block may look as follows: $ERROR IPRE = -5 ; arbitrary value; to prevent from run stop due to log domain error IF (F.GT.0) IPRE = LOG(F) ; note: in FORTRAN, LOG() means natural logarithm, not decimal! Y = IPRE + EPS(1) BTW, the magnitude of SIGMA depends not only on the assay error. Nevertheless, if you know the precision of the bioanalytical method decreases as concentration drops below a certain level you may consider the model with 2 EPS. Best regards, Vladimir

From: Luann Phillips Subject:Re: [NMusers] model for OMEGA and SIGMA Date:Tue, 11 Feb 2003 10:13:10 -0500 NM Users, I would like to offer an alternative method for coding the Y=F*EXP(EPS(1)) error model using the 'transform-both-side' approach. $ERROR FLAG=0 IF(AMT.NE.0)FLAG=1 ;dosing records only IPRED=LOG(F+FLAG) ;transform the prediction to the log of the prediction ; IPRED=log(f) for concentration records and log(f+1) for dose records W=1 ;additive error model Y= IPRED + W*EPS(1) This will allow NONMEM to continue running when a predicted concentration of 0 occurs on any dosing record. Since predictions for dose records do not contribute to the minimum value of the objective function this change to the F (or IPRED) does not influence the outcome of the analyses. However, if code is used to alter the predicted concentration on a PK sample record the minimum value of the objective function is changed and its value can be highly dependent upon what value of IPRED is chosen as the 'new' predicted concentration. Using the above code, if NONMEM predicts a concentration of 0 on a PK sample record the run will still terminate (on some systems) with errors because LOG(0) is negative infinity. In this case, the patient ID and the observation within that patient for which the error occured will be provided. If this occurs, you may want to consider the following options: (1) Check the dosing and sampling times and the dose amounts preceding the observation for errors. Is it reasonable that a patient would have an observable concentration, given the time since last dose for the sample? (2) Is NONMEM predicting a zero concentration because of a modeled absorption lag time? Consider removing the absorption lag time or using a MIXTURE model to allow some subjects to have a lag time and others to have a lag time of zero. (3) Test a combined additive + constant CV error model (Y= F + F*EPS(1) + EPS(2)) using DV=original concentration instead of DV=log(concentration). (4) Consider temporarily excluding measured concentrations with a predicted value of zero. Work out the key components of the model and then re-introduce the concentrations. The concentrations may no longer have a predicted value of zero. (5) If none of the above works, you could switch back to the code that Vladimir suggested. Because the minimum value of the objective function will be dependent upon the 'new' value of log(F) (or log(IPRED)), I would test smaller values (-3, -5, -7, -9, etc.) until the change in minimum value of the OBJ is not statistically significant for 2 successive choices (alpha less than the values used for covariate analyses). If this is not done then any change to the model that would allow the model to predict a small non-zero value for the observation could result in a statistically significant change in the minimum value of the objective function. This type of model behavior could lead one to think that a covariate is statistically significant based upon the covariate changing the predicted value for 1 observation instead of its inclusion improving the predictions for the population in general. Regards, Luann Phillips _______________________________________________________