Optimal Designs for Nonlinear Regression Models without Prior Point Parameter Estimates.

摘要

The theory of the optimal design of experiments provides a framework for generating designs that optimize a function of the variance-covariance matrix (or information matrix) of the parameter estimates. If the functional form of the statistical model to be fitted is nonlinear in the parameters, then prior guesses of unknown parameters are necessary to develop optimal designs. Better designs can be achieved if the prior guess is more precise. Our research is focused on developing optimal designs for nonlinear regression models without requiring prior point guesses.;Our methodology proposes a new class of optimality criteria that share characteristics with Maxi-min designs based on efficiency measures (Dette et al., 2006; Kitsos, 2013, p. 34; Muller and Pazman, 1998; Silvey, 1980) and Pseudo-Bayesian designs (Atkinson et al., 2007, chap. 18; Chaloner and Verdinelli, 1995). Namely, we use Monte Carlo sampling to incorporate prior information of parameters (uniform distribution used if only the range is available) and for the objective function, we employ a relative efficiency measure. However, there are two key differences. Firstly, our criterion metric is based on a Value-at-Risk (VaR) metric such as VaR5% , CVaR1%, MeanToVaR10%. Secondly, rather than picking the design having the best VaR objective function value (a scalar measure), we recommend evaluating the quality of competing VaR based designs across the entire relative efficiency distribution. We have empirically demonstrated consistency in the results by applying VaR methodology across three response models used in clinical, biological and engineering contexts. We believe that in light of the parameter uncertainty and the consequent nonlinear nature of the relative efficiency distribution for sampled parameter values, the VaR methodology will lead to more informed choices by the experimenter on the right design for a particular context.