RE: Rounding errors

From: "KOWALSKI, KENNETH G. [PHR/1825]" <kenneth.g.kowalski@pharmacia.com> Subject: RE: Rounding errors Date: Fri, 23 Mar 2001 11:19:57 -0600 Paul, I was referring to removing etas and restrictions on the elements of Omega (eg., use of block diagonal structures). Also, I have encountered on numerous occasions where the correlation between etas for say V and CL is near unity. When this occurs one can get rounding errors or R matrix (hessian) singular or non-positive semi-definite problems resulting from the over-parameterization of Omega. In this setting I have had success in assuming a common eta for V and CL with a different scale parameter to account for differences in variances between V and CL. For example, if we model CL and V as: CL=THETA(1)*EXP(ETA(1)) V=THETA(2)*EXP(ETA(2)) and assuming a full unstructured Omega, we have 3 elements of Omega to be estimated. If omega12/sqrt(omega11*omega22) is near 1 then the following restriction can help: CL=THETA(1)*EXP(ETA(1)) V=THETA(2)*EXP(THETA(3)*ETA(1)) With this restriction we have only 2 elements of Omega, ie., omega11=var(ETA1) and THETA(3)=sqrt(var(ETA2)/var(ETA1)) where ETA2=THETA(3)*ETA1 provides the restriction that ETA1 and ETA2 are perfectly correlated but with different variances, ie., var(ETA2)=THETA(3)*THETA(3)*var(ETA1). It is my understanding that NONMEM VI will allow one to postulate that Omega obeys an inverse-Wishart distribution which will provide another way to reduce the number of parameters in Omega relative to a full unstructured matrix. Ken