BSV and BOV interaction

-----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of [email protected] Sent: 21 December 2009 08:18 To: Jia Ji Cc: [email protected] Subject: Re: [NMusers] BSV and BOV interaction Jia, you are overparameterized. Take this snippet from your code: IOV2=0 IF (DESC.EQ.1) IOV2=ETA(5) IF (DESC.EQ.2) IOV2=ETA(6) ETCL = ETA(1)+IOV1 Now consider the two possibilites: a) DESC.EQ.1: ETCL = ETA(1) + ETA(5) b) DESC.EQ2.2: ETCL = ETA(1) + ETA(6) In other words, you have two equations to identify 3 parameters. Usually you associate the "base" random effect with one case and add a deviation parameter to the other case. An example would be IOV2=0 IF (DESC.EQ.2) IOV2=1 ETCL = ETA(1)+IOV2*ETA(5) Thus, ETA(1) estimates your random effect variation for the case DESC.EQ.1 and ETA(1) + ETA(5) is the random effect variation for the case DESC.EQ.2. ETA(5) is thus the additional random effect variation for the second case compared to the first. Watch out that this implies that the random effect variation is larger for DESC.EQ.2 than for DESC.EQ.1 since ETA(5) is (hopefully) not negative. You could multiply the two to allow for the variation being smaller or larger in the latter case but multiplication makes the estimation more unstable. Why do you see the need to link the two? Why don't you define IF(DESC.EQ.1) ETCL=ETA(5) IF(DESC.EQ.2) ETCL=ETA(6) CL=THETA(1)*EXP(ETCL) and get rid of ETA(1)? That decouples the two estimates entirely. Andreas Jia Ji <[email protected]> Sent by: [email protected] 12/19/2009 12:32 AM To [email protected] cc Subject [NMusers] BSV and BOV interaction Dear All, I am trying to model our data with a two-compartment model now. In our trial, some patients received escalated dose at the second cycle so they have one more set of kinetics data. So there were BSV and BOV on PK parameters in the model. Objective function value is significantly improved (compared with the model not having BOV) and SE of ETAs are around 40% or less. The code is as below: $PK DESC=1 IF (TIME.GE.100) DESC=2 IOV1=0 IF (DESC.EQ.1) IOV1=ETA(2) IF (DESC.EQ.2) IOV1=ETA(3) IOV2=0 IF (DESC.EQ.1) IOV2=ETA(5) IF (DESC.EQ.2) IOV2=ETA(6) ETCL = ETA(1)+IOV1 ETQ = ETA(4)+IOV2 ETV2 = ETA(7) CL=THETA(1)*EXP(ETCL) V1=THETA(2) Q=THETA(3)*EXP(ETQ) V2=THETA(4)*EXP(ETV2) ;OMEGA initial estimates $OMEGA 0.0529 $OMEGA BLOCK(1) 0.05 $OMEGA BLOCK(1) SAME $OMEGA 0.318 $OMEGA BLOCK(1) 0.05 $OMEGA BLOCK(1) SAME $OMEGA 0.711 When I looked at scatterplot of ETA, I found that there is strong correlation between ETA(1) and ETA(2), which is BSV and BOV of CL. And the same thing happened to BSV and BOV of Q. Worrying about over-parameterization (I am not NONMEM 7 user), I tried to define a THETA for this correlation as the code below (just test on CL only first): $PK DESC=1 IF (TIME.GE.100) DESC=2 IOV1=0 IF (DESC.EQ.1) IOV1=THETA(1)*ETA(1) IF (DESC.EQ.2) IOV1=THETA(1)*ETA(1) ETCL = ETA(1)+IOV1 ETQ = ETA(2) ETV2 = ETA(3) CL=THETA(2)*EXP(ETCL) V1=THETA(3) Q=THETA(4)*EXP(ETQ) V2=THETA(5)*EXP(ETV2) The objective function value is exactly the same as the model not having IOV. BSV of CL is decreased and SE of THETAs are also improved, though. The same thing happend to Q when tested individually. Then I tried another way to account for this correlation: $PK DESC=1 IF (TIME.GE.100) DESC=2 IOV1=0 IF (DESC.EQ.1) IOV1=ETA(2) IF (DESC.EQ.2) IOV1=ETA(3) ETCL = ETA(1)+IOV1 ETQ = ETA(4) ETV2 = ETA(5) CL=THETA(1)*EXP(ETCL) V1=THETA(2) Q=THETA(3)*EXP(ETQ) V2=THETA(4)*EXP(ETV2) ;OMEGA initial estimates $OMEGA BLOCK(2) 0.0529 0.01 0.05 $OMEGA BLOCK(1) 0.05 ;BTW, I don't know how to do SAME here, it's not working when putting SAME here $OMEGA 0.318 $OMEGA 0.711 This time I got significantly decreased objective function value, compared with the model not having IOV. But, SE of ETA(1), ETA(2) and ETA(3) are huge! All together, does it mean that there is no need to have BOV on CL and Q? Or I don't get the right solution to solve correlation problem? Any suggestion is highly appreciated! Thank you so much! Happy Holidays! Jia The information of this email and in any file transmitted with it is strictly confidential and may be legally privileged. It is intended solely for the addressee. If you are not the intended recipient, any copying, distribution or any other use of this email is prohibited and may be unlawful. In such case, you should please notify the sender immediately and destroy this email. The content of this email is not legally binding unless confirmed by letter. Any views expressed in this message are those of the individual sender, except where the message states otherwise and the sender is authorised to state them to be the views of the sender's company. For further information about Actelion please see our website at http://www.actelion.com

-----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of [email protected] Sent: Monday, December 21, 2009 10:41 AM To: Nick Holford Cc: nmusers Subject: Re: [NMusers] BSV and BOV interaction Nick, overparameterization refers to the parameters, the variances play only an indirect role. Putting the SAME constraint on the covariance thus restricts the set of random effects but not necessarily the set of random effects for, say, subject i. The SAME option thus might keep the estimation process a bit more under control but I still think there is an overparameterization problem for each individual subject. It should be interesting to take out those ETA values containing the SAME lines by specifying 0.0 FIX instead of SAME and comparing the results. Andreas PS. Shouldn't we all be off for some holidays? Nick Holford <[email protected]> Sent by: [email protected] 12/21/2009 09:52 AM To nmusers <[email protected]> cc Subject Re: [NMusers] BSV and BOV interaction Andreas, The code is not overparameterized because the SAME option is used for the OMEGA block defining ETA(6). This means that there is only one parameter being estimated for the variance of the distribution from which ETA(5) and ETA(6) are sampled i.e. ETA(5) and ETA(6) come from an eta distribution with the SAME variance. Best wishes, Nick [email protected] wrote: Jia, you are overparameterized. Take this snippet from your code: IOV2=0 IF (DESC.EQ.1) IOV2=ETA(5) IF (DESC.EQ.2) IOV2=ETA(6) ETCL = ETA(1)+IOV1 Now consider the two possibilites: a) DESC.EQ.1: ETCL = ETA(1) + ETA(5) b) DESC.EQ2.2: ETCL = ETA(1) + ETA(6) In other words, you have two equations to identify 3 parameters. Usually you associate the "base" random effect with one case and add a deviation parameter to the other case. An example would be IOV2=0 IF (DESC.EQ.2) IOV2=1 ETCL = ETA(1)+IOV2*ETA(5) Thus, ETA(1) estimates your random effect variation for the case DESC.EQ.1 and ETA(1) + ETA(5) is the random effect variation for the case DESC.EQ.2. ETA(5) is thus the additional random effect variation for the second case compared to the first. Watch out that this implies that the random effect variation is larger for DESC.EQ.2 than for DESC.EQ.1 since ETA(5) is (hopefully) not negative. You could multiply the two to allow for the variation being smaller or larger in the latter case but multiplication makes the estimation more unstable. Why do you see the need to link the two? Why don't you define IF(DESC.EQ.1) ETCL=ETA(5) IF(DESC.EQ.2) ETCL=ETA(6) CL=THETA(1)*EXP(ETCL) and get rid of ETA(1)? That decouples the two estimates entirely. Andreas Jia Ji <[email protected]> Sent by: [email protected] 12/19/2009 12:32 AM To [email protected] cc Subject [NMusers] BSV and BOV interaction Dear All, I am trying to model our data with a two-compartment model now. In our trial, some patients received escalated dose at the second cycle so they have one more set of kinetics data. So there were BSV and BOV on PK parameters in the model. Objective function value is significantly improved (compared with the model not having BOV) and SE of ETAs are around 40% or less. The code is as below: $PK DESC=1 IF (TIME.GE.100) DESC=2 IOV1=0 IF (DESC.EQ.1) IOV1=ETA(2) IF (DESC.EQ.2) IOV1=ETA(3) IOV2=0 IF (DESC.EQ.1) IOV2=ETA(5) IF (DESC.EQ.2) IOV2=ETA(6) ETCL = ETA(1)+IOV1 ETQ = ETA(4)+IOV2 ETV2 = ETA(7) CL=THETA(1)*EXP(ETCL) V1=THETA(2) Q=THETA(3)*EXP(ETQ) V2=THETA(4)*EXP(ETV2) ;OMEGA initial estimates $OMEGA 0.0529 $OMEGA BLOCK(1) 0.05 $OMEGA BLOCK(1) SAME $OMEGA 0.318 $OMEGA BLOCK(1) 0.05 $OMEGA BLOCK(1) SAME $OMEGA 0.711 When I looked at scatterplot of ETA, I found that there is strong correlation between ETA(1) and ETA(2), which is BSV and BOV of CL. And the same thing happened to BSV and BOV of Q. Worrying about over-parameterization (I am not NONMEM 7 user), I tried to define a THETA for this correlation as the code below (just test on CL only first): $PK DESC=1 IF (TIME.GE.100) DESC=2 IOV1=0 IF (DESC.EQ.1) IOV1=THETA(1)*ETA(1) IF (DESC.EQ.2) IOV1=THETA(1)*ETA(1) ETCL = ETA(1)+IOV1 ETQ = ETA(2) ETV2 = ETA(3) CL=THETA(2)*EXP(ETCL) V1=THETA(3) Q=THETA(4)*EXP(ETQ) V2=THETA(5)*EXP(ETV2) The objective function value is exactly the same as the model not having IOV. BSV of CL is decreased and SE of THETAs are also improved, though. The same thing happend to Q when tested individually. Then I tried another way to account for this correlation: $PK DESC=1 IF (TIME.GE.100) DESC=2 IOV1=0 IF (DESC.EQ.1) IOV1=ETA(2) IF (DESC.EQ.2) IOV1=ETA(3) ETCL = ETA(1)+IOV1 ETQ = ETA(4) ETV2 = ETA(5) CL=THETA(1)*EXP(ETCL) V1=THETA(2) Q=THETA(3)*EXP(ETQ) V2=THETA(4)*EXP(ETV2) ;OMEGA initial estimates $OMEGA BLOCK(2) 0.0529 0.01 0.05 $OMEGA BLOCK(1) 0.05 ;BTW, I don't know how to do SAME here, it's not working when putting SAME here $OMEGA 0.318 $OMEGA 0.711 This time I got significantly decreased objective function value, compared with the model not having IOV. But, SE of ETA(1), ETA(2) and ETA(3) are huge! All together, does it mean that there is no need to have BOV on CL and Q? Or I don't get the right solution to solve correlation problem? Any suggestion is highly appreciated! Thank you so much! Happy Holidays! Jia The information of this email and in any file transmitted with it is strictly confidential and may be legally privileged. It is intended solely for the addressee. If you are not the intended recipient, any copying, distribution or any other use of this email is prohibited and may be unlawful. In such case, you should please notify the sender immediately and destroy this email. The content of this email is not legally binding unless confirmed by letter. Any views expressed in this message are those of the individual sender, except where the message states otherwise and the sender is authorised to state them to be the views of the sender's company. For further information about Actelion please see our website at http://www.actelion.com -- Nick Holford, Professor Clinical Pharmacology Dept Pharmacology & Clinical Pharmacology University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand tel:+64(9)923-6730 fax:+64(9)373-7090 mobile:+64(21)46 23 53 email: [email protected] http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford The information of this email and in any file transmitted with it is strictly confidential and may be legally privileged. It is intended solely for the addressee. If you are not the intended recipient, any copying, distribution or any other use of this email is prohibited and may be unlawful. In such case, you should please notify the sender immediately and destroy this email. The content of this email is not legally binding unless confirmed by letter. Any views expressed in this message are those of the individual sender, except where the message states otherwise and the sender is authorised to state them to be the views of the sender's company. For further information about Actelion please see our website at http://www.actelion.com