Comparison of designs for multivariate generalized linear models

Optimal design of stress levels in accelerated degradation testing for multivariate linear degradation models

In recent years, more attention has been paid prominently to accelerated degradation testing (ADT) in order to characterize accurate estimation of reliability properties for systems that are designed to work properly for years or even decades. In this paper, we propose optimal experimental designs for repeated measures ADTs with competing failure modes that correspond to multiple response components. The marginal degradation paths are expressed using linear mixed effects models. The optimal design is obtained by minimizing the asymptotic variance of the estimator of some quantile of the failure time distribution at the normal use conditions. Numerical examples are introduced to ensure the robustness of the proposed optimal designs and compare their efficiency with standard experimental designs.

Optimal Designs for Multi-Response Nonlinear Regression Models With Several Factors via Semidefinite Programming

We use semi-definite programming (SDP) to find a variety of optimal designs for multiresponse linear models with multiple factors, and for the first time, extend the methodology to find optimal designs for multi-response nonlinear models and generalized linear models with multiple factors. We construct transformations that (i) facilitate improved formulation of the optimal design problems into SDP problems, (ii) enable us to extend SDP methodology to find optimal designs from linear models to nonlinear multi-response models with multiple factors and (iii) correct erroneously reported optimal designs in the literature caused by formulation issues. We also derive invariance properties of optimal designs and their dependence on the covariance matrix of the correlated errors, which are helpful for reducing the computation time for finding optimal designs. Our applications include finding A-, A _s -, c- and D-optimal designs for multi-response multi-factor polynomial models, locally c- and D-optimal designs for a bivariate E _max response model and for a bivariate Probit model useful in the biosciences.

Optimal designs for active controlled dose-finding trials with efficacy-toxicity outcomes

We derive optimal designs to estimate efficacy and toxicity in active controlled dose-finding trials when the bivariate continuous outcomes are described using nonlinear regression models. We determine upper bounds on the required number of different doses and provide conditions under which the boundary points of the design space are included in the optimal design. We provide an analytical description of minimally supported optimal designs and show that they do not depend on the correlation between the bivariate outcomes.