Optimal design of experiments with unknown parameters in variance.

摘要

In many areas of research, and particularly in biomedical research, investigators are faced with multiresponse models in which variation of the response is dependent upon unknown model parameters. This is a common issue, for example, in pharmacokinetics, bioassay, dose response, repeated measures, time series, and econometrics. The issue frequently is complicated by limitations in sample size (both the number of available experimental units, and the number of samples possible per unit) and/or cost.; Any reasonable experimental design provides the experimenter with conditions which enable the acquisition of information within an acceptable time or cost. The optimal design will describe the most information-rich choice of factor (controlled variable) settings for a given number of observations (or cost, or time). Convex design theory based on functions of the information matrix, implemented via numerical algorithms, provides the experimenter with optimal design settings. For simple linear models, in which the variance does not depend upon unknown parameters, the statistical theory for optimal design is relatively simple, and well studied. In cases where the variance function depends upon unknown parameters, the process of obtaining an optimal design increases in complexity. To date, neither commercial nor academically available optimal design software programs provide satisfactory methodologies for finding optimal designs for these types of models. Nor does the literature, to date, describe approaches to design optimization for general forms of these models. In this dissertation, we develop a unified approach which applies parameter estimation and convex design methods to obtain optimal designs for experiments with unknown parameters in the variance. We introduce models with cost constraints and study these designs within traditional experimental design paradigms. We include algorithms for finding optimal designs utilizing the described methodologies.; Application of the optimal design techniques are illustrated via examples from pharmacokinetic compartmental modelling, models for prostate specific antigen monitoring, and concentration-response models. For the general case of pharmacokinetic modelling, any combination of single or multiple dosing, loading dose, unequal dosing intervals, and any form of the parameter covariance matrix, can be optimized. This is unprecedented in the literature.