# RE: Very small P-Value for ETABAR

From: Ribbing, Jakob <Jakob.Ribbing>
Date: Thu, 13 Nov 2008 21:18:35 -0000

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