navin goyal wrote:
Hi Matt,
Maybe I dont understand the coding part completely.... however in the
suggested..
IPRED=F+M ; Individual prediction (regular scale)
IF(COMACT.EQ.1)COM(1)=IPRED
PPRED=COM(1) ; Population prediction (regular scale)
PRED=DV-PPRED
IPRED=DV-IPRED ?????? IPRED=IPRED??
Sorry, I mistyped the residuals:
PRED should have been PRES which is the population residuals on a normal
scale.
IRED should have been IRES which is the individual residuals on a normal
scale.
Unfortunately, since DV is log transformed this does not quite work
(sorry for not checking the residuals).
On a log scale, the population residuals, population weighted residuals,
and indivdual residuals can be calculated as with the following code.
M=THETA(x)
IPRED=F+M
IRES=DV-LOG(IPRED)
IF(COMACT.EQ.1)COM(1)=IPRED
PPRED=COM(1) ; Population Prediction (regular scale)
PRES=DV-LOG(PPRED)
PW=SQRT((PPRED-M)**2/(PPRED**2)+M**2/PPRED**2)
PWRES=PRES/PW
Y=LOG(IPRED)+F/IPRED*EPS(1)+M/IPRED*EPS(2)
Outside NONMEM, the Individual Weighted residuals can be calculated as:
w=sqrt(((IPRED-m)^2*vareps1+m.^2*vareps2)/(ipred^2));
iwres=ires/w;
I was wondering what is
PRED=DV-PPRED
IPRED=DV-IPRED
Also could you please elaborate on the code with regards to data
transformation. Does it mean that I use my untransformed data to run
the code ???
DV should be on a log scale.
Thanks again
Thanks to everyone for their replies
Navin
On 10/10/07, [EMAIL PROTECTED]
<mailto:[EMAIL PROTECTED]>* <
[EMAIL PROTECTED]
<mailto:[EMAIL PROTECTED]>> wrote:
Nidal,
Another method that would give slightly different results is by using
the EPS terms to code a model like (11) in Beals' paper
Using a first order taylors series expansion to the log equaivalant of
Beal's (11) we have:
Y= F*exp(eps(1)) + m*exp(eps(2))
log Y = log(f*exp(eps(1))+m*exp(eps(2))
Using a Taylor Series expansion this becomes
log Y = log(f+m) + f/(f+m)*eps(1) + m/(f+m)*eps(2)
Using an eps allows unique points to get different values (thetas
would
allow a population estimate of the variability).
Since the expectation of log Y is not F, the PRED is miscalculated by
NONMEM and should be calculated separately (as well as
RES). Therefore
a possibility for the error model discussed by Beal is:
$ABBREVIATED COMRES=1 COMSAV=1
...
$ERR
M=THETA(x)
IPRED=F+M ; Individual prediction (regular scale)
IF(COMACT.EQ.1)COM(1)=IPRED
PPRED=COM(1) ; Population prediction (regular scale)
PRED=DV-PPRED
IPRED=DV-IPRED
Y=LOG(IPRED)+F/IPRED*EPS(1)+M/IPRED*EPS(2)
IWRES can be calculated outsider or by using a ratio for EPS(1) and
EPS(2), setting it to be a theta and then multiplying by a unfixed
THETA.
This requires an assumptions that:
* EPS(1) is positive, EPS(2) is positive as well (this is
also true
the additive+proprotional case but is used often to
calculated IWRES.)
* One of the error terms is better described at a population level
For example
$ABBREVIATED COMRES=1 COMSAV=1
...
$ERR
M=THETA(x)
S=THETA(x+1)
IPRED=F+M ; Individual prediction (regular scale)
IF(COMACT.EQ.1)COM(1)=IPRED
PPRED=COM(1) ; Population prediction (regular scale)
PRED=DV-PPRED
IPRED=DV-IPRED
Y=LOG(IPRED)+F/IPRED*S+M/IPRED*S*EPS(2)
IWRES=IPRED-log(F+M)/(sqrt(F^2/((F+M)^2)+M^2S^2/((F+M)^2)))
S=sqrt(var(EPS(2))/var(EPS(1)))
Nidal gives another model that assumes that both the error terms are
explained at a population level and should be related to 11.
Matt Fidler (not that Mat refered to in Nidals' email I think its
Mats K.)
[EMAIL PROTECTED] <mailto:[EMAIL PROTECTED]> wrote:
> Hi James,
>
> We should divide by F (that is what happens when write an email
at 3
> AM). Anyway this error model was proposed by Mat and discussed
in Beal
> 's paper ( /Ways to Fit a PK Model with Some Data Below the
> Qunatification Limit/ J. Pharmacokin.Pharamcodyn. 28, p. 481-504.)
>
> So the code should be as in Eq. 11 (above paper)
> Y=LOG(F)+SQRT(THETA(n-1)**2+THETA(n)**2/F**2)*EPS(1)
> with
> $SIGMA 1 FIX
> Best,
> Nidal
>
>
> On 10/8/07, *James G Wright* < [EMAIL PROTECTED]
<mailto:[EMAIL PROTECTED]>
> <mailto:[EMAIL PROTECTED] <mailto:[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 <http://www.wright-dose.com>
<http://www.wright-dose.com/>
>
> -----Original Message-----
> *From:* [EMAIL PROTECTED]
<mailto:[EMAIL PROTECTED]>
> <mailto:[EMAIL PROTECTED]
<mailto:[EMAIL PROTECTED]>>
> [mailto:[EMAIL PROTECTED]
<mailto:[EMAIL PROTECTED]>
> <mailto:[EMAIL PROTECTED]
<mailto:[EMAIL PROTECTED]>>] *On Behalf Of *
> [EMAIL PROTECTED]
<mailto:[EMAIL PROTECTED]> <mailto:
[EMAIL PROTECTED] <mailto:[EMAIL PROTECTED]>>
> *Sent:* 05 October 2007 17:32
> *To:* James G Wright
> *Cc:* [email protected]
<mailto:[email protected]> <mailto:[email protected]
<mailto:[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>
> <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]
<mailto:[EMAIL PROTECTED]>
> <mailto:[EMAIL PROTECTED]
<mailto:[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 <http://www.wright-dose.com>
<http://www.wright-dose.com/>
>
>
> -----Original Message-----
> From: Leonid Gibiansky
[mailto:[EMAIL PROTECTED] <mailto:[EMAIL PROTECTED]>
> <mailto:[EMAIL PROTECTED]
<mailto:[EMAIL PROTECTED]>>]
> Sent: 05 October 2007 13:33
> To: James G Wright
> Cc: [email protected]
<mailto:[email protected]> <mailto: [email protected]
<mailto:[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
<http://www.quantpharm.com>
> <http://www.quantpharm.com/>
> e-mail: LGibiansky at quantpharm.com
<http://quantpharm.com> <http://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>
<http://www.wright-dose.com/ <http://www.wright-dose.com/>>
> <http://www.wright-dose.com/>
>>
>> -----Original Message-----
>> *From:* [EMAIL PROTECTED]
<mailto:[EMAIL PROTECTED]>
> <mailto:[EMAIL PROTECTED]
<mailto:[EMAIL PROTECTED]>>
>> [mailto: [EMAIL PROTECTED]
<mailto:[EMAIL PROTECTED]>
> <mailto:[EMAIL PROTECTED]
<mailto:[EMAIL PROTECTED]>>] *On Behalf Of
>> [EMAIL PROTECTED] <mailto:[EMAIL PROTECTED]>
> <mailto:[EMAIL PROTECTED]
<mailto:[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]
<mailto:[EMAIL PROTECTED]>><mailto:[EMAIL PROTECTED]
<mailto:[EMAIL PROTECTED]>
> <mailto: [EMAIL PROTECTED]
<mailto:[EMAIL PROTECTED]>>>
>>
>>
>>
>>
>>
>> On 10/4/07, *navin goyal* < [EMAIL PROTECTED]
<mailto:[EMAIL PROTECTED]>
> <mailto:[EMAIL PROTECTED]
<mailto:[EMAIL PROTECTED]>>
>> <mailto: [EMAIL PROTECTED] <mailto:[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
>>
>>
>
>
>
--
--Navin
