RE: OMEGA priors using modes of inverse Wishart matrix

Dear Joachim, We did not respond very quickly but think we might still have something to contribute. A way to avoid having to approximate the number f degrees of freedom for the OMEGA prior would be to estimate the random effect variance (or SD), and the covariance (or correlation) in the form of THETAS. This way only the variance covariance matrix is needed to weight the prior information. An example of how to parameterize such a model is presented below. ;; -------------------------------------------------------------- ;; Standard code $PK TVCL = THETA(1) CL = TVCL*EXP(ETA(1)) TVV = THETA(2) V = TVV*EXP(ETA(2)) $THETA (0,30) ; CL $THETA (0,100) ; V $OMEGA BLOCK(2) 0.09 ; CL_VAR 0.072 ; CL_V_COVAR 0.09 ; V_VAR ;; Alternative code with no estimated OMEGA block $PK TVCL = THETA(1) SDCL = THETA(3) ; Standard deviation for random effect on CL CL = TVCL*EXP(SDCL*ETA(1)) TVV = THETA(2) SDV = THETA(4) ; Standard deviation for random effect on V CR12 = THETA(5) ; Correlation between random effect 1 and 2 RE2 = CR12*ETA(1)+ SQRT(1- SQRT(CR12**4))*ETA(2) ; Random effect 2 with CR12 correlation to ETA1 V = TVV*EXP(SDV*RE2) $THETA (0,30) ; CL $THETA (0,100) ; V $THETA (0,0.3) ; SD_CL $THETA (0,0.3) ; SD_V $THETA (-1,0.8,1) ; Corr_1o2 $OMEGA 1 FIX ; VAR_ETA1 $OMEGA 1 FIX ; VAR_ETA2 ;; -------------------------------------------------------------- The above coding alternatives does from our experience result in identical parameter estimates and model fit (i.e. OFV). The coding has to be altered to accommodate a block of more than two parameters (if no correlation structure is estimated it is trivial). In case of an OMEGA block with more than two random effect parameterization can to our knowledge not be done in form of an estimated correlation but similar performance can be achieved. Kind regards, Martin Bergstrand, Frank Kloprogge and the MORU Pharmacometrics group. Mahidol-Oxford Tropical Medicine Research Unit, Bangkok, Thailand