Evaluating Standards for Protecting Aquatic Life in Washington ' s Surface Water Quality Standards Temperature Criteria Draft Discussion Paper and Literature Summary
This paper is admirable in that it presents a general framework that allows the user to focus on the pharmacokinetic modeling rather than on the computational and statistical details of estimation. The authors set up a reasonable-seeming model and obtain a good t to the pain-relief data with plausible parameter values, while accounting for the kind of complications that typically arise in clinical trials. We would like to focus on the following features of this work: (1) analysis of the missing data (dropouts), (2) the pharmacokinetic model, (3) checking the t of the model, (4) modeling and display of individual variation, and (5) extrapolation to other dosing strategies. Analysis of the dropouts Although the analysis of dropouts appears to be a major complication in the analysis (and is certainly a problem of general interest in this eld; see, e.g., Ten Have et al., 1997), it is, we believe, a minor concern in this particular example. As noted in the article, the pain relief level just preceding dropout was 0 (no pain relief) in nearly all the cases. Considering the design of the study (with dropouts allowed to switch to an eeective analgesic), it seems reasonable to impute pain relief scores of 0 for the responses that were unobserved because of dropout. Our Figure 1 shows the aggregate results for the completed dataset (including both observed and imputed responses). In addition to the imputation, we have altered Figure 1 of the article by separating the \dose = 0" respondents into three groups corresponding to the three diierent experiments. We believe that our Figure 1, with imputations included, gives We thank the National Science Foundation for grant DMS-9404305 and Young Investigator award DMS-9457824; the Research Council of Katholieke Universiteit Leuven for fellowship F/96/9; and Lewis Sheiner for providing the data and model predictions for the ketorolac analysis.