Robust designs for generalized linear mixed models with possible model misspecification

We study robust designs for generalized linear mixed models (GLMMs) with protections against possible departures from underlying model assumptions. Among various types of model departures, an imprecision in the assumed linear predictor or the link function has a great impact on predicting the conditional mean response function in a GLMM. We develop methods for constructing adaptive sequential designs when the fitted mean response or the link function is possibly of an incorrect parametric form. We adopt the maximum likelihood method for estimating the parameters in GLMMs and investigate both I-optimal and D-optimal design criteria for the construction of robust sequential designs. To study the empirical properties of these sequential designs, we ran a series of simulations using both logistic and Poisson mixed models. As indicated in the simulation results, the I-optimal design generally outperforms the D-optimal design for all scenarios considered. Both designs are more efficient than the conventionally used uniform design and the classical D-optimal design obtained under the assumption that the fitted models are correctly specified. The proposed designs are also illustrated in an example using actual data from a dose-response experiment. (C) 2020 Elsevier B.V. All rights reserved.