RE: Error model

-----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/99apr232002.html http://www.cognigencorp.com/nonmem/nm/98jun022003.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]> > [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]> <mailto:[EMAIL PROTECTED]> > > > > > > On 10/4/07, *navin goyal* <[EMAIL PROTECTED] <mailto:[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 > >