Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (p. 105-107).

To shorten the time for drug development and regulatory approval, a growing number of clinical trials are being conducted in multiple regions simultaneously. One of the challenges to multi-regional clinical trials (MRCT) is how to utilize the data obtained from other regions within the entire trial to help make local approval decisions. In addition to the global efficacy, the evidence of consistency in treatment effects between the local region and the entire trial is usually required for regional approval. In recent years, a number of statistical models and consistency criteria have been proposed. The sample size requirement for the region of interest was also studied. However, there is no specific regional requirement being broadly accepted; sample size planning considering regional requirement of all regions of interest is not well developed; how to apply the adaptive design to MRCT has not been studied. In this dissertation, we have made a number of contributions. First, we propose a unified regional requirement for the consistency assessment of MRCT, which generalizes the requirements proposed by Ko et al. (2010), Chen et al. (2012) and Tsong et al. (2012), make recommendations for choosing the value of parameters defining the proposed requirement, and determine the sample size increase needed to preserve power. Second, we propose two optimal designs for MRCT: minimal total sample size design and maximal utility design, which will provide more effective sample size allocation to ensure certain overall power and assurance probabilities of all interested regions. We also introduce the factors which should be considered in designing MRCT and analyze how each factor affects sample size planning. Third, we propose an unblinded region-level adaptive design to perform sample size re-estimation and re-allocation at interim based on the observed values of each region. We can determine not only whether to stop the whole MRCT based on the conditional power, but also whether to stop any individual region based on the conditional success rate at interim. The simulation results support that the proposed adaptive design has better performance than the classical design in terms of overall power and success rate of each region.

abstract: In this era of fast computational machines and new optimization algorithms, there have been great advances in Experimental Designs. We focus our research on design issues in generalized linear models (GLMs) and functional magnetic resonance imaging(fMRI). The first part of our research is on tackling the challenging problem of constructing exact designs for GLMs, that are robust against parameter, link and model uncertainties by improving an existing algorithm and providing a new one, based on using a continuous particle swarm optimization (PSO) and spectral clustering. The proposed algorithm is sufficiently versatile to accomodate most popular design selection criteria, and we concentrate on providing robust designs for GLMs, using the D and A optimality criterion. The second part of our research is on providing an algorithm that is a faster alternative to a recently proposed genetic algorithm (GA) to construct optimal designs for fMRI studies. Our algorithm is built upon a discrete version of the PSO. / Dissertation/Thesis / Doctoral Dissertation Statistics 2014

abstract: Mixture experiments are useful when the interest is in determining how changes in the proportion of an experimental component affects the response. This research focuses on the modeling and design of mixture experiments when the response is categorical namely, binary and ordinal. Data from mixture experiments is characterized by the perfect collinearity of the experimental components, resulting in model matrices that are singular and inestimable under likelihood estimation procedures. To alleviate problems with estimation, this research proposes the reparameterization of two nonlinear models for ordinal data -- the proportional-odds model with a logistic link and the stereotype model. A study involving subjective ordinal responses from a mixture experiment demonstrates that the stereotype model reveals useful information about the relationship between mixture components and the ordinality of the response, which the proportional-odds fails to detect. The second half of this research deals with the construction of exact D-optimal designs for binary and ordinal responses. For both types, the base models fall under the class of Generalized Linear Models (GLMs) with a logistic link. First, the properties of the exact D-optimal mixture designs for binary responses are investigated. It will be shown that standard mixture designs and designs proposed for normal-theory responses are poor surrogates for the true D-optimal designs. In contrast with the D-optimal designs for normal-theory responses which locate support points at the boundaries of the mixture region, exact D-optimal designs for GLMs tend to locate support points at regions of uncertainties. Alternate D-optimal designs for binary responses with high D-efficiencies are proposed by utilizing information about these regions. The Mixture Exchange Algorithm (MEA), a search heuristic tailored to the construction of efficient mixture designs with GLM-type responses, is proposed. MEA introduces a new and efficient updating formula that lessens the computational expense of calculating the D-criterion for multi-categorical response systems, such as ordinal response models. MEA computationally outperforms comparable search heuristics by several orders of magnitude. Further, its computational expense increases at a slower rate of growth with increasing problem size. Finally, local and robust D-optimal designs for ordinal-response mixture systems are constructed using MEA, investigated, and shown to have high D-efficiency performance. / Dissertation/Thesis / Doctoral Dissertation Industrial Engineering 2016

abstract: This dissertation explores different methodologies for combining two popular design paradigms in the field of computer experiments. Space-filling designs are commonly used in order to ensure that there is good coverage of the design space, but they may not result in good properties when it comes to model fitting. Optimal designs traditionally perform very well in terms of model fitting, particularly when a polynomial is intended, but can result in problematic replication in the case of insignificant factors. By bringing these two design types together, positive properties of each can be retained while mitigating potential weaknesses. Hybrid space-filling designs, generated as Latin hypercubes augmented with I-optimal points, are compared to designs of each contributing component. A second design type called a bridge design is also evaluated, which further integrates the disparate design types. Bridge designs are the result of a Latin hypercube undergoing coordinate exchange to reach constrained D-optimality, ensuring that there is zero replication of factors in any one-dimensional projection. Lastly, bridge designs were augmented with I-optimal points with two goals in mind. Augmentation with candidate points generated assuming the same underlying analysis model serves to reduce the prediction variance without greatly compromising the space-filling property of the design, while augmentation with candidate points generated assuming a different underlying analysis model can greatly reduce the impact of model misspecification during the design phase. Each of these composite designs are compared to pure space-filling and optimal designs. They typically out-perform pure space-filling designs in terms of prediction variance and alphabetic efficiency, while maintaining comparability with pure optimal designs at small sample size. This justifies them as excellent candidates for initial experimentation. / Dissertation/Thesis / Ph.D. Industrial Engineering 2013

When approaching a new research problem, we often use screening designs to determine which factors are worth exploring in more detail. Before exploring a problem, we don't know which factors are important. When examining a large number of factors, it is likely that only a handful are significant and that even fewer two-factor interactions will be significant. If there are important interactions, it is likely that they are connected with the handful of significant main effects. Since we don't know beforehand which factors are significant, we want to choose a design that gives us the highest probability a priori of being able to estimate all significant main effects with their associated two-factor interactions. This project examines the methodology of finding designs that do not rely on an assumed model. We propose a method of modifying the D-Optimality criteria that averages over models with a common set of main effects and varying subsets of two-factor interations. We also calculate the proportion of the subsets that produce estimable designs. We use these results to find the best models for given run size and number of main effects.

Impaired reproduction studies with Poisson responses are among a growing class of toxicity studies in the biological and medical realm. In recent years, little effort has been focused on the development of efficient experimental designs for impaired reproduction studies. This research concentrates on two areas: 1) the use of Bayesian techniques to make single regressor designs robust to parameter misspecification and 2) the extension of design optimality methods to the k-regressor model. The standard Poisson model with log link is used. Bayesian designs with priors on the parameters are explored using both the D and F-optimality criteria for the single regressor Poisson exponential model. Since these designs are found via numeric optimization techniques, Bayesian equivalence theory functions are derived to verify the optimality of these designs. Efficient Bayesian designs which provide for lack-of-fit testing are discussed. Characterizations of D, D_s, and interaction optimal designs which are factorial in nature are demonstrated for models involving interaction through k factors. The optimality of these designs is verified using equivalence theory. In addition, augmentations of these designs that result in desirable lack of fit properties are discussed. Also, a structure for fractional factorials is given in which specific points are added one at a time to the main effect design in order to gain estimability of the desired interactions. Robustness properties are addressed as well. Finally, this entire line of research is extended to industrial exponential models where different regressors work to increase and/or decrease a count data response produced by a process. / Ph. D.

No description available.

Researchers conduct life testing on objects of interest in an attempt to determine their life distribution as a means of studying their reliability (or survivability). Determining the life distribution of the objects under study helps manufacturers to identify potential faults, and to improve quality. Researchers sometimes conduct accelerated life tests (ALTs) to ensure that failure among the tested units is earlier than what could result under normal operating (or environmental) conditions. Moreover, such experiments allow the experimenters to examine the effects of high levels of one or more stress factors on the lifetimes of experimental units. Examples of stress factors include, but not limited to, cycling rate, dosage, humidity, load, pressure, temperature, vibration, voltage, etc. A special class of ALT is step-stress accelerated life testing. In this type of experiments, the study sample is tested at initial stresses for a given period of time. Afterwards, the levels of the stress factors are increased in agreement with prefixed points of time called stress-change times. In practice, time and resources are limited; thus, any experiment is expected to be constrained to a deadline which is called a termination time. Hence, the observed information may be subjected to Type-I censoring. This study discusses maximum likelihood inferential methods for the parameters of multiple step-stress models from a generalized Birnbaum-Saunders distribution under time constraint alongside other inference-related problems. A couple of general inference frameworks are studied; namely, the observed likelihood (OL) framework, and the expectation-maximization (EM) framework. The last-mentioned framework is considered since there is a possibility that Type-I censored data are obtained. In the first framework, the scoring algorithm is used to get the maximum likelihood estimators (MLEs) for the model parameters. In the second framework, EM-based algorithms are utilized to determine the required MLEs. Obtaining observed information matrices under both frameworks is also discussed. Accordingly, asymptotic and bootstrap-based interval estimators for the model parameters are derived. Model discrimination within the considered generalized Birnbaum-Saunders distribution is carried out by likelihood ratio test as well as by information-based criteria. The discussed step-stress models are illustrated by analyzing three real-life datasets. Accordingly, establishing optimal multiple step-stress test plans based on cost considerations and three optimality criteria is discussed. Since maximum likelihood estimators are obtained by numerical optimization that involves maximizing some objective functions, optimization methods used, and their software implementations in R are discussed. Because of the computational aspects are in focus in this study, the benefits of parallel computing in R, as a high-performance computational approach, are briefly addressed. Numerical examples and Monte Carlo simulations are used to illustrate and to evaluate the methods presented in this thesis. / Thesis / Doctor of Science (PhD)

在工業、農業、或醫藥界的實驗中，經常必須拿數個不同的試驗處理 (test treatments)和一個已使用過的對照處理(control treatment)比較 。所謂的試驗處理可能是數組新的儀器、不同配方的新藥、或不同成份的 肥料等。以實驗新藥為例，研藥者想決定是否能以新藥取代原來所使用的 藥，故對v種新藥與原藥做比較，評估其藥效之差異。為了降低實驗中不 必要的誤差以增加其準確性，集區設計成為實驗者常用的設計方法之一； 又因A式最適設計是我們欲估計的對照處理效果(effect)與試驗處理效果 之差異之估計值最小的設計，基於此良好的統計特性，我們選擇A式最適 性為評判根據。古典的A式最適性並未將對照處理與試驗處理所具備的先 前資訊(prior information)加以考慮，以上例而言，我們不可能對原來 使用的藥一無所知，經由過去的實驗或臨床的反應，研藥者必已對其藥性 有某種程度的了解，直觀上，這種過去經驗的累積，影響到實驗配置上， 可能使對照處理的實驗次數減少，相對地可對試驗處理多做實驗，設計遂 更具意義。因而本文考慮在k>v的情形下之貝式最適集區設計，對先前分 配施以某種限制，依據準確設計理論(exact design theory)，推導單項 異種消除模型(one- way elimination of heterogeneity model)之下的 貝氏A式最適設計與Γ- minimax最適設計，使Majumdar(1992)的結果能適 用於完全集區設計。此種設計對先前分配具有強韌性，即當先前分配有所 偏誤，且其誤差在某一範圍內時，此設計仍為最適設計或仍可維持所謂的 高效度(high efficiency)。本文將列舉許多實例以說明此一特性。 We consider the problem of comparing a set of v test treatments simultaneously with a control treatment when k>v. Following the work of Majumdar(1992), we use exact design theory to derive Bayes A-optimal designs and optimal Γ-minimax designs for the one-way elimination of heterogeneity model. These designs have the same properties as of Bayes A-optimal incomplete block designs. We also provide several examples of robust optimal designs and highly efficient designs.