Re: [NMusers] Error model

Hi James,
I am sorry, I missed it, indeed, it was a typo in the original e-mail.
It should be:

W=SQRT(THETA(n-1)**2+THETA(n)**2/F**2)

If really needed, defense against F=0 could be introduced

TY=F
IF(F.LT.0.001) TY=0.001
IPRED=LOG(TY)
W=SQRT(THETA(n-1)**2+THETA(n)**2/TY**2)
Y=IPRED+W*EPS(1)


$SIGMA
1 FIXED


In my experience, this is working better than the original scale + allow
to avoid problems in simulations when additive or combined error model
may result in negative concentrations

To avoid problems on the dosing records (where F could be = 0) one can
use CALLFL=0 in the error block. Note that in this case concentration at
the dosing records is not computed and simply equal to the value at the
preceding record.

To give proper credit: I learned this trick from Mats Karlsson (see below)

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

Best,
Leonid

Citation:
------------
Hi,

To get the same error structure for log-transformed data as the
additive+proportional on the normal scale, I use
Y=LOG(F)+SQRT(THETA(x)**2+THETA(y)**2/F**2)*EPS(1)
with
$SIGMA 1 FIX

THETA(x) and THETA(y) will have the same meaning as on the untransformed
scale
with

Y=F+SQRT(THETA(y)**2+THETA(x)**2*F**2)*EPS(1)
with
$SIGMA 1 FIX

As for zero predictions with lag-time models, you would have to
condition this
LOG(F)-variance model. Alternatively, compared to a lag-time model, I
have not
seen worse behaviour with a chain of transit compartments (all with the
same rate
constant) and often better (lower OFV, more stable). A chain of transit
compartments will not predict a zero concentration. The only drawback is
sometimes longer runtimes. I usually use 3-5 compartments in the chain.
If you
want really lag-time like behaviour (still without zero predictions),
you could
increase that further.

In general with log-transformation, I have found that run-times can be both
considerably longer and considerably shorter than without
transformation. I have
not seen a pattern that allows me to make a prediction which will
happen. Maybe
someone has an explanation.

Best regards,
Mats

Mats Karlsson, PhD
----------


James G Wright 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
>
>
Received on Fri Oct 05 2007 - 12:19:17 EDT