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

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

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

Construction and analysis of experimental designs

This thesis seeks to put into focus the analysis of experimental designs and their construction. It concentrates on the construction of fractional factorial designs (FFDs) using various aspects and applications. These dierent experimental designs and their applications, including how they are constructed with respect to the situation under consideration, are of interest in this study. While there is a wide range of experimental designs and numerous dierent constructions, this thesis focuses on FFDs and their applications. Experimental design is a test or a series of tests in which purposeful changes are made to the input variables of a process or system so that we may observe and identify the reasons for changes that may be noted in the output response (Montgomery (2014)). Experimental designs are important because their design and analysis can in uence the outcome and response of the intended action. In this research, analysing experimental designs and their construction intends to reveal how important they are in research experiments. Chapter 1 introduces the concept of experimental designs and their principal and oers a general explanation for factorial experiment design and FFDs. Attention is then given to the general construction and analysis of FFDs, including one-half and one-quarter fractions, Hadamard matrices (H), Balanced Incomplete Block Design (BIBD), Plackett-Burman (PB) designs and regression modelling. Chapter 2 presents an overview of the screening experiments and the literature review regarding the project. Chapter 3 introduces the rst part of the project, which is construction and analysis of edge designs from skew-symmetric supplementary dierence sets (SDSs). Edge designs were introduced by Elster and Neumaier (1995) using conference matrices and were proved to be robust. One disadvantage is that the known edge designs in the literature can be constructed when a conference matrix exists. In this chapter, we introduce a new class of edge designs- these are constructed from skew-symmetric SDSs. These designs are particularly useful, since they can be applied in experiments with an even number of factors, and they may exist for orders where conference matrices do not exist. The same model robustness is archived, as with traditional edge designs. We give details of the methodology used and provide some illustrative examples of this new approach. We also show that the new designs have good D-eciencies when applied to rst-order models, then complete the experiment with interaction in the second stage. We also show the application of models for new constructions. Chapter 4 presents the second part of the project, which is construction and analysis two-level supersaturated designs (SSDs) from Toeplitz matrices. The aim of the screening experiments was to identify the active factors from a large quantity of factors that may in uence the response y. SSDs represent an important class of screening experiments, whereby many factors are investigated using only few experimental runs; this process costs less than classical factorial designs. In this chapter, we introduce new SSDs that are constructed from Toeplitz matrices. This construction uses Toeplitz and permutation matrices of order n to obtain E(s2)- optimal two-level SSDs. We also study the properties of the constructed designs and use certain established criteria to evaluate these designs. We then give some detailed examples regarding this approach, and consider the performance of these designs with respect to dierent data analysis methods. Chapter 5 introduces the third part of the project, which is examples and comparison of the constructed design using real data in mathematics. Mathematics has strong application in dierent elds of human life. The Trends in International Mathematics and Science Study(TIMSS) is one of the worlds most eective global assessments of student achievement in both mathematics and science. The research in this thesis sought to determine the most eective factors that aect student achievement in mathematics. Four identied factors aect this problem. The rst is student factors: age, health, number of students in a class, family circumstances, time of study, desire, behaviour, achievements, media (audio and visual), rewards, friends, parents' goals and gender. The second is classroom environment factors: suitable and attractive and equipped with educational tools. The third is curriculum factors: easy or dicult. The fourth is the teacher: wellquali ed or not, and punishment. In this chapter, we detailed the methodology and present some examples, and comparisons of the constructed designs using real data in mathematics . The data comes from surveys contacted in schools in Saudi Arabia. The data are collected by the middle stage schools in the country and are available to Saudi Arabian citizen. Two main methods to collect real data were used: 1/ the mathematics scores for students' nal exams were collected from the schools; 2/ student questionnaires were conducted by disseminating 16-question questionnaires to students. The target population was 2,585 students in 22 schools. Data were subjected to regression analyses and the edge design method, with the nding that the main causes of low achievement were rewards, behaviour, class environment, educational tools and health. Chapter 6 surveys the work of this thesis and recommends further avenues of research

Air Force Institute of Technology Research Report 2007

This report summarizes the research activities of the Air Force Institute of Technology’s Graduate School of Engineering and Management. It describes research interests and faculty expertise; lists student theses/dissertations; identifies research sponsors and contributions; and outlines the procedures for contacting the school. Included in the report are: faculty publications, conference presentations, consultations, and funded research projects. Research was conducted in the areas of Aeronautical and Astronautical Engineering, Electrical Engineering and Electro-Optics, Computer Engineering and Computer Science, Systems and Engineering Management, Operational Sciences, Mathematics, Statistics and Engineering Physics

SciTech News Volume 69, No. 4

Table of Contents: Columns and Reports From the Editor 5 SciTech News Call for Articles 5 Division News Science-Technology Division 6 Preliminary Results from SciTech Survey 15 Chemistry Division 18 Membership Survey Report 19 Appendix: Summary of DCHE 2015 Membership Survey Result 20 Engineering Division 42 Engineering Division Executive Board Election Results 44 Aerospace Section of the Engineering Division 45 Call for Nominations & Applications Engineering Division: First call - 2016 award nominations & applications 43 Reviews Sci-Tech Book News Reviews 46 Advertisements Annual Reviews 3 CRC Press