Re: [NMusers] Error model

Hi James,

This error model was discussed in the following NM threads.

http://www.cognigencorp.com/nonmem/nm/99apr232002.html



http://www.cognigencorp.com/nonmem/nm/98jun022003.html


To prevent division by zero



$ERROR

   TY=F

   IF(F.GT.1) THEN

   TY=LOG(F)

   ELSE

   TY=0.025

   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




On 10/5/07, James G Wright <james_at_wright-dose.com> wrote:
>
> Hi Leonid,
>
> In the original email, IPRED = LOG(F) and division by LOG(F) leads to a
> division by zero when F=1, hence there was definitely a typo
> somewhere...
>
> Of course, this isn't the case in your revised version, however you have
> introduced a dependence on F (as a reciprocal for the additive term)
> which reintroduces all of the ELS problems (where your variances can
> bias your means) that we were trying to avoid by going to the log-scale
> in the first place. Because F is now entering as a reciprocal which
> leads to very big numbers when F is small, I expect this method would
> perform worse than working on the original scale.
>
> Best regards, James
>
>
>
>
>
>
> James G Wright PhD
> Scientist
> Wright Dose Ltd
> Tel: 44 (0) 772 5636914
> www.wright-dose.com
>
>
> -----Original Message-----
> From: Leonid Gibiansky [mailto:LGibiansky_at_quantpharm.com]
> Sent: 05 October 2007 13:33
> To: James G Wright
> Cc: nmusers_at_globomaxnm.com
> Subject: 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 - 12:32:13 EDT