Re: 95% CI of paramter estimate

From: Nick Holford <n.holford@auckland.ac.nz> Subject: Re: 95% CI of paramter estimate Date: Tue, 14 Nov 2000 12:05:03 +1300 Joern, I think there are 4 methods for creating 95% confidence intervals on parameter estimates. 1. Simulate say 1000+ sets of data using your model and a design similar to your original data. Determine empirically the range of parameter estimates that cover 95% of the values you get from these 1000+ runs. This is the gold standard method. 2. Bootstrap 1000+ data sets from your original data and fit these with your model. Determine CI as in method 1. This method is conditional on your original data and its properties in relation to method 1 when used with NONMEM are not described in the literature as far as I know. 3. Compute a log likelihood profile for each parameter you are interested in. You do this by fixing the parameter of interest to values close to the final estimate from your model and refitting your original data. Empirically determine (e.g. by interpolation) the parameter values on either side of the final estimate that produce a 3.84 change in objective function. This relies on the assumption that the chi-square distribution is an appropriate way to describe the change in objective function. Might be OK for FOCE but almost certainly not for FO. 4. Use the asymptotic standard errors reported by NONMEM (if the covariance step runs). The CI obtained in this way will necessarily be symmetrical. CIs determined using the other methods above are often asymmetrical. You may be lucky and the asymptotic SEs may agree with the more reliable computationally intensive methods. -- Nick Holford, Divn Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand email:n.holford@auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556 http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm