RE: 95% CI of parameter estimate

From: "Gibiansky, Leonid" <gibianskyl@globomax.com> Subject: RE: 95% CI of parameter estimate Date: Tue, 14 Nov 2000 08:31:30 -0500 My concern with Method 1 is that it does not use original data at all, except for the model building. If the model poorly describes the data, it still can have very small Method 1 parameter CI. This method may be good in simulations for study design, when one vary design and study how well the PK model is recovered from the simulated data. The other goal can be to understand how confident you can be in the model derived from the real data. I think that in this situation it is better to use CI approaches that use original data in some form. Otherwise, CI are conditional on the quality of the model: they may be relevant if the model is good, and can be misleading if the model does not reflect the data. As to the other methods, we just finished the work (joint work with Katya Gibiansky) where we compared 4 methods for CI. 1. NONMEM (FO, FOCE, FOCI with interaction) 2. Bootstrap (method 2 below) 3. Profiling (method 3 below) 4. Jackknife (compute partial estimates for data sub-sets, and use partial estimates to obtain parameter estimates and confidence intervals) These methods were compared on 3 real data sets, one was done with FO, the other with FOCE, the third one with FOCE with interaction estimation methods. NONMEM was remarkably successful: in most cases, parameter estimates and CI obtained via NONMEM were in good to perfect agreement with the CI given by other methods. With (3), FOCE or FOCE with interaction was needed to produce a 3.84 change in objective function for the CI (as Nick mentioned). We found only 2 or 3 parameters (out of 30+ parameters in three models) with non-symmetric CI where NONMEM CI differed from profiling, bootstrap or Jackknife. One was the correlation coefficient (off-diagonal term in the variance-covariance matrix). It was bounded from above by 1, but NONMEM CI upper bound was larger. The other was variance of the random effect, bounded by 0, with the NONMEM CI being below 0. Jackknife estimates and CI were biased on several occasions, but in those situations NONMEM results were more relevant and in agreement with bootstrap and profiling. Overall conclusion FROM THE EXAMPLES THAT WE STUDIED was that it was sufficient to use NONMEM CI. More CPU-intensive methods just confirmed NONMEM findings. Regards Leonid