# Re: Very small P-Value for ETABAR

From: XIA LI <lix4>
Date: Thu, 13 Nov 2008 15:31:09 -0500 (EST)

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 - 15:31:09 EST

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