Re: Error model

On 10/8/07, James G Wright <[EMAIL PROTECTED]> wrote: > > Hi Nidal, > > As you have modified the code to prevent F going below 1, it looks > like you did intend to divide by IPRED (set equal to LOG(F)) in the > weighting expression..? > > If so, this gives an F/LOG(F) weighting term, which is an innovative error > model, never previously mentioned before on the NMuser list to my > knowledge. > > Best regards, James > > James G Wright PhD > Scientist > Wright Dose Ltd > Tel: 44 (0) 772 5636914 > www.wright-dose.com > > -----Original Message----- > *From:* [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] > *On Behalf Of [EMAIL PROTECTED] > *Sent:* 05 October 2007 17:32 > *To:* James G Wright > *Cc:* [email protected] > *Subject:* 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 <[EMAIL PROTECTED]> 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:[EMAIL PROTECTED] > > Sent: 05 October 2007 13:33 > > To: James G Wright > > Cc: [email protected] > > 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:* [EMAIL PROTECTED] > > > [mailto:[EMAIL PROTECTED] *On Behalf Of > > > [EMAIL PROTECTED] > > > *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 > > > > > > [EMAIL PROTECTED] <mailto:[EMAIL PROTECTED]> > > > > > > > > > > > > > > > > > > On 10/4/07, *navin goyal* <[EMAIL PROTECTED] > > > <mailto:[EMAIL PROTECTED]>> 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 > > > > > > > > > > >