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: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of XIA LI Sent: 13 November 2008 20:31 To: nmusers@globomaxnm.com 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
