# RE: Negative OFV number

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

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