RE: 95% CI of parameter estimate

From: "HUTMACHER, MATTHEW" <MATTHEW.HUTMACHER@chi.monsanto.com> Subject: RE: 95% CI of parameter estimate Date: Fri, 17 Nov 2000 12:12:07 -0600 Ken Kowalski and I call Method 1 for CI's (see Nick Holford's message below) the parametric bootstrap. This method requires the analyst to specify the probabilistic mechanisms by which all the data are generated. The parametric bootstrap is heavily assumption dependent, can provide the most knowledge from exhaustively looking at the data, and requires the greatest amount of modeling effort. Some issues that complicate this method are: i) does one parametrically model the covariates, ii) how does one handle censored data due to assay sensitivity, iii) how does one verify that the model (structural and stochastic) is adequate? The nonparametric bootstrap is appealing since the probabilistic mechanisms that generate the data (and covariates) manifest themselves within the observed data; i.e. re-sampling the actual data maintains the correlations and relationships in the observed data. Essentially, the nonparametric bootstrap puts less of a burden on the analyst with some expense, perhaps, in knowledge of the data compared to method 1. I would like also to comment on Mats' statement about misspecified models (I do not mean to take his statement too literally here). Model misspecification is not a black/white issue. Models are never specified correctly - do we ever feel that we have modeled the true OMEGA matrix? Some models are just more misspecified than others. In general, the greater number of key features the model adequately describes (structure, variability, etc.), the more confidence the analyst has in making inference using it. Even when a model is largely misspecifed, it may still be useful for specific purposes. Ken Kowalski and I have a paper (Statistics in Medicine - tentatively scheduled for the January 2001 issue) on this concept. We show that a 1-compartment model can approximate a 2-compartment model for the estimation of CL/F in a certain sparse-sampling setting (i.e., at steady-state sampling within the dosing interval). The paper deals with evaluating a design and powering the study to detect a pre-specified difference in CL/F in an arbitrary sub-population. We acknowledge that the fixed-effects estimates of ka and Vc/F will be biased (in our example, V/F from a 1-compartment model provides a relatively unbiased estimate of Vss/F of the 2-compartment model), but the estimates of CL/F and the difference parameter (delta CL/F) were unbiased (median bias <=5%). Using the "wrong" model does have a type I error implication, but it can be corrected by changing the difference in the likelihood needed for significance. Since, hypothesis testing and CI's are related, it seems that a reasonable confidence interval could be constructed on these parameters (CL/F and delta CL/F). , Verification of the coverage, if one were to use the nonparametric bootstrap for the CI's, would take considerable computing resources, however.