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RE: Very small P-Value for ETABAR

From: Ribbing, Jakob <Jakob.Ribbing>
Date: Thu, 13 Nov 2008 23:27:55 -0000

Dear all,

First of all, I am not sure that there is any assumption of etas having
a normal distribution when estimating a parametric model in NONMEM. The
variance of eta (OMEGA) does not carry an assumption of normality. I
believe that Stuart used to say the assumption of normality is only when
simulating. I guess the assumption also affects EBE:s unless the
individual information is completely dominating? If the assumption of
normality is wrong, the weighting of information may not be optimal, but
as long as the true distribution is symmetric the estimated parameters
are in principle correct (but again, the model may not be suitable for
simulation if the distributional assumption was wrong). I will be off
line for a few days, but I am sure somebody will correct me if I am
wrong about this.

If etas are shrunk, you can not expect a normal distribution of that
(EBE) eta. That does not invalidate parameterization/distributional
assumptions. Trying other semi-parametric distributions or a
non-parametric distribution (or a mixture model) may give more
confidence in sticking with the original parameterization or else reject
it as inadequate. In the end, you may feel confident about the model
even if the EBE eta distribution is asymmetric and biased (I mentioned
two examples in my earlier posting).

Connecting to how PsN may help in this case: http://psn.sourceforge.net/
In practice to evaluate shrinkage, you would simply give the command
(assuming the model file is called run1.mod):
execute --shrinkage run1.mod

Another quick evaluation that can be made with this program is to
produce mirror plots (PsN links in nicely with Xpose for producing the
diagnostic plots):

execute --mirror=3 run1.mod

This will give you three simulation table files that have been derived
by simulating under the model and then fitting the simulated data using
the same model (using the design of the original data). If you see a
similar pattern in the mirror plots as in the original diagnostic plots,
this gives you more confidence in the model. That brings us back to
Leonids point about it being more useful to look at diagnostic plots
than eta bar.

Wishing you a great weekend!

Jakob

-----Original Message-----
From: BAE, KYUN-SEOP
Sent: 13 November 2008 22:05
To: Ribbing, Jakob; XIA LI; nmusers
Subject: RE: [NMusers] Very small P-Value for ETABAR

Dear All,

Realized etas (EBEs, MAPs) is estimated under the assumption of normal
distribution.
However, the resultant distribution of EBEs may not be normal or mean of
them may not be 0.
To pass t-test, one may use "CENTERING" option at $ESTIMATION.
But, this practice is discouraged by some (and I agree).

Normal assumption cannot coerce the distribution of EBE to be normal,
and furthermore non-normal (and/or not-zero-mean) distribution of EBE
can be nature's nature.
One simple example is mixture population with polymorphism.

If I could not get normal(?) EBEs even after careful examination of
covariate relationships as others suggested,
I would bear it and assume nonparametric distribution.

Regards,

Kyun-Seop
=====================
Kyun-Seop Bae MD PhD
Email: kyun-seop.bae

-----Original Message-----
From: owner-nmusers
On Behalf Of Ribbing, Jakob
Sent: Thursday, November 13, 2008 13:19
To: XIA LI; nmusers
Subject: RE: [NMusers] Very small P-Value for ETABAR

Hi Xia,

Just to clarify one thing (I agree with almost everything you said):

The p-value indeed is related to the test of ETABAR=0. However, this =
is
not a test of normality, only a test that may reject the mean of the
etas being zero (H0). Therefore, shrinkage per se does not lead to
rejection of HO, as long as both tails of the eta distribution are
shrunk to a similar degree.

I agree with the assumption of normality. This comes into play when you
simulate from the model and if you got the distribution of individual
parameters wrong, simulations may not reflect even the data used to fit
the model.

Best Regards

Jakob

-----Original Message-----
From: owner-nmusers
On Behalf Of XIA LI
Sent: 13 November 2008 20:31
To: nmusers
Subject: Re: [NMusers] Very small P-Value for ETABAR

Dear All,

Just some quick statistical points...

P value is usually associated with hypothesis test. As far as I know,
NONMEM assume normal distribution for ETA, ETA~N(0,omega), which means
the null hypothesis to test is H0: ETABAR=0. A small P value indicates =
a
significant test. You reject the null hypothesis.
 
More...
As we all know, ETA is used to capture the variation among individual
parameters and model's unexplained error. We usually use the function
(or model) parameter=typical value*exp (ETA), which leads to a =
lognormal
distribution assumption for all fixed effect parameters (i.e., CL, V,
Ka, Ke...).

By some statistical theory, the variation of individual parameter equals
a function of the typical value and the variance of ETA.

VAR (CL) = typical value*exp (omega/2). NO MATH PLS!!

If your typical value captures all overall patterns among patients
clearance, then ETA will have a nice symmetric normal distribution with
small variance. Otherwise, you leave too many patterns to ETA and will
see some deviation or shrinkage (whatever you call).

Why adding covariates is a good way to deal with this situation? You
model become CL=typical value*exp (covariate)*exp (ETA). The variation
of individual parameter will be changed to:

VAR (CL) = (typical value + covariate)*exp (omega/2)).

You have one more item to capture the overall patterns, less leave to
ETA. So a 'good' covariate will reduce both the magnitude of omega and
ETA's deviation from normal.

Understanding this is also useful when you are modeling BOV studies.
When you see variation of PK parameters decrease with time (or
occasions). Adding a covariate that make physiological sense and also
decrease with time may help your modeling.

Best,
Xia
==========================
=============
Xia Li
Mathematical Science Department
University of Cincinnati
Received on Thu Nov 13 2008 - 18:27:55 EST

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