From: Jean-Marie MARTINEZ <Jean-Marie.Martinez@sanofi-synthelabo.com> Subject: [NMusers] Calculation of WRES... Date: 8/12/2003 10:34 AM Hello NM Users, I'm trying to understand how NonMem computes WRES, and I'm in trouble with this topic... Indeed, one can read in several documentations that "WRES are the RES expressed in (i.e. as fractions of) population standard deviation units", or that "The WRES is a simple normalization of the RES, viz. the RES divided by the population standard deviation of the observation." (NonMem topic 6). The problem is that I cannot recalculate WRES 'by hand', due to the fact that the expression of PopSD remains unclear to me: while IWRES is easily obtained by dividing IRES by W, the same applied to RES does not give WRES ! Thank you for your help. Regards, Jean-Marie MARTINEZ Clinical Pharmacokineticist Department of Clinical Metabolism and Pharmacokinetics SANOFI-SYNTHELABO RECHERCHE 371 rue du Professeur Joseph Blayac 34184 MONTPELLIER Cedex 04 - FRANCE _______________________________________________________ From: William Bachman <bachmanw@globomax.com> Subject: RE: [NMusers] Calculation of WRES... Date: 8/12/2003 1:26 PM WRES's for an individual are given by the vector Ri(THETA,OMEGA,SIGMA) described at the bottom of page 37 of NONMEM Users Guide I. Also, from NONMEM Users Guide VIII: WRES The weighted residuals for an individual are formed by transform- ing the individual's residuals so that under the population model, assuming the true values of the population parameters are given by the estimates of those parameters, all weighted residu- als have unit variance and are uncorrelated. As with the predic- tion and residual, the weights are also computed at eta = 0. nmconsult@globomaxnm.com GloboMax LLC 7250 Parkway Drive, Suite 430 Hanover, MD 21076 Voice: (410) 782-2205 FAX: (410) 712-0737 _______________________________________________________ From: Matthew Hutmacher <matthew.hutmacher@pharmacia.com> Subject: RE: [NMusers] Calculation of WRES... Date: 8/12/2003 4:52 PM Jean-Marie, In a heuristic sense: Let y(i) represent the data vector for individual i. Let f(i) represent the mean of y(i). Let V(i) represent the estimated (and approximated) variance of y(i) Let H(i) represent the inverse of V(i). In a similar fashion to univariate standardization, standardization of RES is accomplished: WRES(i)=(y(i)-f(i)*K(i) where K(i) is the "root" matrix of H(i). This "root" matrix is not unique. Two popular methods of computing K(i) are: 1) The Cholesky decomposition. 2) (PD)(PD)' where P is the matrix of eigenvectors and D is a diagonal matrix of the square roots of the eigenvalues. K(i) from each method will not be the same. I had the same question you have some years ago, and far as I can remember, I pursued it to the point of determining that NONMEM does not use the Cholesky decomposition (I think). My guess is to try the eigenvalue method and see if you can compute it from there, but I would suggest that whenever possible, try to have NONMEM calculate them. Matt _______________________________________________________