# Re: different parameterizations of OMEGA matrix vs. chance of getting flip-flop estimates

From: Leonid Gibiansky <LGibiansky>
Date: Fri, 22 Jun 2012 13:18:06 -0400

Yaming

You started from different initial conditions

(0,0.01) ; 5 [THETA5, IIV ON CL, SD(ETA1)
(0,0.01) ; 6 [THETA6, IIV ON V, SD(ETA2)]
(0,0.01) ; 7 [THETA7, IIV ON KA, SD(ETA3)]

corresponds to

\$OMEGA
0.0001

Try

(0,0.316) ; 5 [THETA5, IIV ON CL, SD(ETA1)
(0,0.316) ; 6 [THETA6, IIV ON V, SD(ETA2)]
(0,0.316) ; 7 [THETA7, IIV ON KA, SD(ETA3)]

Leonid

--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566

On 6/22/2012 12:36 PM, Yaming Hang wrote:
> Dear NONMEM Users,
>
> One of the tricks people often use is to specify the SD(ETA) as a THETA
> and fix the OMEGA to be 1, which is a trick I often use when I determine
> which parameter should I put an ETA on.
>
> Most of the time, I will get the same results whether I use this trick,
> or just the normal way of specifying the OMEGA matrix. So my
> understanding is that these two approaches are equivalent. Today I run
> into some problem – I got a flip-flop estimate. All other aspects of the
> codes are the same, including same initial values and estimation method.
> In this one compartment first order absorption and first order
> elimination model, the estimation of CL and residual error magnitude
> SIGMA is not impacted by the method used, but V and Ka are totally
> different (as a result of flip-flop), and accordingly, their OMEGA estimate.
>
> Has anyone encountered similar situation? What kind of difference does
> these two approaches make in terms of searching for the minimizer? I’d
> appreciate if someone can help me to understand what’s going on here.
>
> Here are my codes and NONMEM outcome:
>
> *Approach 1 (the usual way):*
>
> \$SUBROUTINES ADVAN2 TRANS2
>
> \$PK
>
> TVCL=THETA(1)
>
> CL=TVCL*EXP(ETA(1))
>
> TVV=THETA(2)
>
> V=TVV*EXP(ETA(2))
>
> TVKA=THETA(3)
>
> KA=TVKA*EXP(ETA(3))
>
> S2=V
>
> \$ERROR
>
> DEL=0
>
> IF(F.LE.0) DEL=1
>
> W1=1
>
> IPRED=0
>
> IF(F.GT.0) IPRED=LOG(F)
>
> IRES=DV-IPRED
>
> W2=THETA(4)
>
> IWRES=IRES/(W1*DEL+W2)
>
> Y=IPRED + W2*ERR(1)
>
> \$OMEGA DIAGONAL(3)
>
> 0.1
>
> 0.1
>
> 0.1
>
> \$SIGMA 1 FIX
>
> \$THETA
>
> (0, 31) ; 1 [THETA1, TVCL]
>
> (0, 300) ; 2 [THETA2, TVV]
>
> (0,2) ; 3 [THETA3, TVKA]
>
> (0,0.2) ; 4 [THETA4, SD(EPISILON)]
>
> \$EST METHOD=1 INTERACTION PRINT=5 MAX=9999 SIG=3 NOABORT MSFO=103.MSF
>
> \$COV PRINT=E
>
> *The results:*
>
> *THETA OMEGA SIGMA *
>
> *THETA1 27.68 (0.03513) OMEGA(1,1) 0.371 (0.2428) SIGMA(1,1) 1 (........) *
>
> *THETA2 298.9 (0.01969) OMEGA(2,2) 0.1585 (0.2042) *
>
> *THETA3 0.8336 (0.05652) OMEGA(3,3) 0.6265 (0.1491) *
>
> *THETA4 0.4441 (0.03294) *
>
> *Approach 2 (using the trick):*
>
> \$SUBROUTINES ADVAN2 TRANS2
>
> \$PK
>
> TVCL=THETA(1)
>
> CL=TVCL*EXP(THETA(5)*ETA(1))
>
> TVV=THETA(2)
>
> V=TVV*EXP(THETA(6)*ETA(2))
>
> TVKA=THETA(3)
>
> KA=TVKA*EXP(THETA(7)*ETA(3))
>
> S2=V
>
> \$ERROR
>
> DEL=0
>
> IF(F.LE.0) DEL=1
>
> W1=1
>
> IPRED=0
>
> IF(F.GT.0) IPRED=LOG(F)
>
> IRES=DV-IPRED
>
> W2=THETA(4)
>
> IWRES=IRES/(W1*DEL+W2)
>
> Y=IPRED + W2*ERR(1)
>
> \$OMEGA DIAGONAL(3)
>
> 1 FIX
>
> 1 FIX
>
> 1 FIX
>
> \$SIGMA 1 FIX
>
> \$THETA
>
> (0, 31) ; 1 [THETA1, TVCL]
>
> (0, 300) ; 2 [THETA2, TVV]
>
> (0,2) ; 3 [THETA3, TVKA]
>
> (0,0.2) ; 4 [THETA4, SD(EPISILON)]
>
> (0,0.01) ; 5 [THETA5, IIV ON CL, SD(ETA1)
>
> (0,0.01) ; 6 [THETA6, IIV ON V, SD(ETA2)]
>
> (0,0.01) ; 7 [THETA7, IIV ON KA, SD(ETA3)]
>
> \$EST METHOD=1 INTERACTION PRINT=5 MAX=9999 SIG=3 NOABORT MSFO=104.MSF
>
> \$COV PRINT=E
>
> *Results:*
>
> *THETA OMEGA SIGMA *
>
> *THETA1 27.68 (0.03569) OMEGA(1,1) 1 (........) SIGMA(1,1) 1 (........) *
>
> *THETA2 33.57 (0.06407) OMEGA(2,2) 1 (........) *
>
> *THETA3 0.09296 (0.03003) OMEGA(3,3) 1 (........) *
>
> *THETA4 0.4442 (0.03295) *
>
> *THETA5 0.4001 (0.117) *
>
> *THETA6 0.6873 (0.08321) *
>
> *THETA7 0.3336 (0.1125) *
>
> Yaming Hang, Ph.D.
>
> Pharmacometrics
>
> Biogen Idec
>
> 14 Cambridge Center
>
> Cambridge, MA 02142
>
> Office: 781-464-1741
>
> Fax: 617-679-2804
>
> Email: Yaming.Hang
>
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>
Received on Fri Jun 22 2012 - 13:18:06 EDT

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