Practical restrictions on randomization are commonplace in industrial experiments due to the presence of hard-to-change or costly-to-change factors. Employing a split-plot design structure minimizes the number of required experimental settings for the hard-to-change factors. In this research, we propose classes of equivalent estimation second-order response surface split-plot designs for which the ordinary least squares estimates of the model are equivalent to the generalized least squares estimates. Designs that possess the equivalence property enjoy the advantages of best linear unbiased estimates and design selection that is robust to model misspecification and independent of the variance components. We present a generalized proof of the equivalence conditions that enables the development of several systematic design construction strategies and provides the ability to verify numerically that a design provides equivalent estimates, resulting in a broad catalog of designs. We explore the construction of balanced and unbalanced split-plot versions of the central composite and Box-Behnken designs. In addition, we illustrate the utility of numerical verification in generating D-optimal and minimal point designs, including split-plot versions of the Notz, Hoke, Box and Draper, and hybrid designs. Finally, we consider the practical implications of analyzing a near-equivalent design when a suitable equivalent design is not available. By simulation, we compare methods of estimation to provide a practitioner with guidance on analysis alternatives when a best linear unbiased estimator is not available. Our goal throughout this research is to develop practical experimentation strategies for restricted randomization that are consistent with the philosophy of traditional response surface methodology. / Ph. D.

Background: The cluster randomized trial design randomly assigns groups of people to different treatment arms. This dissertation aimed to (1) develop machine learning algorithms to identify cluster trials in bibliographic databases, (2) assess reporting of methodological and ethical elements in hemodialysis-related cluster trials, and (3) assess how well two covariate-constrained randomization methods balanced baseline characteristics compared with simple randomization. Methods: In study 1, we developed three machine learning algorithms that classify whether a bibliographic citation is a CRT report or not. We only used the information available in an article citation, including the title, abstract, keywords, and subject headings. In study 2, we conducted a systematic review of CRTs in the hemodialysis setting to review the reporting of key methodological and ethical issues. We reviewed CRTs published in English between 2000 and 2019 and indexed in MEDLINE or EMBASE. In study 3, we assessed how well two covariate-constrained randomization methods balanced baseline characteristics compared with simple randomization. Results: In study 1, we successfully developed high-performance algorithms that identified whether a citation was a CRT. Our algorithms had greater than 97% sensitivity and 77% specificity in identifying CRTs. For study 2, we found suboptimal conduct and reporting of methodological issues of CRTs in the hemodialysis setting and incomplete reporting of key ethical issues. For study 3, where we randomized 72 clusters, constraining the randomization using historical information achieved a better balance on baseline characteristics than simple randomization; however, the magnitude of benefit was modest. Conclusions: This dissertation's results will help researchers quickly identify cluster trials in bibliographic databases (study 1) and inform the design and analyses of future Canadian trials conducted within the hemodialysis setting (study 2 & 3). / Thesis / Doctor of Philosophy (PhD) / The cluster trial design randomly assigns groups of people to different treatment arms rather than individuals. Cluster trials are commonly used in research areas such as education, public health, and health service research. Examples of clusters can include villages/communities, worksites, schools, hospitals, hospital wards, and physicians. This dissertation aimed to (1) develop machine learning algorithms to identify cluster trials in bibliographic databases, (2) assess reporting of methodological and ethical elements in hemodialysis-related cluster trials, and (3) identified best practices for randomly assigning hemodialysis centers in cluster trials. We conducted three studies to address these aims. The results of this dissertation will help researchers quickly identify cluster trials in bibliographic databases (study 1) and inform the design and analyses of future Canadian trials conducted within the hemodialysis setting (study 2 & 3).