Optimal designs for nonlinear regression models without prior point parameter estimates

Abstract

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 〖VaR〗_(5%) , 〖CVaR〗_(1%), 〖MeanToVaR〗_(10%). 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.