Robust designs for multivariate logistic regression

In this paper, the author investigates optimal designs for multivariate binary regression models used in many clinical experiments. As the computation of a joint likelihood for multiple binary outcomes is often tedious, the author proposes and explores a pseudo-likelihood approach for choosing an optimal design under minimal parametric assumptions. The proposed design is considered robust in the sense that it provides estimators that are almost as efficient as those obtained from D-optimal designs under correctly specified likelihood functions and it can provide more efficient estimators as compared to D-optimal designs under misspecified likelihood functions. The asymptotic relative efficiencies of the maximum pseudo-likelihood estimators with respect to the exact maximum likelihood estimators are investigated. Monte Carlo simulations are carried out to explore the finite-sample properties of the maximum pseudo-likelihood estimators obtained under the proposed design scheme. The method is also illustrated in an example using actual data from a clinical study. Copyright Sapienza Università di Roma 2013