Re: [NMusers] Error model

James,
The division in the expression for the error is not a typo.
The line of thoughts is:

Y=F*EXP(sqrt(theta^2+(theta/F)^2)eps) ;
   F*(1+sqrt(theta^2+(theta/F)^2)eps) ; linearization
   F+F* eps1 + F*eps2/F= ; rewiring as 2 epsilons
   F(1+eps1)+ eps2 ; combined error model

Leonid


--------------------------------------
Leonid Gibiansky, President
QuantPharm LLC: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566


James G Wright wrote:
> If Y is the original observed data, then the log-transformed error model is
>
> LOG (Y) = LOG (F) + EPS(1)
>
> We can exponentiate both sides to get an approximately proportional
> error model:-
>
> Y = F * EXP( EPS(1) ).
>
> The advantage of the above approach is that the mean and variance terms
> are independent (if the data are log-transformed in the data file).
> This avoids instabilities caused by NONMEM biasing the mean prediction
> to get "better" variance terms - a known problem for ELS-type methods
> since 1980. Unfortunately, we can't apply the same trick to the ETAs
> because they are not directly observed.
>
> However, the model proposed as "additive and proportional" by Nidal is
>
> LOG (Y) = LOG (F) + W*EPS(1)
>
> Exponentiating to get
>
> Y = F*EXP( W*EPS(1) )
>
> where W= SQRT (THETA(n-1)**2 + THETA(n)**2 * LOG(F)**2). I'm assuming
> the division sign in the original email was a typo, as
> THETA(n)**2/LOG(F)**2 goes to infinity when F approaches 1. Rewriting
> with separate estimated epsilons instead of estimated thetas for clarity
> gives:-
>
> Y = F * EXP( EPS(1) + LOG(F)*EPS(2) )
> = F * EXP( EPS(1) ) * EXP( LOG(F)*EPS(2) )
>
> which is vaguely like having an error term proportional to LOG(F)
> working multiplicatively with a standard proportional error model.
> After linearization, you obtain something like
>
> Y = F + F * EPS(1) + F * LOG(F) * EPS(2)
>
> which gives a F * LOG(F) weighting term, as opposed to the constant
> weighting term required for an additive model.
>
> Incidentally, IF (F.EQ.0) "TY" should equal a very large negative number
> (well, minus infinity). Either you replace zeroes in a log-proportional
> model with a small number or you discard them, setting LOG (F) = 0 is
> like setting F=1 if (F.EQ.0).
>
> Best regards,
>
>
> James G Wright PhD
> Scientist
> Wright Dose Ltd
> Tel: 44 (0) 772 5636914
> www.wright-dose.com <http://www.wright-dose.com/>
>
> -----Original Message-----
> *From:* owner-nmusers_at_globomaxnm.com
> [mailto:owner-nmusers_at_globomaxnm.com] *On Behalf Of
> *nidal.alhuniti_at_gmail.com
> *Sent:* 05 October 2007 08:13
> *To:* navin goyal
> *Cc:* nmusers
> *Subject:* Re: [NMusers] Error model
>
> Hi Navin,
>
> You could try both additive and proportional error model
> $ERROR
>
> TY=F
>
> IF(F.GT.0) THEN
>
> TY=LOG(F)
>
> ELSE
>
> TY=0
>
> ENDIF
>
> IPRED=TY
>
> W=SQRT(THETA(n-1)**2+THETA(n)**2/IPRED**2) ; log transformed data
> Y=TY+W*EPS(1)
>
>
>
> $SIGMA 1 FIX
>
> Best,
>
> Nidal
>
>
>
> Nidal Al-Huniti, PhD
>
> Strategic Consulting Services
>
> Pharsight Corporation
>
> nal-huniti_at_pharsight.com <mailto:nal-huniti_at_pharsight.com>
>
>
>
>
>
> On 10/4/07, *navin goyal* <navin1180_at_gmail.com
> <mailto:navin1180_at_gmail.com>> wrote:
>
> Dear Nonmem users,
>
> I am analysing a POPPK data with sparse sampling
> The dosing is an IV infusion over one hour and we have data for
> time points 0 (predose), 1 (end of infusion) and 2 (one hour
> post infusion)
> The drug has a half life of approx 4 hours. The dose is given
> once every fourth day
> When I ran my control stream and looked at the output table, I
> got some IPREDs at time predose time points where the DV was 0
> the event ID EVID for these time points was 4 (reset)
> (almost 20 half lives)
> I was wondering why did NONMEM predict concentrations at these
> time points ?? there were a couple of time points like this.
>
> I started with untransformed data and fitted my model.
> but after bootstrapping the errors on etas and sigma were
> very high.
> I log transformed the data , which improved the etas but the
> sigma shot upto more than 100%
> ( is it because the data is very sparse ??? or I need to use a
> better error model ???)
> Are there any other error models that could be used with the log
> transformed data, apart from the
> Y=Log(f)+EPS(1)
>
>
> Any suggestions would be appreciated
> thanks
>
> --
> --Navin
>
>
Received on Fri Oct 05 2007 - 08:32:58 EDT