Proper way to handle the pre-first dose PK observation for non-endogenous drug

10 messages 7 people Latest: Nov 08, 2012
Dear NONMEM Users, I'd like to get some advice from you with regard to how to handle the pre-first dose PK observation when the drug is not an endogenous substance. I tried too different approaches, one approach is treating them as missing values (DV=0, EVID=0, MDV=1), another is treating them as true 0s (DV=0, EVID=0, MDV=0). My error structure is proportional + additive. There were very little difference for all parameters except for the SD of the additive error. When these pre-first dose concentrations were treated as missing, the estimated omega for additive error is 3.92, and when they were treated as true 0s, the sigma became 2.85. To me, in theory, these values provide no information about the model parameters because the system will predict them to be 0 at time 0 anyway for any point in the parameter space. Is what happened here that because DV is exactly the same as prediction, therefore the estimation of additive residual error variance has been brought down? Which way is more appropriate? I'd really appreciate it if you can share your experience/insight. Yaming Hang, Ph.D. Pharmacometrics Biogen Idec 14 Cambridge Center Cambridge, MA 02142 Office: 781-464-1741 Fax: 617-679-2804 Email: [email protected]<mailto:[email protected]>
Yaming, As you pointed-out DV=Prediction. Including these data-points biases your estimate of the additive component of variability. My opinion is just to exclude the observations to get a better estimate of additive variability. On a side note Additive+Proportortional is similar to a lognormal-error structure. In a lognormal error structure zero observations have to be excluded anyway. Matt.
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From: [email protected] [mailto:[email protected]] On Behalf Of Yaming Hang Sent: Wednesday, November 07, 2012 4:04 PM To: [email protected] Subject: [NMusers] Proper way to handle the pre-first dose PK observation for non-endogenous drug Dear NONMEM Users, I'd like to get some advice from you with regard to how to handle the pre-first dose PK observation when the drug is not an endogenous substance. I tried too different approaches, one approach is treating them as missing values (DV=0, EVID=0, MDV=1), another is treating them as true 0s (DV=0, EVID=0, MDV=0). My error structure is proportional + additive. There were very little difference for all parameters except for the SD of the additive error. When these pre-first dose concentrations were treated as missing, the estimated omega for additive error is 3.92, and when they were treated as true 0s, the sigma became 2.85. To me, in theory, these values provide no information about the model parameters because the system will predict them to be 0 at time 0 anyway for any point in the parameter space. Is what happened here that because DV is exactly the same as prediction, therefore the estimation of additive residual error variance has been brought down? Which way is more appropriate? I'd really appreciate it if you can share your experience/insight. Yaming Hang, Ph.D. Pharmacometrics Biogen Idec 14 Cambridge Center Cambridge, MA 02142 Office: 781-464-1741 Fax: 617-679-2804 Email: [email protected]<mailto:[email protected]> ________________________________ This e-mail (including any attachments) is confidential and may be legally privileged. If you are not an intended recipient or an authorized representative of an intended recipient, you are prohibited from using, copying or distributing the information in this e-mail or its attachments. If you have received this e-mail in error, please notify the sender immediately by return e-mail and delete all copies of this message and any attachments. Thank you.
Yaming, Matt, I would do exactly what Yaming has done already. Treat the pre-dose measurements as true observations for when the predicted conc is zero. It is not true to say they provide no information about model parameters. They are the best way to improve your estimate of the additive error parameter (independent of PK model misspecification). By improving the residual error model you may also have benefits in improving your PK model. Although the PK model benefit may be small in principle it is foolish to ignore data that could be helpful. A major weakness of using log transformed both sides approach is that it cannot use these real observations which is why I have rarely used it. Best wishes, Nick
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On 8/11/2012 11:23 a.m., Fidler,Matt,FORT WORTH,R&D wrote: > Yaming, > > As you pointed-out DV=Prediction. Including these data-points biases your estimate of the additive component of variability. My opinion is just to exclude the observations to get a better estimate of additive variability. > > On a side note Additive+Proportortional is similar to a lognormal-error structure. In a lognormal error structure zero observations have to be excluded anyway. > > Matt. > > *From:* [email protected] [ mailto: [email protected] ] *On Behalf Of *Yaming Hang > > *Sent:* Wednesday, November 07, 2012 4:04 PM > *To:* [email protected] > > *Subject:* [NMusers] Proper way to handle the pre-first dose PK observation for non-endogenous drug > > Dear NONMEM Users, > > I’d like to get some advice from you with regard to how to handle the pre-first dose PK observation when the drug is not an endogenous substance. > > I tried too different approaches, one approach is treating them as missing values (DV=0, EVID=0, MDV=1), another is treating them as true 0s (DV=0, EVID=0, MDV=0). My error structure is proportional + additive. There were very little difference for all parameters except for the SD of the additive error. When these pre-first dose concentrations were treated as missing, the estimated omega for additive error is 3.92, and when they were treated as true 0s, the sigma became 2.85. > > To me, in theory, these values provide no information about the model parameters because the system will predict them to be 0 at time 0 anyway for any point in the parameter space. Is what happened here that because DV is exactly the same as prediction, therefore the estimation of additive residual error variance has been brought down? > > Which way is more appropriate? I’d really appreciate it if you can share your experience/insight. > > Yaming Hang, Ph.D. > > Pharmacometrics > > Biogen Idec > > 14 Cambridge Center > > Cambridge, MA 02142 > > Office: 781-464-1741 > > Fax: 617-679-2804 > > Email: [email protected] <mailto:[email protected]> > > ------------------------------------------------------------------------ > > This e-mail (including any attachments) is confidential and may be legally privileged. If you are not an intended recipient or an authorized representative of an intended recipient, you are prohibited from using, copying or distributing the information in this e-mail or its attachments. If you have received this e-mail in error, please notify the sender immediately by return e-mail and delete all copies of this message and any attachments. > > Thank you. -- Nick Holford, Professor Clinical Pharmacology Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A 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
Hi Nick, I disagree with the suggestion to use exact zero for predose. Residual error models are, for a perfect structural model, a model for assay uncertainty. By including many observations at predose as precise zero, you are modeling non assay observations with an assay model. Result is your estimate of assay variance is biased below actual assay noise, just as observed by Yamings test. Yaming you can either exclude, or if you like you could try the typical censored data approaches. But i usually exclude predose myself as it doesn't inform the model. Best regards Dan Sent from my iPhone
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On Nov 7, 2012, at 6:19 PM, "Nick Holford" <[email protected]> wrote: > Yaming, Matt, > > I would do exactly what Yaming has done already. Treat the pre-dose > measurements as true observations for when the predicted conc is zero. > > It is not true to say they provide no information about model > parameters. They are the best way to improve your estimate of the > additive error parameter (independent of PK model misspecification). By > improving the residual error model you may also have benefits in > improving your PK model. Although the PK model benefit may be small in > principle it is foolish to ignore data that could be helpful. > > A major weakness of using log transformed both sides approach is that it > cannot use these real observations which is why I have rarely used it. > > Best wishes, > > Nick > > On 8/11/2012 11:23 a.m., Fidler,Matt,FORT WORTH,R&D wrote: >> >> Yaming, >> >> As you pointed-out DV=Prediction. Including these data-points biases >> your estimate of the additive component of variability. My opinion is >> just to exclude the observations to get a better estimate of additive >> variability. >> >> On a side note Additive+Proportortional is similar to a >> lognormal-error structure. In a lognormal error structure zero >> observations have to be excluded anyway. >> >> Matt. >> >> *From:*[email protected] >> [mailto:[email protected]] *On Behalf Of *Yaming Hang >> *Sent:* Wednesday, November 07, 2012 4:04 PM >> *To:* [email protected] >> *Subject:* [NMusers] Proper way to handle the pre-first dose PK >> observation for non-endogenous drug >> >> Dear NONMEM Users, >> >> I’d like to get some advice from you with regard to how to handle the >> pre-first dose PK observation when the drug is not an endogenous >> substance. >> >> I tried too different approaches, one approach is treating them as >> missing values (DV=0, EVID=0, MDV=1), another is treating them as true >> 0s (DV=0, EVID=0, MDV=0). My error structure is proportional + >> additive. There were very little difference for all parameters except >> for the SD of the additive error. When these pre-first dose >> concentrations were treated as missing, the estimated omega for >> additive error is 3.92, and when they were treated as true 0s, the >> sigma became 2.85. >> >> To me, in theory, these values provide no information about the model >> parameters because the system will predict them to be 0 at time 0 >> anyway for any point in the parameter space. Is what happened here >> that because DV is exactly the same as prediction, therefore the >> estimation of additive residual error variance has been brought down? >> >> Which way is more appropriate? I’d really appreciate it if you can >> share your experience/insight. >> >> Yaming Hang, Ph.D. >> >> Pharmacometrics >> >> Biogen Idec >> >> 14 Cambridge Center >> >> Cambridge, MA 02142 >> >> Office: 781-464-1741 >> >> Fax: 617-679-2804 >> >> Email: [email protected] <mailto:[email protected]> >> >> >> ------------------------------------------------------------------------ >> This e-mail (including any attachments) is confidential and may be >> legally privileged. If you are not an intended recipient or an >> authorized representative of an intended recipient, you are prohibited >> from using, copying or distributing the information in this e-mail or >> its attachments. If you have received this e-mail in error, please >> notify the sender immediately by return e-mail and delete all copies >> of this message and any attachments. >> >> Thank you. > > -- > Nick Holford, Professor Clinical Pharmacology > Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A > 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 > > 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.
Daniel Sorry -- thanks for picking that up! It seems I didn't read what Yaming wrote properly. Perhaps because I couldn't imagine why anyone would replace a real measurement with zero! Beal pointed out the folly of replacing BLQ values with zero in 2001. Notice that I said to use the pre-dose MEASUREMENTS --- not imputed values of zero. What I wanted to recommend was using the measured pre-dose value and including that in the data. Its important not to censor those measured values and include negative measurements as well as positive (or even zero) measurements. With a true additive error model and true prediction of zero there can be both negative and positive measurements. Of course if the chemical analysts refuse to tell the truth and report this as BLQ then you may resort to using a missing data method such as that proposed by Beal (e.g. M3 or M4). Nick Beal SL. Ways to fit a PK model with some data below the quantification limit. Journal of Pharmacokinetics & Pharmacodynamics 2001; 28: 481-504.
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On 8/11/2012 12:35 p.m., Tatosian, Daniel wrote: > Hi Nick, > > I disagree with the suggestion to use exact zero for predose. Residual error > models are, for a perfect structural model, a model for assay uncertainty. By > including many observations at predose as precise zero, you are modeling non > assay observations with an assay model. Result is your estimate of assay > variance is biased below actual assay noise, just as observed by Yamings test. > > Yaming you can either exclude, or if you like you could try the typical > censored data approaches. But i usually exclude predose myself as it doesn't > inform the model. > > Best regards > Dan > > Sent from my iPhone > > On Nov 7, 2012, at 6:19 PM, "Nick Holford" <[email protected]> wrote: > > > Yaming, Matt, > > > > I would do exactly what Yaming has done already. Treat the pre-dose > > measurements as true observations for when the predicted conc is zero. > > > > It is not true to say they provide no information about model > > parameters. They are the best way to improve your estimate of the > > additive error parameter (independent of PK model misspecification). By > > improving the residual error model you may also have benefits in > > improving your PK model. Although the PK model benefit may be small in > > principle it is foolish to ignore data that could be helpful. > > > > A major weakness of using log transformed both sides approach is that it > > cannot use these real observations which is why I have rarely used it. > > > > Best wishes, > > > > Nick > > > > On 8/11/2012 11:23 a.m., Fidler,Matt,FORT WORTH,R&D wrote: > > > > > Yaming, > > > > > > As you pointed-out DV=Prediction. Including these data-points biases > > > your estimate of the additive component of variability. My opinion is > > > just to exclude the observations to get a better estimate of additive > > > variability. > > > > > > On a side note Additive+Proportortional is similar to a > > > lognormal-error structure. In a lognormal error structure zero > > > observations have to be excluded anyway. > > > > > > Matt. > > > > > > *From:*[email protected] > > > [mailto:[email protected]] *On Behalf Of *Yaming Hang > > > *Sent:* Wednesday, November 07, 2012 4:04 PM > > > *To:* [email protected] > > > *Subject:* [NMusers] Proper way to handle the pre-first dose PK > > > observation for non-endogenous drug > > > > > > Dear NONMEM Users, > > > > > > I’d like to get some advice from you with regard to how to handle the > > > pre-first dose PK observation when the drug is not an endogenous > > > substance. > > > > > > I tried too different approaches, one approach is treating them as > > > missing values (DV=0, EVID=0, MDV=1), another is treating them as true > > > 0s (DV=0, EVID=0, MDV=0). My error structure is proportional + > > > additive. There were very little difference for all parameters except > > > for the SD of the additive error. When these pre-first dose > > > concentrations were treated as missing, the estimated omega for > > > additive error is 3.92, and when they were treated as true 0s, the > > > sigma became 2.85. > > > > > > To me, in theory, these values provide no information about the model > > > parameters because the system will predict them to be 0 at time 0 > > > anyway for any point in the parameter space. Is what happened here > > > that because DV is exactly the same as prediction, therefore the > > > estimation of additive residual error variance has been brought down? > > > > > > Which way is more appropriate? I’d really appreciate it if you can > > > share your experience/insight. > > > > > > Yaming Hang, Ph.D. > > > > > > Pharmacometrics > > > > > > Biogen Idec > > > > > > 14 Cambridge Center > > > > > > Cambridge, MA 02142 > > > > > > Office: 781-464-1741 > > > > > > Fax: 617-679-2804 > > > > > > Email: [email protected] <mailto:[email protected]> > > > > > > ------------------------------------------------------------------------ > > > This e-mail (including any attachments) is confidential and may be > > > legally privileged. If you are not an intended recipient or an > > > authorized representative of an intended recipient, you are prohibited > > > from using, copying or distributing the information in this e-mail or > > > its attachments. If you have received this e-mail in error, please > > > notify the sender immediately by return e-mail and delete all copies > > > of this message and any attachments. > > > > > > Thank you. > > > > -- > > Nick Holford, Professor Clinical Pharmacology > > Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A > > 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 > > 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. -- Nick Holford, Professor Clinical Pharmacology Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A 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
Dear all, I guess to know what is the best way to treat these data you need to know something more about the assay than what has been told. If the additive error component is related in any way to drug being administrated (such as when metabolites may interfere), then Matt's position may more relevant. If it is not, Nick's is more appropriate. Best regards, Mats Mats Karlsson, PhD Professor of Pharmacometrics Dept of Pharmaceutical Biosciences Faculty of Pharmacy Uppsala University Box 591 75124 Uppsala Phone: +46 18 4714105 Fax + 46 18 4714003
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-----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Nick Holford Sent: 07 November 2012 23:55 To: nmusers Subject: Re: [NMusers] RE: Proper way to handle the pre-first dose PK observation for non-endogenous drug Yaming, Matt, I would do exactly what Yaming has done already. Treat the pre-dose measurements as true observations for when the predicted conc is zero. It is not true to say they provide no information about model parameters. They are the best way to improve your estimate of the additive error parameter (independent of PK model misspecification). By improving the residual error model you may also have benefits in improving your PK model. Although the PK model benefit may be small in principle it is foolish to ignore data that could be helpful. A major weakness of using log transformed both sides approach is that it cannot use these real observations which is why I have rarely used it. Best wishes, Nick On 8/11/2012 11:23 a.m., Fidler,Matt,FORT WORTH,R&D wrote: > > Yaming, > > As you pointed-out DV=Prediction. Including these data-points biases > your estimate of the additive component of variability. My opinion is > just to exclude the observations to get a better estimate of additive > variability. > > On a side note Additive+Proportortional is similar to a > lognormal-error structure. In a lognormal error structure zero > observations have to be excluded anyway. > > Matt. > > *From:*[email protected] > [mailto:[email protected]] *On Behalf Of *Yaming Hang > *Sent:* Wednesday, November 07, 2012 4:04 PM > *To:* [email protected] > *Subject:* [NMusers] Proper way to handle the pre-first dose PK > observation for non-endogenous drug > > Dear NONMEM Users, > > I'd like to get some advice from you with regard to how to handle the > pre-first dose PK observation when the drug is not an endogenous > substance. > > I tried too different approaches, one approach is treating them as > missing values (DV=0, EVID=0, MDV=1), another is treating them as true > 0s (DV=0, EVID=0, MDV=0). My error structure is proportional + > additive. There were very little difference for all parameters except > for the SD of the additive error. When these pre-first dose > concentrations were treated as missing, the estimated omega for > additive error is 3.92, and when they were treated as true 0s, the > sigma became 2.85. > > To me, in theory, these values provide no information about the model > parameters because the system will predict them to be 0 at time 0 > anyway for any point in the parameter space. Is what happened here > that because DV is exactly the same as prediction, therefore the > estimation of additive residual error variance has been brought down? > > Which way is more appropriate? I'd really appreciate it if you can > share your experience/insight. > > Yaming Hang, Ph.D. > > Pharmacometrics > > Biogen Idec > > 14 Cambridge Center > > Cambridge, MA 02142 > > Office: 781-464-1741 > > Fax: 617-679-2804 > > Email: [email protected] <mailto:[email protected]> > > > ---------------------------------------------------------------------- > -- This e-mail (including any attachments) is confidential and may be > legally privileged. If you are not an intended recipient or an > authorized representative of an intended recipient, you are prohibited > from using, copying or distributing the information in this e-mail or > its attachments. If you have received this e-mail in error, please > notify the sender immediately by return e-mail and delete all copies > of this message and any attachments. > > Thank you. -- Nick Holford, Professor Clinical Pharmacology Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A 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
All, I agree. As a side note, if you have the actual BLQ observations that are above zero, then a lognormal error model can be used. No observations will be excluded. Matt.
Quoted reply history
-----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Nick Holford Sent: Wednesday, November 07, 2012 5:50 PM To: nmusers Subject: Re: [NMusers] RE: Proper way to handle the pre-first dose PK observation for non-endogenous drug Daniel Sorry -- thanks for picking that up! It seems I didn't read what Yaming wrote properly. Perhaps because I couldn't imagine why anyone would replace a real measurement with zero! Beal pointed out the folly of replacing BLQ values with zero in 2001. Notice that I said to use the pre-dose MEASUREMENTS --- not imputed values of zero. What I wanted to recommend was using the measured pre-dose value and including that in the data. Its important not to censor those measured values and include negative measurements as well as positive (or even zero) measurements. With a true additive error model and true prediction of zero there can be both negative and positive measurements. Of course if the chemical analysts refuse to tell the truth and report this as BLQ then you may resort to using a missing data method such as that proposed by Beal (e.g. M3 or M4). Nick Beal SL. Ways to fit a PK model with some data below the quantification limit. Journal of Pharmacokinetics & Pharmacodynamics 2001; 28: 481-504. On 8/11/2012 12:35 p.m., Tatosian, Daniel wrote: > Hi Nick, > > I disagree with the suggestion to use exact zero for predose. Residual error > models are, for a perfect structural model, a model for assay uncertainty. By > including many observations at predose as precise zero, you are modeling non > assay observations with an assay model. Result is your estimate of assay > variance is biased below actual assay noise, just as observed by Yamings test. > > Yaming you can either exclude, or if you like you could try the typical > censored data approaches. But i usually exclude predose myself as it doesn't > inform the model. > > Best regards > Dan > > Sent from my iPhone > > On Nov 7, 2012, at 6:19 PM, "Nick Holford" <[email protected]> wrote: > >> Yaming, Matt, >> >> I would do exactly what Yaming has done already. Treat the pre-dose >> measurements as true observations for when the predicted conc is zero. >> >> It is not true to say they provide no information about model >> parameters. They are the best way to improve your estimate of the >> additive error parameter (independent of PK model misspecification). By >> improving the residual error model you may also have benefits in >> improving your PK model. Although the PK model benefit may be small in >> principle it is foolish to ignore data that could be helpful. >> >> A major weakness of using log transformed both sides approach is that it >> cannot use these real observations which is why I have rarely used it. >> >> Best wishes, >> >> Nick >> >> On 8/11/2012 11:23 a.m., Fidler,Matt,FORT WORTH,R&D wrote: >>> Yaming, >>> >>> As you pointed-out DV=Prediction. Including these data-points biases >>> your estimate of the additive component of variability. My opinion is >>> just to exclude the observations to get a better estimate of additive >>> variability. >>> >>> On a side note Additive+Proportortional is similar to a >>> lognormal-error structure. In a lognormal error structure zero >>> observations have to be excluded anyway. >>> >>> Matt. >>> >>> *From:*[email protected] >>> [mailto:[email protected]] *On Behalf Of *Yaming Hang >>> *Sent:* Wednesday, November 07, 2012 4:04 PM >>> *To:* [email protected] >>> *Subject:* [NMusers] Proper way to handle the pre-first dose PK >>> observation for non-endogenous drug >>> >>> Dear NONMEM Users, >>> >>> I’d like to get some advice from you with regard to how to handle the >>> pre-first dose PK observation when the drug is not an endogenous >>> substance. >>> >>> I tried too different approaches, one approach is treating them as >>> missing values (DV=0, EVID=0, MDV=1), another is treating them as true >>> 0s (DV=0, EVID=0, MDV=0). My error structure is proportional + >>> additive. There were very little difference for all parameters except >>> for the SD of the additive error. When these pre-first dose >>> concentrations were treated as missing, the estimated omega for >>> additive error is 3.92, and when they were treated as true 0s, the >>> sigma became 2.85. >>> >>> To me, in theory, these values provide no information about the model >>> parameters because the system will predict them to be 0 at time 0 >>> anyway for any point in the parameter space. Is what happened here >>> that because DV is exactly the same as prediction, therefore the >>> estimation of additive residual error variance has been brought down? >>> >>> Which way is more appropriate? I’d really appreciate it if you can >>> share your experience/insight. >>> >>> Yaming Hang, Ph.D. >>> >>> Pharmacometrics >>> >>> Biogen Idec >>> >>> 14 Cambridge Center >>> >>> Cambridge, MA 02142 >>> >>> Office: 781-464-1741 >>> >>> Fax: 617-679-2804 >>> >>> Email: [email protected] <mailto:[email protected]> >>> >>> >>> ------------------------------------------------------------------------ >>> This e-mail (including any attachments) is confidential and may be >>> legally privileged. If you are not an intended recipient or an >>> authorized representative of an intended recipient, you are prohibited >>> from using, copying or distributing the information in this e-mail or >>> its attachments. If you have received this e-mail in error, please >>> notify the sender immediately by return e-mail and delete all copies >>> of this message and any attachments. >>> >>> Thank you. >> -- >> Nick Holford, Professor Clinical Pharmacology >> Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A >> 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 >> >> > 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. -- Nick Holford, Professor Clinical Pharmacology Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A 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 This e-mail (including any attachments) is confidential and may be legally privileged. If you are not an intended recipient or an authorized representative of an intended recipient, you are prohibited from using, copying or distributing the information in this e-mail or its attachments. If you have received this e-mail in error, please notify the sender immediately by return e-mail and delete all copies of this message and any attachments. Thank you.
Dear Matt, Dan, Nick and Mats, Thanks for sharing your thoughts and the enlightening discussion, it is really helpful! Yaming Hang, Ph.D. Pharmacometrics Biogen Idec 14 Cambridge Center Cambridge, MA 02142 Office: 781-464-1741 Fax: 617-679-2804 Email: [email protected]
Quoted reply history
-----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Fidler,Matt,FORT WORTH,R&D Sent: Thursday, November 08, 2012 9:29 AM To: Nick Holford; nmusers Subject: RE: [NMusers] RE: Proper way to handle the pre-first dose PK observation for non-endogenous drug All, I agree. As a side note, if you have the actual BLQ observations that are above zero, then a lognormal error model can be used. No observations will be excluded. Matt. -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Nick Holford Sent: Wednesday, November 07, 2012 5:50 PM To: nmusers Subject: Re: [NMusers] RE: Proper way to handle the pre-first dose PK observation for non-endogenous drug Daniel Sorry -- thanks for picking that up! It seems I didn't read what Yaming wrote properly. Perhaps because I couldn't imagine why anyone would replace a real measurement with zero! Beal pointed out the folly of replacing BLQ values with zero in 2001. Notice that I said to use the pre-dose MEASUREMENTS --- not imputed values of zero. What I wanted to recommend was using the measured pre-dose value and including that in the data. Its important not to censor those measured values and include negative measurements as well as positive (or even zero) measurements. With a true additive error model and true prediction of zero there can be both negative and positive measurements. Of course if the chemical analysts refuse to tell the truth and report this as BLQ then you may resort to using a missing data method such as that proposed by Beal (e.g. M3 or M4). Nick Beal SL. Ways to fit a PK model with some data below the quantification limit. Journal of Pharmacokinetics & Pharmacodynamics 2001; 28: 481-504. On 8/11/2012 12:35 p.m., Tatosian, Daniel wrote: > Hi Nick, > > I disagree with the suggestion to use exact zero for predose. Residual error > models are, for a perfect structural model, a model for assay uncertainty. By > including many observations at predose as precise zero, you are modeling non > assay observations with an assay model. Result is your estimate of assay > variance is biased below actual assay noise, just as observed by Yamings test. > > Yaming you can either exclude, or if you like you could try the typical > censored data approaches. But i usually exclude predose myself as it doesn't > inform the model. > > Best regards > Dan > > Sent from my iPhone > > On Nov 7, 2012, at 6:19 PM, "Nick Holford" <[email protected]> wrote: > >> Yaming, Matt, >> >> I would do exactly what Yaming has done already. Treat the pre-dose >> measurements as true observations for when the predicted conc is zero. >> >> It is not true to say they provide no information about model >> parameters. They are the best way to improve your estimate of the >> additive error parameter (independent of PK model misspecification). >> By improving the residual error model you may also have benefits in >> improving your PK model. Although the PK model benefit may be small >> in principle it is foolish to ignore data that could be helpful. >> >> A major weakness of using log transformed both sides approach is that >> it cannot use these real observations which is why I have rarely used it. >> >> Best wishes, >> >> Nick >> >> On 8/11/2012 11:23 a.m., Fidler,Matt,FORT WORTH,R&D wrote: >>> Yaming, >>> >>> As you pointed-out DV=Prediction. Including these data-points biases >>> your estimate of the additive component of variability. My opinion >>> is just to exclude the observations to get a better estimate of >>> additive variability. >>> >>> On a side note Additive+Proportortional is similar to a >>> lognormal-error structure. In a lognormal error structure zero >>> observations have to be excluded anyway. >>> >>> Matt. >>> >>> *From:*[email protected] >>> [mailto:[email protected]] *On Behalf Of *Yaming Hang >>> *Sent:* Wednesday, November 07, 2012 4:04 PM >>> *To:* [email protected] >>> *Subject:* [NMusers] Proper way to handle the pre-first dose PK >>> observation for non-endogenous drug >>> >>> Dear NONMEM Users, >>> >>> I’d like to get some advice from you with regard to how to handle >>> the pre-first dose PK observation when the drug is not an endogenous >>> substance. >>> >>> I tried too different approaches, one approach is treating them as >>> missing values (DV=0, EVID=0, MDV=1), another is treating them as >>> true 0s (DV=0, EVID=0, MDV=0). My error structure is proportional + >>> additive. There were very little difference for all parameters >>> except for the SD of the additive error. When these pre-first dose >>> concentrations were treated as missing, the estimated omega for >>> additive error is 3.92, and when they were treated as true 0s, the >>> sigma became 2.85. >>> >>> To me, in theory, these values provide no information about the >>> model parameters because the system will predict them to be 0 at >>> time 0 anyway for any point in the parameter space. Is what happened >>> here that because DV is exactly the same as prediction, therefore >>> the estimation of additive residual error variance has been brought down? >>> >>> Which way is more appropriate? I’d really appreciate it if you can >>> share your experience/insight. >>> >>> Yaming Hang, Ph.D. >>> >>> Pharmacometrics >>> >>> Biogen Idec >>> >>> 14 Cambridge Center >>> >>> Cambridge, MA 02142 >>> >>> Office: 781-464-1741 >>> >>> Fax: 617-679-2804 >>> >>> Email: [email protected] >>> <mailto:[email protected]> >>> >>> >>> -------------------------------------------------------------------- >>> ---- This e-mail (including any attachments) is confidential and may >>> be legally privileged. If you are not an intended recipient or an >>> authorized representative of an intended recipient, you are >>> prohibited from using, copying or distributing the information in >>> this e-mail or its attachments. If you have received this e-mail in >>> error, please notify the sender immediately by return e-mail and >>> delete all copies of this message and any attachments. >>> >>> Thank you. >> -- >> Nick Holford, Professor Clinical Pharmacology Dept Pharmacology & >> Clinical Pharmacology, Bldg 503 Room 302A 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 >> >> > 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. -- Nick Holford, Professor Clinical Pharmacology Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A 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 This e-mail (including any attachments) is confidential and may be legally privileged. If you are not an intended recipient or an authorized representative of an intended recipient, you are prohibited from using, copying or distributing the information in this e-mail or its attachments. If you have received this e-mail in error, please notify the sender immediately by return e-mail and delete all copies of this message and any attachments. Thank you.
Dear All, >From a practical perspective I do not see the value of adding these data in >general. Since residual error is a composed of measurement error (assay) and >lack of fit (to which Nick alluded), including these pre-first dose data could >bias your residual variance estimates (so there is potential for bias with >little gain otherwise - this could cause poor weighting for the part of the >data that will actually inform parameter estimation - ie after dosing). >Rarely have I had PK data so exquisite (single IV bolus with a half life such >that measurement errors in time are inconsequential) such that my residual >error was that close to assay error. It seems the key utility of these samples >is to confirm that subjects were not on drug prior to initiating treatment for >the study. Best regards, Matt
Quoted reply history
-----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Fidler,Matt,FORT WORTH,R&D Sent: Thursday, November 08, 2012 9:29 AM To: Nick Holford; nmusers Subject: RE: [NMusers] RE: Proper way to handle the pre-first dose PK observation for non-endogenous drug All, I agree. As a side note, if you have the actual BLQ observations that are above zero, then a lognormal error model can be used. No observations will be excluded. Matt. -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Nick Holford Sent: Wednesday, November 07, 2012 5:50 PM To: nmusers Subject: Re: [NMusers] RE: Proper way to handle the pre-first dose PK observation for non-endogenous drug Daniel Sorry -- thanks for picking that up! It seems I didn't read what Yaming wrote properly. Perhaps because I couldn't imagine why anyone would replace a real measurement with zero! Beal pointed out the folly of replacing BLQ values with zero in 2001. Notice that I said to use the pre-dose MEASUREMENTS --- not imputed values of zero. What I wanted to recommend was using the measured pre-dose value and including that in the data. Its important not to censor those measured values and include negative measurements as well as positive (or even zero) measurements. With a true additive error model and true prediction of zero there can be both negative and positive measurements. Of course if the chemical analysts refuse to tell the truth and report this as BLQ then you may resort to using a missing data method such as that proposed by Beal (e.g. M3 or M4). Nick Beal SL. Ways to fit a PK model with some data below the quantification limit. Journal of Pharmacokinetics & Pharmacodynamics 2001; 28: 481-504. On 8/11/2012 12:35 p.m., Tatosian, Daniel wrote: > Hi Nick, > > I disagree with the suggestion to use exact zero for predose. Residual error > models are, for a perfect structural model, a model for assay uncertainty. By > including many observations at predose as precise zero, you are modeling non > assay observations with an assay model. Result is your estimate of assay > variance is biased below actual assay noise, just as observed by Yamings test. > > Yaming you can either exclude, or if you like you could try the typical > censored data approaches. But i usually exclude predose myself as it doesn't > inform the model. > > Best regards > Dan > > Sent from my iPhone > > On Nov 7, 2012, at 6:19 PM, "Nick Holford" <[email protected]> wrote: > >> Yaming, Matt, >> >> I would do exactly what Yaming has done already. Treat the pre-dose >> measurements as true observations for when the predicted conc is zero. >> >> It is not true to say they provide no information about model >> parameters. They are the best way to improve your estimate of the >> additive error parameter (independent of PK model misspecification). >> By improving the residual error model you may also have benefits in >> improving your PK model. Although the PK model benefit may be small >> in principle it is foolish to ignore data that could be helpful. >> >> A major weakness of using log transformed both sides approach is that >> it cannot use these real observations which is why I have rarely used it. >> >> Best wishes, >> >> Nick >> >> On 8/11/2012 11:23 a.m., Fidler,Matt,FORT WORTH,R&D wrote: >>> Yaming, >>> >>> As you pointed-out DV=Prediction. Including these data-points biases >>> your estimate of the additive component of variability. My opinion >>> is just to exclude the observations to get a better estimate of >>> additive variability. >>> >>> On a side note Additive+Proportortional is similar to a >>> lognormal-error structure. In a lognormal error structure zero >>> observations have to be excluded anyway. >>> >>> Matt. >>> >>> *From:*[email protected] >>> [mailto:[email protected]] *On Behalf Of *Yaming Hang >>> *Sent:* Wednesday, November 07, 2012 4:04 PM >>> *To:* [email protected] >>> *Subject:* [NMusers] Proper way to handle the pre-first dose PK >>> observation for non-endogenous drug >>> >>> Dear NONMEM Users, >>> >>> I’d like to get some advice from you with regard to how to handle >>> the pre-first dose PK observation when the drug is not an endogenous >>> substance. >>> >>> I tried too different approaches, one approach is treating them as >>> missing values (DV=0, EVID=0, MDV=1), another is treating them as >>> true 0s (DV=0, EVID=0, MDV=0). My error structure is proportional + >>> additive. There were very little difference for all parameters >>> except for the SD of the additive error. When these pre-first dose >>> concentrations were treated as missing, the estimated omega for >>> additive error is 3.92, and when they were treated as true 0s, the >>> sigma became 2.85. >>> >>> To me, in theory, these values provide no information about the >>> model parameters because the system will predict them to be 0 at >>> time 0 anyway for any point in the parameter space. Is what happened >>> here that because DV is exactly the same as prediction, therefore >>> the estimation of additive residual error variance has been brought down? >>> >>> Which way is more appropriate? I’d really appreciate it if you can >>> share your experience/insight. >>> >>> Yaming Hang, Ph.D. >>> >>> Pharmacometrics >>> >>> Biogen Idec >>> >>> 14 Cambridge Center >>> >>> Cambridge, MA 02142 >>> >>> Office: 781-464-1741 >>> >>> Fax: 617-679-2804 >>> >>> Email: [email protected] >>> <mailto:[email protected]> >>> >>> >>> -------------------------------------------------------------------- >>> ---- This e-mail (including any attachments) is confidential and may >>> be legally privileged. If you are not an intended recipient or an >>> authorized representative of an intended recipient, you are >>> prohibited from using, copying or distributing the information in >>> this e-mail or its attachments. If you have received this e-mail in >>> error, please notify the sender immediately by return e-mail and >>> delete all copies of this message and any attachments. >>> >>> Thank you. >> -- >> Nick Holford, Professor Clinical Pharmacology Dept Pharmacology & >> Clinical Pharmacology, Bldg 503 Room 302A 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 >> >> > 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. -- Nick Holford, Professor Clinical Pharmacology Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A 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 This e-mail (including any attachments) is confidential and may be legally privileged. If you are not an intended recipient or an authorized representative of an intended recipient, you are prohibited from using, copying or distributing the information in this e-mail or its attachments. If you have received this e-mail in error, please notify the sender immediately by return e-mail and delete all copies of this message and any attachments. Thank you.
Hi Matt/Nick/All, It is my understanding that if analytical labs were to report the measured concentrations below the BLQ that negative concentration values could be reported from the standard curve predictions. Thus, reporting the pre-first-dose PK observations and including them in the analysis could still be problematic for the lognormal error model. While this is a limitation of the log-normal model in that it can't properly describe background assay error, the motivation for the use of the log-normal error model is to handle the right-skewness in the distribution of the residual errors that we often observe at higher concentrations. Note that the additive + proportional error model can deal with the heterogeneous residual variability that increases with increasing concentration but it assumes that the residual errors are symmetrically distributed about the individual prediction regardless of the magnitude of the prediction...this assumption may not always be reasonable. Thus, there are limitations with both the log-normal error model and the additive+proportional residual error model. The challenge for any given dataset is whether or not one or the other is a better approximation of the residual error distribution within the range of observed data. Ken
Quoted reply history
-----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Nick Holford Sent: Thursday, November 08, 2012 12:16 PM To: nmusers Subject: Re: [NMusers] RE: Proper way to handle the pre-first dose PK observation for non-endogenous drug Matt, When you say "if you have the actual BLQ observations that are above zero" you have just excluded all zero and negative observations. This is called censoring which is a well understood cause of bias. Logarithms don't fix that. Nick On 9/11/2012 3:28 a.m., Fidler,Matt,FORT WORTH,R&D wrote: > All, > > I agree. > > As a side note, if you have the actual BLQ observations that are above zero, > then a lognormal error model can be used. No observations will be excluded. > > > Matt. > > -----Original Message----- > From: [email protected] > [mailto:[email protected]] On Behalf Of Nick Holford > Sent: Wednesday, November 07, 2012 5:50 PM > To: nmusers > Subject: Re: [NMusers] RE: Proper way to handle the pre-first dose PK > observation for non-endogenous drug > > Daniel > > Sorry -- thanks for picking that up! It seems I didn't read what > Yaming wrote properly. Perhaps because I couldn't imagine why anyone > would replace a real measurement with zero! Beal pointed out the > folly of replacing BLQ values with zero in 2001. Notice that I said > to use the pre-dose MEASUREMENTS --- not imputed values of zero. > > What I wanted to recommend was using the measured pre-dose value and > including that in the data. Its important not to censor those measured > values and include negative measurements as well as positive (or even > zero) measurements. With a true additive error model and true > prediction of zero there can be both negative and positive measurements. > > Of course if the chemical analysts refuse to tell the truth and report > this as BLQ then you may resort to using a missing data method such as > that proposed by Beal (e.g. M3 or M4). > > Nick > > Beal SL. Ways to fit a PK model with some data below the > quantification limit. Journal of Pharmacokinetics & Pharmacodynamics 2001; > 28: 481-504. > > On 8/11/2012 12:35 p.m., Tatosian, Daniel wrote: >> Hi Nick, >> >> I disagree with the suggestion to use exact zero for predose. Residual error >> models are, for a perfect structural model, a model for assay uncertainty. >> By including many observations at predose as precise zero, you are modeling >> non assay observations with an assay model. Result is your estimate of assay >> variance is biased below actual assay noise, just as observed by Yamings >> test. >> >> Yaming you can either exclude, or if you like you could try the typical >> censored data approaches. But i usually exclude predose myself as it doesn't >> inform the model. >> >> Best regards >> Dan >> >> Sent from my iPhone >> >> On Nov 7, 2012, at 6:19 PM, "Nick Holford" <[email protected]> wrote: >> >>> Yaming, Matt, >>> >>> I would do exactly what Yaming has done already. Treat the pre-dose >>> measurements as true observations for when the predicted conc is zero. >>> >>> It is not true to say they provide no information about model >>> parameters. They are the best way to improve your estimate of the >>> additive error parameter (independent of PK model misspecification). >>> By improving the residual error model you may also have benefits in >>> improving your PK model. Although the PK model benefit may be small >>> in principle it is foolish to ignore data that could be helpful. >>> >>> A major weakness of using log transformed both sides approach is >>> that it cannot use these real observations which is why I have rarely used >>> it. >>> >>> Best wishes, >>> >>> Nick >>> >>> On 8/11/2012 11:23 a.m., Fidler,Matt,FORT WORTH,R&D wrote: >>>> Yaming, >>>> >>>> As you pointed-out DV=Prediction. Including these data-points >>>> biases your estimate of the additive component of variability. My >>>> opinion is just to exclude the observations to get a better >>>> estimate of additive variability. >>>> >>>> On a side note Additive+Proportortional is similar to a >>>> lognormal-error structure. In a lognormal error structure zero >>>> observations have to be excluded anyway. >>>> >>>> Matt. >>>> >>>> *From:*[email protected] >>>> [mailto:[email protected]] *On Behalf Of *Yaming Hang >>>> *Sent:* Wednesday, November 07, 2012 4:04 PM >>>> *To:* [email protected] >>>> *Subject:* [NMusers] Proper way to handle the pre-first dose PK >>>> observation for non-endogenous drug >>>> >>>> Dear NONMEM Users, >>>> >>>> I’d like to get some advice from you with regard to how to handle >>>> the pre-first dose PK observation when the drug is not an >>>> endogenous substance. >>>> >>>> I tried too different approaches, one approach is treating them as >>>> missing values (DV=0, EVID=0, MDV=1), another is treating them as >>>> true 0s (DV=0, EVID=0, MDV=0). My error structure is proportional + >>>> additive. There were very little difference for all parameters >>>> except for the SD of the additive error. When these pre-first dose >>>> concentrations were treated as missing, the estimated omega for >>>> additive error is 3.92, and when they were treated as true 0s, the >>>> sigma became 2.85. >>>> >>>> To me, in theory, these values provide no information about the >>>> model parameters because the system will predict them to be 0 at >>>> time 0 anyway for any point in the parameter space. Is what >>>> happened here that because DV is exactly the same as prediction, >>>> therefore the estimation of additive residual error variance has been >>>> brought down? >>>> >>>> Which way is more appropriate? I’d really appreciate it if you can >>>> share your experience/insight. >>>> >>>> Yaming Hang, Ph.D. >>>> >>>> Pharmacometrics >>>> >>>> Biogen Idec >>>> >>>> 14 Cambridge Center >>>> >>>> Cambridge, MA 02142 >>>> >>>> Office: 781-464-1741 >>>> >>>> Fax: 617-679-2804 >>>> >>>> Email: [email protected] >>>> <mailto:[email protected]> >>>> >>>> >>>> ------------------------------------------------------------------- >>>> ----- This e-mail (including any attachments) is confidential and >>>> may be legally privileged. If you are not an intended recipient or >>>> an authorized representative of an intended recipient, you are >>>> prohibited from using, copying or distributing the information in >>>> this e-mail or its attachments. If you have received this e-mail in >>>> error, please notify the sender immediately by return e-mail and >>>> delete all copies of this message and any attachments. >>>> >>>> Thank you. >>> -- >>> Nick Holford, Professor Clinical Pharmacology Dept Pharmacology & >>> Clinical Pharmacology, Bldg 503 Room 302A 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 >>> >>> >> 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. > -- > Nick Holford, Professor Clinical Pharmacology Dept Pharmacology & > Clinical Pharmacology, Bldg 503 Room 302A 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 > > > > This e-mail (including any attachments) is confidential and may be legally > privileged. If you are not an intended recipient or an authorized > representative of an intended recipient, you are prohibited from using, > copying or distributing the information in this e-mail or its attachments. If > you have received this e-mail in error, please notify the sender immediately > by return e-mail and delete all copies of this message and any attachments. > > Thank you. -- Nick Holford, Professor Clinical Pharmacology Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A 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