Statistics electronic theses and dissertations (MU)The electronic theses and dissertations of the Department of Statistics.https://hdl.handle.net/10355/52442020-07-07T03:33:22Z2020-07-07T03:33:22ZAdaptive optimal design with application to a two drug combination trial based on efficiency-toxicity responseYao, Ping, Ph. D.https://hdl.handle.net/10355/96872020-05-18T22:43:45Z2009-01-01T00:00:00ZAdaptive optimal design with application to a two drug combination trial based on efficiency-toxicity response
Yao, Ping, Ph. D.
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] The first part of this dissertation develops an adaptive optimal design for dose-finding with combination therapies that accounts for both efficacy and toxicity. The bivariate probit model is used as a working model for the dose-response relationship. A desirable therapy is defined to be the dose combination that achieves a preset probability of efficacy and toxicity. The goal is to estimate the dose that exists closest to the desirable therapy, but within the therapeutic range. A-optimal designs that minimizes the variance of the estimate of this dose and D-optimal designs that minimize the (approximate) confidence ellipsoid for all model parameters are obtained. The next part addresses important outstanding questions concerning the information measure used in implementing adaptive optimal designs. Four measures of information are important in the literature on inference for stochastic processes. The measure used in adaptive optimal designs to construct treatment allocation procedures is none of these. I explore these information measures in the context of adaptive optimal designs.
Title from PDF of title page (University of Missouri--Columbia, viewed on September 20, 2010).; The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file.; Dissertation advisor: Dr. Nancy Flournoy.; Vita.; Ph. D. University of Missouri--Columbia 2009.
2009-01-01T00:00:00ZAdaptive optimal designs for dose-finding studies and an adaptive multivariate CUSUM control chartWang, Tianhuahttps://hdl.handle.net/10355/378392020-01-22T18:41:15Z2013-01-01T00:00:00ZAdaptive optimal designs for dose-finding studies and an adaptive multivariate CUSUM control chart
Wang, Tianhua
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] There are many areas where optimal designs are applied to, for example, the development of a new drug, where a conventional dose- finding study involves learning about the dose-response curve in order to bring forward right doses of drug to late-stage development. The first part of this dissertation focus on three pharmacodynamics sigmoid Emax models, we derive the corresponding simple formats of the adaptive optimal designs regardless of the optimality criteria or parameters of interest. An algorithm for deriving a specific adaptive optimal design is developed. A simulation study comparing the adaptive optimal designs and the uniform designs is also performed. The second part of this dissertation focuses on the statistical process control, we proposed an adaptive approach for the multivariate CUSUM statistical process control chart for signaling a range of location shifts. This method is based on the multivariate CUSUM control chart proposed by Pignatiello and Runger in 1990. We used the exponentially moving weighted average (EMWA) statistic to estimate the current process mean shift and change the reference value adaptively in each run. By specifying the minimal magnitude of the mean shift through the non-centrality parameter, our proposed control chart can achieve an overall good performance for detecting a range of shifts rather than a single value.
2013-01-01T00:00:00ZA ballooned beta-logistic modelYi, Minhttps://hdl.handle.net/10355/491262019-08-15T18:25:56Z2015-01-01T00:00:00ZA ballooned beta-logistic model
Yi, Min
The beta distribution is a simple and flexible model in which responses are naturally confined to the finite interval (0,1). Its parameters can be related to covariates such as dose and gender through a regression model. The Ballooned Beta-logistic (BBL) model expands the response boundaries from (0,1) to (L,U), where L and U are unknown parameters. Under the BBL model, expected responses follow a logistic function which can be made equal to that of the Four Parameter Logistic (4PL) model. But the distribution of responses differs from the classical 4PL model which has additive normal errors. In contrast, the BBL model naturally has bounded responses and inhomogeneous variance. The asymptotic normality of maximum likelihood estimators (MLEs) is obtained even though the support of this non-regular regression model depends on unknown parameters. We find MLEs converge faster to L and U than do extreme values at the minimum and maximum concentrations. Given enzyme-linked immunosorbent assay data from different plates, we study a motivating validation objective, which is to set suitability criteria for estimates of L and U; after this plates with boundary estimates outside these limits would be considered ”reference failures”. We show the BBL model has advantages over the 4PL model.
2015-01-01T00:00:00ZBayes factor consistency in linear models when p grows with nGuo, Ruixin, 1983-https://hdl.handle.net/10355/96862020-05-18T22:43:43Z2009-01-01T00:00:00ZBayes factor consistency in linear models when p grows with n
Guo, Ruixin, 1983-
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] This dissertation examines consistency of Bayes factors in the model comparison problem for linear models. Common approaches to Bayesian analysis of linear models use Zellner's g-prior, a partially conjugate normal prior on the model parameters indexed by a single parameter g. More generally, a hyper-prior can be placed on g, providing a mixture of g-priors. When comparing nested models, flat priors are often placed on the common parameters with the g-prior used for the other parameters, forcing the prior on g to be proper for a determinate Bayes factor. Even for the non-nested case, an "encompassing" approach comparing all models to a base model is often used, where the base model has a flat prior and the prior on g must be proper. In this dissertation, we consider the Jeffreys prior on g, an improper prior that is also the reference prior. We show consistency of the Bayes factor associated with the reference prior for g and a broad range of proper priors for the fixed model dimension case. We also discuss consistency and inconsistency for the Bayes factor associated with the reference prior for the growing dimension case. We obtain consistency and inconsistency depending on the limiting behavior of [rho/nu]. Laplace approximations are derived for bayes factors under different situations.
Title from PDF of title page (University of Missouri--Columbia, viewed on September 17, 2010).; The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file.; Dissertation advisor: Dr. Paul Speckman.; Vita.; Ph. D. University of Missouri--Columbia 2009.
2009-01-01T00:00:00Z