Re: Log-transformation

From: Luann Phillips Subject:Re: [NMusers] Log-transformation Date:Fri, 04 Apr 2003 10:52:30 -0500 NM Users, Sorry about the delay in response to this posting. Below is a note that I posted to the users group sometime in Feb. (99feb072003.html) It was about a similar topic. This code differs from Bill Bachman's reply to Daniel's question. In Bill's code, predicted concentrations of zero are not transformed. Because the DV is log(cp), keeping the IPRED=0 in essence changes the predicted Cp from 0 to 1(log(1)=0) and will impact MVOF. The code below will prevent your run from terminating because of a predicted Cp=0 on dosing records (a frequent occurence). Below the code is a list of things that can be done when a predicted Cp of zero occurs for a concentration record. Regards, Luann /*****Previous note**************/ $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 ; IPRED=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(see below). 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 /******Vladimir's original note***************/ > VPIOTROV@PRDBE.jnj.com wrote: > > 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