Standardized maximim D-optimal designs for enzyme kineticinhibition models

Locally optimal designs for nonlinear models require a single set of nominal values for the unknown parameters.An alternative is the maximin approach that allows the user to specify a range of values for each parameter ofinterest. However, the maximin approach is difficult because we first have to determine the locally optimal designfor each set of nominal values before maximin types of optimal designs can be found via a nested optimizationprocess. We show that particle swarm optimization (PSO) techniques can solve such complex optimizationproblems effectively. We demonstrate numerical results from PSO can help find, for the first time, formulae forstandardized maximin D-optimal designs for nonlinear model with 3 or 4 parameters on the compact andnonnegative design space. Additionally, we show locally and standardized maximin D-optimal designs for inhibitionmodels are not necessarily supported at a minimum number of points. To facilitate use of such designs, wecreate a web-based tool for practitioners to find tailor-made locally and standardized maximin optimal designs

d-QPSO: A Quantum-Behaved Particle Swarm Technique for Finding D-Optimal Designs With Discrete and Continuous Factors and a Binary Response

Identifying optimal designs for generalized linear models with a binary response can be a challengingtask, especially when there are both discrete and continuous independent factors in the model. Theoreticalresults rarely exist for such models, and for the handful that do, they usually come with restrictive assumptions.In this article, we propose the d-QPSO algorithm, a modified version of quantum-behaved particleswarm optimization, to find a variety of D-optimal approximate and exact designs for experiments withdiscrete and continuous factors and a binary response. We show that the d-QPSO algorithm can efficientlyfind locally D-optimal designs even for experiments with a large number of factors and robust pseudo-Bayesian designs when nominal values for the model parameters are not available. Additionally, we investigaterobustness properties of the d-QPSO algorithm-generated designs to variousmodel assumptions andprovide real applications to design a bio-plastics odor removal experiment, an electronic static experiment,and a 10-factor car refueling experiment. Supplementary materials for the article are available online

A comparison of general-purpose optimization algorithms forfinding optimal approximate experimental designs

Several common general purpose optimization algorithms are compared for findingA- and D-optimal designs for different types of statistical models of varying complexity,including high dimensional models with five and more factors. The algorithms of interestinclude exact methods, such as the interior point method, the Nelder–Mead method, theactive set method, the sequential quadratic programming, and metaheuristic algorithms,such as particle swarm optimization, simulated annealing and genetic algorithms.Several simulations are performed, which provide general recommendations on theutility and performance of each method, including hybridized versions of metaheuristicalgorithms for finding optimal experimental designs. A key result is that general-purposeoptimization algorithms, both exact methods and metaheuristic algorithms, perform wellfor finding optimal approximate experimental designs

Extended two-stage adaptive designswith three target responses forphase II clinical trials

We develop a nature-inspired stochastic population-based algorithm and call it discrete particle swarm optimization tofind extended two-stage adaptive optimal designs that allow three target response rates for the drug in a phase II trial.Our proposed designs include the celebrated Simon’s two-stage design and its extension that allows two target responserates to be specified for the drug. We show that discrete particle swarm optimization not only frequently outperformsgreedy algorithms, which are currently used to find such designs when there are only a few parameters; it is also capableof solving design problems posed here with more parameters that greedy algorithms cannot solve. In stage 1 of ourproposed designs, futility is quickly assessed and if there are sufficient responders to move to stage 2, one tests one ofthe three target response rates of the drug, subject to various user-specified testing error rates. Our designs aretherefore more flexible and interestingly, do not necessarily require larger expected sample size requirements thantwo-stage adaptive designs. Using a real adaptive trial for melanoma patients, we show our proposed design requires onehalf fewer subjects than the implemented design in the study

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

Digital Filter Design Using Improved Teaching-Learning-Based Optimization

Digital filters are an important part of digital signal processing systems. Digital filters are divided into finite impulse response (FIR) digital filters and infinite impulse response (IIR) digital filters according to the length of their impulse responses. An FIR digital filter is easier to implement than an IIR digital filter because of its linear phase and stability properties. In terms of the stability of an IIR digital filter, the poles generated in the denominator are subject to stability constraints. In addition, a digital filter can be categorized as one-dimensional or multi-dimensional digital filters according to the dimensions of the signal to be processed. However, for the design of IIR digital filters, traditional design methods have the disadvantages of easy to fall into a local optimum and slow convergence. The Teaching-Learning-Based optimization (TLBO) algorithm has been proven beneficial in a wide range of engineering applications. To this end, this dissertation focusses on using TLBO and its improved algorithms to design five types of digital filters, which include linear phase FIR digital filters, multiobjective general FIR digital filters, multiobjective IIR digital filters, two-dimensional (2-D) linear phase FIR digital filters, and 2-D nonlinear phase FIR digital filters. Among them, linear phase FIR digital filters, 2-D linear phase FIR digital filters, and 2-D nonlinear phase FIR digital filters use single-objective type of TLBO algorithms to optimize; multiobjective general FIR digital filters use multiobjective non-dominated TLBO (MOTLBO) algorithm to optimize; and multiobjective IIR digital filters use MOTLBO with Euclidean distance to optimize. The design results of the five types of filter designs are compared to those obtained by other state-of-the-art design methods. In this dissertation, two major improvements are proposed to enhance the performance of the standard TLBO algorithm. The first improvement is to apply a gradient-based learning to replace the TLBO learner phase to reduce approximation error(s) and CPU time without sacrificing design accuracy for linear phase FIR digital filter design. The second improvement is to incorporate Manhattan distance to simplify the procedure of the multiobjective non-dominated TLBO (MOTLBO) algorithm for general FIR digital filter design. The design results obtained by the two improvements have demonstrated their efficiency and effectiveness

Statistical Algorithms for Optimal Experimental Design with Correlated Observations

This research is in three parts with different although related objectives. The first part developed an efficient, modified simulated annealing algorithm to solve the D-optimal (determinant maximization) design problem for 2-way polynomial regression with correlated observations. Much of the previous work in D-optimal design for regression models with correlated errors focused on polynomial models with a single predictor variable, in large part because of the intractability of an analytic solution. In this research, we present an improved simulated annealing algorithm, providing practical approaches to specifications of the annealing cooling parameters, thresholds and search neighborhoods for the perturbation scheme, which finds approximate D-optimal designs for 2-way polynomial regression for a variety of specific correlation structures with a given correlation coefficient. Results in each correlated-errors case are compared with the best design selected from the class of designs that are known to be D-optimal in the uncorrelated case: annealing results had generally higher D-efficiency than the best comparison design, especially when the correlation parameter was well away from 0. The second research objective, using Balanced Incomplete Block Designs (BIBDs), wasto construct weakly universal optimal block designs for the nearest neighbor correlation structure and multiple block sizes, for the hub correlation structure with any block size, and for circulant correlation with odd block size. We also constructed approximately weakly universal optimal block designs for the block-structured correlation. Lastly, we developed an improved Particle Swarm Optimization(PSO) algorithm with time varying parameters, and solved D-optimal design for linear regression with it. Then based on that improved algorithm, we combined the non-linear regression problem and decision making, and developed a nested PSO algorithm that finds (nearly) optimal experimental designs with each of the pessimistic criterion, index of optimism criterion, and regret criterion for the Michaelis-Menten model and logistic regression model

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

Nonlinear regression models addressing both efficacy and toxicity outcomes are increasingly used in dose-finding trials, such as in pharmaceutical drug development. However, research on related experimental design problems for corresponding active controlled trials is still scarce. In this paper we derive optimal designs to estimate efficacy and toxicity in an active controlled clinical dose finding trial when the bivariate continuous outcomes are modeled either by polynomials up to degree 2, the Michaelis- Menten model, the Emax model, or a combination thereof. We determine upper bounds on the number of different doses levels required for the optimal design and provide conditions under which the boundary points of the design space are included in the optimal design. We also provide an analytical description of the minimally supported $D$-optimal designs and show that they do not depend on the correlation between the bivariate outcomes. We illustrate the proposed methods with numerical examples and demonstrate the advantages of the $D$-optimal design for a trial, which has recently been considered in the literature.Comment: Keywords and Phrases: Active controlled trials, dose finding, optimal design, admissible design, Emax model, Equivalence theorem, Particle swarm optimization, Tchebycheff syste