Box-Cox transformation in NONMEM

From: "Piotrovskij, Vladimir [JanBe]" <VPIOTROV@janbe.jnj.com> Subject: Box-Cox transformation in NONMEM Date: 25 Sep 1998 03:56:48 -0400 Dear NONMEM users, If residuals are highly skewed log transformation of observations and model predictions may help. There is, however, a more general approach in regression called Transform Both Side (TBS) approach (see Carroll & Ruppert 'Transformation and weighting in regression'). Log transformation is a particular case of Box-Cox modified power transformation (y^lambda-1)/lambda for lambda=0. Generally, lambda is a parameter which can be estimated together with other parameters of a regression model. Has anybody experience in applying Box-Cox transformation in NONMEM? Kind regards, Vladimir -------------- Vladimir Piotrovsky Clinical Pharmacokinetics Janssen Research Foundation 2340 Beerse, Belgium e-mail: vpiotrov@janbe.jnj.com

From: Mats Karlsson <Mats.Karlsson@biof.uu.se> Subject: Re: Box-Cox transformation in NONMEM Date: 25 Sep 1998 10:20:16 -0400 Dear Vladimir, We applied a Box-Cox transformation when analyzing leucopenia data that were highly skewed (Clin. Pharm&Ther 1995;57:325-34). We didn't try to estimate lambda as part of the model though. Best regards, Mats ________________________________________________________ Mats Karlsson, PhD Uppsala University Div. of Biopharmaceutics and Pharmacokinetics Dept. of Pharmacy/ Box 580, SE-751 23 Uppsala, Sweden Internet: mats.karlsson@biof.uu.se Phone: +46 18 471 41 05 Fax: +46 18 471 40 03

From: stuart@c255.ucsf.EDU (S.Beal) Subject: Re: Box-Cox transformation in NONMEM Date: 29 Sep 1998 19:01:54 -0400 Subject: Transform-both-sides We do have some experience with this. Here is a set-up using the Box-Cox power transformation and homoscedastic (uncorrelated, univariate) epsilon error on the transformed scale. It can be modified for other transformations. The set-up requires two user-routines, the use of which is not supported by the NPG. These routines are included. If X gives the prediction for an observation (based on the eta values) Use the statement Y=(X**THETA(xxx)-1)/THETA(xxx)+ERR(1) to set Y in abbreviated code, where xxx is the index of that element of theta serving as the lambda parameter. Include the options OTHER=CONTR OTHER=CCONTR in the $SUBROUTINES record, and the two user routines: subroutine contr (icall,cnt,ier1,ier2) double precision cnt call ncontr (2,cnt,ier1,ier2) return end subroutine ccontr (icall,c1,c2,c3,ier1,ier2) parameter (lth=40,lvr=30) common /rocm0/ theta (lth) common /rocm4/ y double precision c1,c2,c3,theta,y,w,one,two dimension c2(*),c3(lvr,*) data one,two/1.,2./ if (icall.le.1) return w=y y=(y**theta(xxx)-one)/theta(xxx) call cels (c1,c2,c3,ier1,ier2) y=w c1=c1-two*(theta(xxx)-one)*log(y) return end in the NONMEM executable.