RE: FW: Block versus diagonal omega

-----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Leonid Gibiansky Sent: Monday, August 30, 2010 2:48 PM To: Hu, Chuanpu [CNTUS] Cc: [email protected] Subject: Re: FW: [NMusers] Block versus diagonal omega Chuanpu, In all stable problems that I tried, parametrization ETA() $OMEGA 0.1 ; estimated was equivalent (in terms of the estimated value and objective function) to THETA(*)*ETA() $OMEGA 1 FIXED Also, H0: THETA=0, vs. H1: THETA<>0 is the same as H0: OMEGA=0, vs. H1: OMEGA>0 since OMEGA=THETA^2 In theta-form, the problem has two identical solution THETA()=SQRT(OMEGA) and THETA()= -SQRT(OMEGA) Leonid -------------------------------------- Leonid Gibiansky, Ph.D. President, QuantPharm LLC web: www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel: (301) 767 5566 On 8/30/2010 1:41 PM, Hu, Chuanpu [CNTUS] wrote: > *From:* Hu, Chuanpu [CNTUS] > *Sent:* Monday, August 30, 2010 8:46 AM > *To:* 'Mark Sale' > *Cc:* 'nmusers' > *Subject:* RE: [NMusers] Block versus diagonal omega > > Mark, > > Nice thought - the test can be conducted, but the devil is in the > details. This has to do with the intricacies of the role alternative > hypothesis plays in hypothesis testing: > > For the original parameterization testing OMEGA, the hypothesis test is > > H0: OMEGA=0, vs. H1: OMEGA>0 > > For the THETA parameterization testing OMEGA, the hypothesis test is > > H0: THETA=0, vs. H1: THETA<>0 > > So without getting into the math, the intuitive argument is that the > alternative hypotheses in the 2 situations are different, therefore it > is logical that the testing criteria must change. The world of math does > not contain contradictions even though it may appear so at times. J > > Chuanpu > > *From:* Mark Sale [mailto:[email protected]] > *Sent:* Sunday, August 29, 2010 9:19 AM > *To:* Hu, Chuanpu [CNTUS] > *Cc:* nmusers > *Subject:* RE: [NMusers] Block versus diagonal omega > > Chuanpu, > Do I extrapolate correctly then that: > > V = THETA(1)*EXP(THETA(2)*ETA(1)) > . > . > . > $OMEGA > (1,FIXED). > > Can be tested (THETA(2) <> 0), since it is not a truncated distribution? > might be an interesting exercise to do this with LRT and compare to the > randomization test with the usual specification. > > > Mark > > > --- On *Fri, 8/27/10, Hu, Chuanpu [CNTUS] /<[email protected]>/* wrote: > > > From: Hu, Chuanpu [CNTUS] <[email protected]> > Subject: RE: [NMusers] Block versus diagonal omega > To: "Mark Sale - Next Level Solutions" <[email protected]>, > "Eleveld,DJ" <[email protected]> > Cc: "nmusers" <[email protected]> > Date: Friday, August 27, 2010, 4:33 PM > > Theoretically, the NONMEM objective function drop for adding a diagonal > element follows a mixture chi-square distribution, from which follows > that using the "usual" chi-square distribution would be conservative. > This has to do with 0 being on the boundary of possible values. (See > Pinheiro and Bates, Mixed Effects Models in S and S-PLUS, Springer, > 2000.) As this boundary issue does not apply to off-diagonal elements, > the "usual" chi-square distribution should be fine (with the usual > statistical asymptotic caveats). > > I'd like to mention that, while the "find the best fit" mindset may be > suitable for the typical exploratory setting, the p-values from repeated > (e.g., stepwise) tests are not statistically interpretable. To have > valid p-values, confirmatory analyses would be needed, which in my mind > deserves a wider use. J > > Chuanpu > > ~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~* > > Chuanpu Hu, Ph.D. > > Director, Pharmacometrics > > Pharmacokinetics > > Biologics Clinical Pharmacology > > Janssen Pharmaceutical Companies of Johnson & Johnson > > C-3-3 > > 200 Great Valley Parkway > > Malvern, PA 19355 > > Tel: 610-651-7423 > > Fax: (610) 993-7801 > > E-mail: [email protected] </mc/[email protected]> > > ~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~* > Notice: This e-mail message, together with any attachments, contains information of Merck & Co., Inc. (One Merck Drive, Whitehouse Station, New Jersey, USA 08889), and/or its affiliates Direct contact information for affiliates is available at http://www.merck.com/contact/contacts.html) that may be confidential, proprietary copyrighted and/or legally privileged. It is intended solely for the use of the individual or entity named on this message. If you are not the intended recipient, and have received this message in error, please notify us immediately by reply e-mail and then delete it from your system.