From: Ken Kowalski <*ken.kowalski*>

Date: Sun, 19 Dec 2010 10:20:07 -0500

Hi Yuhong,

To expand on Serge's response that OFV can be negative for untransformed

data it is important to note that the OFV depends on the scale. You can

show that

OFV(Y/c) =OFV(Y) - 2nlog(c)

where n is the total number of observations and c is an arbitrary constant

such as one might use to change the units of Y. For example, if Y is your

concentration in mcg/mL and you change the units to g/mL (i.e., Y/1000000)

then OFV(Y/1000000) = OFV(Y) -2nlog(1000000). If 2nlog(1000000) > OFV(Y)

then OFV(Y/10000000) will be negative. Note that your parameter estimates

will not change although you will have to modify S2 to ensure that V is

reported in the same units as before; however, note that DOFV is invariant

to the scale change since -2nlog(c) will cancel out when you take the

difference between two models. Thus, the OFV depends on the scale but DOFV

does not. The reason we don't normally observe negative OFV for

untransformed data is because of our choice of units. We generally choose

units so that Y is not extremely small but if we did choose units that

result in very small Ys then you may indeed observe a negative OFV.

Ken

From: owner-nmusers

Behalf Of Serge Guzy

Sent: Saturday, December 18, 2010 12:05 AM

To: Yuhong Chen; nmusers

Subject: RE: [NMusers] Negative OFV number

For each observation (j)associated with an individual (i),you can calculate

the contribution to the overall - log-likelihood (CLIKEIND(K,J))for any PK

set of values (sampled from the current population PK distribution if using

MCPEM).

CONCNORM(K,J)=(DLOG(CONC(I,J))-DLOG(DABS(CPREDICTED(K,J))))/(SD)

CLIKEIND(K,J) =dLOG(SD)+CONCNORM(K,J)**2.0d0/2.0d0

SD is the standard deviation associated with your error variance model.

Dlog(SD) can be negative.

CONC(I,J) is the observed concentration for individual I at its jth

observation and Cpredicted(K,J) is the predicted concentration for that

individual (I has been omitted) for the kth simulated Pk vector (MCPEM

method).

OFV can be negative for both log or not log transformed data.

Serge Guzy

President, CEO; POP_PHARM;INC.

From: owner-nmusers

Behalf Of Yuhong Chen

Sent: Friday, December 17, 2010 1:19 PM

To: nmusers

Subject: [NMusers] Negative OFV number

Dear All,

I am reviewing a PopPK report, and found the OFV is negative. The model used

the log transformed data. Is it can be the reason of negative OFV number? Is

the negative OFV number means the model may have problem? Any suggestion

will be greatly appreciated.

Warm regards,

Yuhong

_____

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named recipient(s). No confidentiality or privilege is waived or lost by any

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Received on Sun Dec 19 2010 - 10:20:07 EST

Date: Sun, 19 Dec 2010 10:20:07 -0500

Hi Yuhong,

To expand on Serge's response that OFV can be negative for untransformed

data it is important to note that the OFV depends on the scale. You can

show that

OFV(Y/c) =OFV(Y) - 2nlog(c)

where n is the total number of observations and c is an arbitrary constant

such as one might use to change the units of Y. For example, if Y is your

concentration in mcg/mL and you change the units to g/mL (i.e., Y/1000000)

then OFV(Y/1000000) = OFV(Y) -2nlog(1000000). If 2nlog(1000000) > OFV(Y)

then OFV(Y/10000000) will be negative. Note that your parameter estimates

will not change although you will have to modify S2 to ensure that V is

reported in the same units as before; however, note that DOFV is invariant

to the scale change since -2nlog(c) will cancel out when you take the

difference between two models. Thus, the OFV depends on the scale but DOFV

does not. The reason we don't normally observe negative OFV for

untransformed data is because of our choice of units. We generally choose

units so that Y is not extremely small but if we did choose units that

result in very small Ys then you may indeed observe a negative OFV.

Ken

From: owner-nmusers

Behalf Of Serge Guzy

Sent: Saturday, December 18, 2010 12:05 AM

To: Yuhong Chen; nmusers

Subject: RE: [NMusers] Negative OFV number

For each observation (j)associated with an individual (i),you can calculate

the contribution to the overall - log-likelihood (CLIKEIND(K,J))for any PK

set of values (sampled from the current population PK distribution if using

MCPEM).

CONCNORM(K,J)=(DLOG(CONC(I,J))-DLOG(DABS(CPREDICTED(K,J))))/(SD)

CLIKEIND(K,J) =dLOG(SD)+CONCNORM(K,J)**2.0d0/2.0d0

SD is the standard deviation associated with your error variance model.

Dlog(SD) can be negative.

CONC(I,J) is the observed concentration for individual I at its jth

observation and Cpredicted(K,J) is the predicted concentration for that

individual (I has been omitted) for the kth simulated Pk vector (MCPEM

method).

OFV can be negative for both log or not log transformed data.

Serge Guzy

President, CEO; POP_PHARM;INC.

From: owner-nmusers

Behalf Of Yuhong Chen

Sent: Friday, December 17, 2010 1:19 PM

To: nmusers

Subject: [NMusers] Negative OFV number

Dear All,

I am reviewing a PopPK report, and found the OFV is negative. The model used

the log transformed data. Is it can be the reason of negative OFV number? Is

the negative OFV number means the model may have problem? Any suggestion

will be greatly appreciated.

Warm regards,

Yuhong

_____

The information contained in this email message may contain confidential or

legally privileged information and is intended solely for the use of the

named recipient(s). No confidentiality or privilege is waived or lost by any

transmission error. If the reader of this message is not the intended

recipient, please immediately delete the e-mail and all copies of it from

your system, destroy any hard copies of it and notify the sender either by

telephone or return e-mail. Any direct or indirect use, disclosure,

distribution, printing, or copying of any part of this message is

prohibited. Any views expressed in this message are those of the individual

sender, except where the message states otherwise and the sender is

authorized to state them to be the views of XOMA.

Received on Sun Dec 19 2010 - 10:20:07 EST