Designs for generalized linear models with random block effects via information matrix approximations

The selection of optimal designs for generalized linear mixed models is complicated by the fact that the Fisher information matrix, on which most optimality criteria depend, is computationally expensive to evaluate. Our focus is on the design of experiments for likelihood estimation of parameters in the conditional model. We provide two novel approximations that substantially reduce the computational cost of evaluating the information matrix by complete enumeration of response outcomes, or Monte Carlo approximations thereof: (i) an asymptotic approximation which is accurate when there is strong dependence between observations in the same block; (ii) an approximation via Kriging interpolators. For logistic random intercept models, we show how interpolation can be especially effective for finding pseudo-Bayesian designs that incorporate uncertainty in the values of the model parameters. The new results are used to provide the first evaluation of the efficiency, for estimating conditional models, of optimal designs from closed-form approximations to the information matrix derived from marginal models. It is found that correcting for the marginal attenuation of parameters in binary-response models yields much improved designs, typically with very high efficiencies. However, in some experiments exhibiting strong dependence, designs for marginal models may still be inefficient for conditional modelling. Our asymptotic results provide some theoretical insights into why such inefficiencies occur

A Metaheuristic Adaptive Cubature Based Algorithm to Find Bayesian Optimal Designs for Nonlinear Models

Finding Bayesian optimal designs for nonlinear models is a difficult task because the optimality criteriontypically requires us to evaluate complex integrals before we perform a constrained optimization. Wepropose a hybridized method where we combine an adaptive multidimensional integration algorithm anda metaheuristic algorithm called imperialist competitive algorithm to find Bayesian optimal designs. Weapply our numerical method to a few challenging design problems to demonstrate its efficiency. Theyinclude finding D-optimal designs for an item response model commonly used in education, Bayesianoptimal designs for survivalmodels, and Bayesian optimal designs for a four-parameter sigmoid Emax doseresponse model. Supplementary materials for this article are available online and they contain an R packagefor implementing the proposed algorithm and codes for reproducing all the results in this paper

JMASM45: A Computer Program for Bayesian D-Optimal Binary Repeated Measurements Designs (Matlab)

Planners of longitudinal studies of binary responses in applied sciences have not yet benefitted from optimal designs, which have been shown to improve precision of model parameter estimates, due to absence of a computer program. An interactive computer program for Bayesian optimal binary repeated measurements designs is presented for this purpose

Optimal Study Designs for Cluster Randomised Trials: An Overview of Methods and Results

There are multiple cluster randomised trial designs that vary in when the clusters cross between control and intervention states, when observations are made within clusters, and how many observations are made at that time point. Identifying the most efficient study design is complex though, owing to the correlation between observations within clusters and over time. In this article, we present a review of statistical and computational methods for identifying optimal cluster randomised trial designs. We also adapt methods from the experimental design literature for experimental designs with correlated observations to the cluster trial context. We identify three broad classes of methods: using exact formulae for the treatment effect estimator variance for specific models to derive algorithms or weights for cluster sequences; generalised methods for estimating weights for experimental units; and, combinatorial optimisation algorithms to select an optimal subset of experimental units. We also discuss methods for rounding weights to whole numbers of clusters and extensions to non-Gaussian models. We present results from multiple cluster trial examples that compare the different methods, including problems involving determining optimal allocation of clusters across a set of cluster sequences, and selecting the optimal number of single observations to make in each cluster-period for both Gaussian and non-Gaussian models, and including exchangeable and exponential decay covariance structures

acebayes: An R Package for Bayesian Optimal Design of Experiments via Approximate Coordinate Exchange

We describe the R package acebayes and demonstrate its use to find Bayesian optimal experimental designs. A decision-theoretic approach is adopted, with the optimal design maximizing an expected utility. Finding Bayesian optimal designs for realistic problems is challenging, as the expected utility is typically intractable and the design space may be high-dimensional. The package implements the approximate coordinate exchange algorithm to optimize (an approximation to) the expected utility via a sequence of conditional one-dimensional optimization steps. At each step, a Gaussian process regression model is used to approximate, and subsequently optimize, the expected utility as the function of a single design coordinate (the value taken by one controllable variable for one run of the experiment). In addition to functions for bespoke design problems with user-defined utility functions, acebayes provides functions tailored to finding designs for common generalized linear and nonlinear models. The package provides a step-change in the complexity of problems that can be addressed, enabling designs to be found for much larger numbers of variables and runs than previously possible. We provide tutorials on the application of the methodology for four illustrative examples of varying complexity where designs are found for the goals of parameter estimation, model selection and prediction. These examples demonstrate previously unseen functionality of acebayes

FULLY EXPONENTIAL LAPLACE APPROXIMATION EM ALGORITHM FOR NONLINEAR MIXED EFFECTS MODELS

Nonlinear mixed effects models provide a flexible and powerful platform for the analysis of clustered data that arise in numerous fields, such as pharmacology, biology, agriculture, forestry, and economics. This dissertation focuses on fitting parametric nonlinear mixed effects models with single- and multi-level random effects. A new, efficient, and accurate method that gives an error of order O(1/n2), fully exponential Laplace approximation EM algorithm (FELA-EM), for obtaining restricted maximum likelihood (REML) estimates in nonlinear mixed effects models is developed. Sample codes for implementing FELA-EM algorithm in R are given. Simulation studies have been conducted to evaluate the accuracy of the new approach and compare it with the Laplace approximation as well as four different linearization methods for fitting nonlinear mixed effects models with single-level and two-crossed-level random effects. Of all approximations considered in the thesis, FELA-EM algorithm is the only one that gives unbiased or close-to-unbiased (%Bias \u3c 1%) estimates for both the fixed effects and variance-covariance parameters. Finally, FELA-EM algorithm is applied to a real dataset to model feeding pigs’ body temperature and a unified strategy for building crossed and nested nonlinear mixed effects models with treatments and covariates is provided

Generalised Linear Mixed Model Specification, Analysis, Fitting, and Optimal Design in R with the glmmr Packages

We describe the \proglang{R} package \pkg{glmmrBase} and an extension \pkg{glmmrOptim}. \pkg{glmmrBase} provides a flexible approach to specifying, fitting, and analysing generalised linear mixed models. We use an object-orientated class system within \proglang{R} to provide methods for a wide range of covariance and mean functions, including specification of non-linear functions of data and parameters, relevant to multiple applications including cluster randomised trials, cohort studies, spatial and spatio-temporal modelling, and split-plot designs. The class generates relevant matrices and statistics and a wide range of methods including full likelihood estimation of generalised linear mixed models using Markov Chain Monte Carlo Maximum Likelihood, Laplace approximation, power calculation, and access to relevant calculations. The class also includes Hamiltonian Monte Carlo simulation of random effects, sparse matrix methods, and other functionality to support efficient estimation. The \pkg{glmmrOptim} package implements a set of algorithms to identify c-optimal experimental designs where observations are correlated and can be specified using the generalised linear mixed model classes. Several examples and comparisons to existing packages are provided to illustrate use of the packages