Bayesian crossover designs for generalized linear models

Bayesian optimal stepped wedge design

Recently, there has been a growing interest in designing cluster trials using stepped wedge design (SWD). An SWD is a type of cluster-crossover design in which clusters of individuals are randomized unidirectional from a control to an intervention at certain time points. The intraclass correlation coefficient (ICC) that measures the dependency of subject within a cluster plays an important role in design and analysis of stepped wedge trials. In this paper, we discuss a Bayesian approach to address the dependency of SWD on the ICC and robust Bayesian SWDs are proposed. Bayesian design is shown to be more robust against the misspecification of the parameter values compared to the locally optimal design. Designs are obtained for the various choices of priors assigned to the ICC. A detailed sensitivity analysis is performed to assess the robustness of proposed optimal designs. The power superiority of Bayesian design against the commonly used balanced design is demonstrated numerically using hypothetical as well as real scenarios.

D-optimal designs of mean-covariance models for longitudinal data

Longitudinal data analysis has been very common in various fields. It is important in longitudinal studies to choose appropriate numbers of subjects and repeated measurements and allocation of time points as well. Therefore, existing studies proposed many criteria to select the optimal designs. However, most of them focused on the precision of the mean estimation based on some specific models and certain structures of the covariance matrix. In this paper, we focus on both the mean and the marginal covariance matrix. Based on the mean-covariance models, it is shown that the trick of symmetrization can generate better designs under a Bayesian D-optimality criterion over a given prior parameter space. Then, we propose a novel criterion to select the optimal designs. The goal of the proposed criterion is to make the estimates of both the mean vector and the covariance matrix more accurate, and the total cost is as low as possible. Further, we develop an algorithm to solve the corresponding optimization problem. Based on the algorithm, the criterion is illustrated by an application to a real dataset and some simulation studies. We show the superiority of the symmetric optimal design and the symmetrized optimal design in terms of the relative efficiency and parameter estimation. Moreover, we also demonstrate that the proposed criterion is more effective than the previous criteria, and it is suitable for both maximum likelihood estimation and restricted maximum likelihood estimation procedures.

Optimal allocation of subjects in a matched pair cluster-randomized trial with fixed number of heterogeneous clusters

In cluster-randomized trials, investigators randomize clusters of individuals such as households, medical practices, schools or classrooms despite the unit of interest are the individuals. It results in the loss of efficiency in terms of the estimation of the unknown parameters as well as the power of the test for testing the treatment effects. To recoup this efficiency loss, some studies pair similar clusters and randomize treatment within pairs. However, the clusters within a treatment arm might be heterogeneous in nature. In this article, we propose a locally optimal design that accounts the clusters heterogeneity and optimally allocates the subjects within each cluster. To address the dependency of design on the unknown parameters, we also discuss Bayesian optimal designs. Performances of proposed designs are investigated numerically through some data examples.