Theses/Dissertations - Statistical Sciences

Permanent URI for this collectionhttps://hdl.handle.net/2104/4798

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Conjugate hierarchical models for spatial data: an application on an optimal selection procedure.
(2006-07-24T15:25:43Z) McBride, John Jacob.; Bratcher, Thomas L.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.
The theory of generalized linear models provides a unifying class of statistical distributions that can be used to model both discrete and continuous events. In this dissertation we present a new conjugate hierarchical Bayesian generalized linear model that can be used to model counts of occurrences in the presence of spatial correlation. We assume that the counts are taken from geographic regions or areal units (zip codes, counties, etc.) and that the conditional distributions of these counts for each area are distributed as Poisson having unknown rates or relative risks. We incorporate the spatial association of the counts through a neighborhood structure which is based on the arrangement of the areal units. Having defined the neighborhood structure we then model this spatial association with a conditionally autoregressive (CAR) model as developed by Besag (1974). Once the spatial model has been created we adapt a subset selection procedure created by Bratcher and Bhalla (1974) to select the areal unit(s) having the highest relative risks.
Bayesian evaluation of surrogate endpoints.
(2006-07-29T17:03:06Z) Feng, Chunyao.; Seaman, John Weldon, 1956-; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.
To save time and reduce the size and cost of clinical trials, surrogate endpoints are frequently measured instead of true endpoints. The proportion of the treatment effect explained by surrogate endpoints (PTE) is a widely used, albeit controversial, validation criteria. Frequentist and Bayesian methods have been developed to facilitate such validation. The former does not formally incorporate prior information; a critical issue since confidence intervals on PTE is often unacceptably wide. Both the Bayesian and frequentist approaches may yield estimates of PTE outside the unit interval. Furthermore, the existing Bayesian method offers no insight into the prior used for PTE, making prior-to-posterior sensitivity analyses problematic. We proposed a fully Bayesian approach that avoids both of these problems. We also consider the effect of interaction on inference for PTE. As an alternative to the use of PTE, we develop a Bayesian model for relative effect and the association between surrogate and true endpoints, making use of power priors.
Bayesian adaptive designs for non-inferiority and dose selection trials.
(2006-07-31T01:02:37Z) Spann, Melissa Elizabeth.; Seaman, John Weldon, 1956-; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.
The process of conducting a pharmaceutical clinical trial often produces information in a way that can be used as the trial progresses. Bayesian methods offer a highly flexible means of using such information yielding inferences and decisions that are consistent with the laws of probability and consequently admit ease of interpretation. Bayesian adaptive sampling methods offer the potential to accelerate the investigation of a drug without compromising the safety of the trial’s participants. These methods select a patient’s treatment based upon prior information and the knowledge accrued from the trial to date which can reduce patient exposure to unsafe or ineffective treatments and therefore improve patient care in clinical trials. Improving the process of clinical trials in this manner is beneficial to all involved including the pharmaceutical companies and more especially the patients; safer and less expensive drugs can make it to market faster. In this research we present a Bayesian approach to determining if an experimental treatment is non-inferior to an active control treatment within a clinical trial that includes a placebo arm. We incorporate this non-inferiority model in a Bayesian adaptive design that uses joint posterior predictive probabilities of safety and efficacy to determine adaptive allocation probabilities. Results from a retrospective study and a simulation are used to illustrate use of the method. We also present a Bayesian adaptive approach to dose selection that uses effect sizes of doses relative to placebo to perform adaptive allocation and to select the most efficacious dose. The proposed design removes treatment arms if their performance relative to placebo or other treatment arms is undesirable. Results from analyses of simulated data will be discussed.
Bayesian inference for correlated binary data with an application to diabetes complication progression.
(2006-10-26T19:07:46Z) Carlin, Patricia M.; Seaman, John Weldon, 1956-; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.
Correlated binary measurements can occur in a variety of practical contexts and afford interesting statistical modeling challenges. In order to model the separate probabilities for each measurement we must somehow account for the relationship between them. We choose to focus our applications to the progression of the complications of diabetic retinopathy and diabetic nephropathy. We first consider probabilistic models which employ Bayes' theorem for predicting the probability of onset of diabetic nephropathy given that a patient has developed diabetic retinopathy, modifying the work of Ballone, Colagrande, Di Nicola, Di Mascio, Di Mascio, and Capani (2003). We consider beta-binomial models using the Sarmanov (1966) framework which allows us to specify the marginal distributions for a given bivariate likelihood. We present both maximum likelihood and Bayesian methods based on this approach. Our Bayesian methods include a fully identified model based on proportional probabilities of disease incidence. Finally, we consider Bayesian models for three different prior structures using likelihoods representing the data in the form of a 2-by-2 table. To do so, we consider the data as counts resulting from two correlated binary measurements: the onset of diabetic retinopathy and the onset of diabetic nephropathy. We compare resulting posterior distributions from a Jeffreys' prior, independent beta priors, and conditional beta priors, based on a structural zero likelihood model and the bivariate binomial model.
A restriction method for the analysis of discrete longitudinal missing data.
(2007-02-07T18:57:26Z) Moore, Page Casey.; Seaman, John Weldon, 1956-; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.
Clinical trial endpoints are traditionally either physical or laboratory responses. However, such endpoints fail to reflect how patients feel or function in their daily activities. Missing data is inevitable in most every clinical trial regardless of the amount of effort and pre-planning that originally went into a study. Many researchers often resort to ad hoc methods(e.g. case-deletion or mean imputation) when they are faced with missing data, which can lead to biased results. An alternative to these ad hoc methods is multiple imputation. Sources of missing data due to patient dropout in health related quality of life (HRQoL) studies most often result from one of the following: toxicity, disease progression, or therapeutic effectiveness. As a result, nonignorable (NMAR) missing data are the most common type of missing data found in HRQoL studies. Studies involving missing data with a NMAR mechanism are the most difficult type of data to analyze primarily for two reasons: a large number of potential models exist for these data and the hypothesis of random dropout can be neither confirmed nor repudiated. The performance of methods used for the analysis of discrete longitudinal clinical trial data considered to have a nonignorable missingness mechanism under the commonly applied restriction of monotone dropout were developed and evaluated in this dissertation. Monotone dropout, or attrition, occurs when responses are available for a patient until a certain occasion and missing for all subsequent occasions. The purpose of this study is to investigate the performance of different imputation methods available to researchers for handling the problem of missing data where the parameters of interest are six QoL assessments scheduled for collection across six equally spaced visits. We evaluate the relative effectiveness of three commonly used imputation methods, along with three restriction methods and a newly developed restriction method, through a simulation study. The new restriction method is a straightforward technique that provides superior overall performance and much higher coverage rates relative to the other methods under investigation.
Selected topics in statistical discriminant analysis.
(2007-02-07T19:01:17Z) Ounpraseuth, Songthip T.; Young, Dean M.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.
This dissertation consists of three selected topics in statistical discriminant analysis: dimension reduction, regularization methods, and imputation methods. In Chapter 2 we first derive a new linear dimension-reduction method to determine a low-dimensional hyperplane that preserves or nearly preserves the separation of the individual populations and the Bayes probability of misclassification. Next, we derive a new low-dimensional representation-space approach for multiple high-dimensional multivariate normal populations. Third, we develop a linear dimension reduction method for quadratic discriminant analysis when the class population parameters must be estimated. Using a Monte Carlo simulation with several different parameter configurations, we compare our new methodology with two competing linear dimension-reduction procedures for statistical discrimination in terms of expected error rates. We find that under certain conditions, our new dimension-reduction method yields superior results for a majority of the configurations we consider. In addition, we determine that in several configurations, classification performance is actually enhanced by our new feature-reduction method when the sample size is sufficiently small relative to the original feature space dimension. In Chapter 3 we compare and contrast the efficacy of seven regularization methods for the quadratic discriminant function under a variety of parameter configurations. In particular, we use the expected error rate to assess the efficacy of these regularized quadratic discriminant functions. A two-parameter family of regularized class covariance-matrix estimators derived by Friedman (1989) yields superior classification results relative to its six competitors for the configurations, training-sample sizes, and original feature dimensions examined here. Finally, in Chapter 4 we consider the statistical classification problem for two multivariate normal populations with equal covariance matrices when the training samples contain observations missing at random. That is, we analyze the effect of missing-at-random data on Anderson's linear discriminant function. We use a Monte Carlo simulation to examine the expected probabilities of misclassification under several single and multiple imputation methods. The seven missing-data algorithms include: complete observation, mean substitution, expectation maximization, regression, predictive mean matching, propensity score, and MCMC. The regression, predictive mean, and propensity score multiple imputation approaches are, in general, superior to the other methods for the configurations and training-sample sizes we consider.
Logistic regression with misclassified response and covariate measurement error: a Bayesian approach.
(2007-12-04T19:56:26Z) McGlothlin, Anna E.; Stamey, James D.; Seaman, John Weldon, 1956-; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.
In a variety of regression applications, measurement problems are unavoidable because infallible measurement tools may be expensive or unavailable. When modeling the relationship between a response variable and covariates, we must account for the uncertainty that is inherently introduced when one or both of these variables are measured with error. In this dissertation, we explore the consequences of and remedies for imperfect measurements. We consider a Bayesian analysis for modeling a binary outcome that is subject to misclassification. We investigate the use of informative conditional means priors for the regression coefficients. Additionally, we incorporate random effects into the model to accommodate correlated responses. Markov chain Monte Carlo methods are utilized to perform the necessary computations. We use the deviance information criterion to aid in model selection. Next, we consider data where measurements are flawed for both the response and explanatory variables. Our interest is in the case of a misclassified dichotomous response and a continuous covariate that is unobservable, but where measurements are available on its surrogate. A logistic regression model is developed to incorporate the measurement error in the covariate as well as the misclassification in the response. The methods developed are illustrated through an example. Results from a simulation experiment are provided illustrating advantages of the approach. Finally, we expand this model to incorporate random effects, resulting in a generalized linear mixed model for a misclassified response and covariate measurement error. We demonstrate the use of this model using a simulated data set.
Bayesian approaches to problems in drug safety and adaptive clinical trial designs.
(2008-06-10T21:19:06Z) Mauldin, Jo A.; Seaman, John Weldon, 1956-; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.
The efficacy, safety, and cost of pharmaceutical products are critical issues in society today. Motivated both financially and ethically by these concerns, the pharmaceutical industry has continually worked to develop methods which provide more efficient and ethical assessments of the safety and efficacy of pharmaceutical products. There is an increased emphasis on more targeted treatments with a focus on better patient outcomes. In this vein, recent applications of advanced statistical methods have allowed companies to reduce the costs of getting safe and effective products to market—savings that can be passed on to consumers in the form of price cuts or additional investment in research and development. Among the methods that have become increasingly important in drug development are adaptive experimental designs. We first investigate the impacts of misclassification of response on a Bayesian adaptive design. A primary argument for the use of adaptive designs is the efficiency one gains over implementing a traditional fixed design. We examine the design’s performance under misclassified responses and compare it to the situation for which we account for the misclassification in a Bayesian model. Next, we examine the utility of safety lab measures collected during the clinical development of a drug. These labs are used to characterize a drug’s safety profile and their scope can be limited when reasonably confident of no associated safety concern, facilitating reduced costs and less subject burden. We consider the use of a Bayesian generalized linear model and investigate the use of conditional means priors and power priors for the regression coefficients used in the analysis of safety lab measures. Finally, we address the need for transparent benefit-risk assessment methods that combine safety and efficacy data and allow straight forward comparisons of treatment options. We begin by developing interval estimates on a commonly-used benefit-risk ratio. We then propose the use of a Bayesian generalized linear model to jointly assess safety and efficacy, allowing for direct comparisons of competing treatment options utilizing posterior 95% credible sets and predictive probabilities.
Sample size determination for Emax model, equivalence / non-inferiority test and drug combination in fixed dose trials.
(2008-06-11T12:13:34Z) Wang, Jie, 1977-; Stamey, James D.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.
Sample size determination is one of the most important aspects in clinical designs. Careful selection of appropriate sample sizes can not only save economic and human resources, but also improve model performance and efficiency. We first explore the sample sizes of Emax model for a simple one group crossover design. Emax model is the one of the most frequently used models defining the relationship of drug efficacy with respect to its dosing levels in pharmacokinetic /pharmacodynamic studies. In frequentist approach, sample sizes are determined by desired accuracy for the parameter of interest ED₅₀. Non-linear mixed effects model is applied to emphasize the within subjects correlation. To allow for different magnitudes of variability of the population parameters in the Emax model, we proposed three different model structures to account for the random effects. In Bayesian approach, sample sizes are determined by desired coverage, average of posterior variances and lengths for the parameter of interest ED₅₀. In our simulation studies, sampling priors are used to generate the data, and non-informative priors are utilized to represent ignorance of key model parameters. Sample sizes for comparative studies are then discussed in Bayesian approach. In the absence of gold standard, sample sizes are determined by the measures of average posterior variances and lengths for the ratio of marginal probabilities of two screening tests; whereas in the presence of gold standard, sample sizes are evaluated under the same criterion to the measures of sensitivity and specificity. Non-informative priors are utilized in this study as well. We have also considered the problem of drug combination in fixed dose trials to test whether a drug mixture, which may combine two or more agents, is more ‘effective’ than each of its components. Informative priors are derived for component drugs and a non-informative prior is assumed for the drug mixture. Sample sizes are evaluated by posterior standard errors, average probability of more effectiveness and Bayesian power.
Statistical monitoring of a process with autocorrlated output and observable autocorrelated measurement error.
(2008-06-11T14:53:49Z) Cuéllar Fuentes, Jesús.; Seaman, John Weldon, 1956-; Tubbs, Jack Dale.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.
Our objective in this work is to monitor a production process yielding output that is correlated and contaminated with autocorrelated measurement error. Often, the elimination of the causes of the autocorrelation of the measurement error and the reduction of the measurement error to a negligible level is not feasible because of regulatory restrictions, technological limitations, or the expense of requisite modifications. In this process, reference material is measured to verify the performance of the measurement process, before the product material is measured. We propose the use of a transfer function to account for measurement error in the product measurements. We obtain the base production signal and use a modified version of the common cause (CC) chart and the special cause control (SCC) chart, originally proposed by Roberts and Alwan (1988), to monitor the base production process. We incorporate control limits in the CC chart as suggested by Alwan (1991) and Montgomery and Mastrangelo (1991) and add MR-chart to the original SCC chart. The common cause control (CCC) chart and SCC charts comprise a flexible monitoring scheme capable of detecting not only changes in the process mean, but also shifts in the mean and the variance of the random shocks that generate the base process.
Logistic regression with covariate measurement error in an adaptive design : a Bayesian approach.
(2008-10-14T16:59:14Z) Crixell, JoAnna Christine, 1979-; Seaman, John Weldon, 1956-; Stamey, James D.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.
Adaptive designs are increasingly popular in clinical trials. This is because such designs have the potential to decrease patient exposure to treatments that are less efficacious or unsafe. The Bayesian approach to adaptive designs is attractive because it makes systematic use of prior data and other information in a way that is consistent with the laws of probability. The goal of this dissertation is to examine the effects of measurement error on a Bayesian adaptive design. Measurement error problems are common in a variety of regression applications where the variable of interest cannot be measured perfectly. This is often unavoidable because infallible measurement tools to account for such error are either too expensive or unavailable. When modeling the relationship between a response variable and other covariates, we must account for any uncertainty introduced when one or both of these variables are measured with error. This dissertation will explore the consequence of imperfect measurements on a Bayesian adaptive design.
Bayesian and maximum likelihood methods for some two-segment generalized linear models.
(2008-10-14T20:38:46Z) Miyamoto, Kazutoshi.; Seaman, John Weldon, 1956-; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.
The change-point (CP) problem, wherein parameters of a model change abruptly at an unknown covariate value, is common in many fields, such as process control, epidemiology, and ecology. CP problems using two-segment regression models, such as those based on generalized linear models, are very flexible and widely used. For two-segment Poisson and logistic regression models, misclassification in the response is well known to cause attenuation of key parameters and other difficulties. How misclassification effects estimation of a CP in such models has not been studied. In this research, we consider the effect of misclassification on CP problems in Poisson and logistic regression. We focus on maximum likelihood and Bayesian methods.
Semiparametric AUC regression for testing treatment effect in clinical trial.
(2008-10-15T12:22:42Z) Zhang, Lin, 1978-; Tubbs, Jack Dale.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.
We investigated distribution free methods for testing covariate adjusted treatment effects. Dodd and Pepe (2003) proposed a semiparametric logistic regression model for the area under the ROC curve (AUC). Their model was motivated by the observation that the commonly used non-parametric Mann-Whitney statistic is a non-parametric estimate of the AUC, where the AUC gives a measure of the separation between two density functions. Their result allows one to test hypotheses using distribution free methods when the covariates are discrete, however, the standard errors generated using standard GLM software were not correct since the Bernoulli data used in the Mann-Whitney statistic are correlated. They used bootstrapping to compute the standard errors. In Chapter 2, we present an analytical method for estimating the standard errors as an alternative to the bootstrap procedure. In Chapter 3, we present a new semiparametric beta regression model for the AUC. This was done by defining the response variable as the placement value of the treatment responses with respect to a placebo population. This model allows for both discrete and continuous covariate effects. In Chapter 4, we expand our model in two ways. The first is for a clinical trial with multiple treatments arms and a placebo. The second extension is for longitudinal or repeated measures data. These extensions are illustrated using both simulated and real data.
Statistical considerations in the analysis of multivariate Phase II testing.
(2009-04-01T12:08:15Z) Hetzer, Joel D.; Johnston, Dennis A.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.
In medical diagnosis and treatment, many diseases are characterized by multiple measurable differences in clinical (e.g., physical or radiological differences) and laboratory parameters (biomarkers from "healthy levels". Each of these differences is a symptom of the disease often correlated with the other symptoms. In Phase II human trials, the level of a single symptom is often used as a surrogate for disease level. In multi-symptom diseases, all relevant symptoms often should be included in the evaluation, thus a multivariate approach to Phase II analysis becomes critical. In this dissertation we formulate seven (7) multivariate tests for use in multivariate Phase II studies. Each method is evaluated using metabolic syndrome with data obtained from the public domain data set, NHANES III as an example to train the algorithms and the associated tests.
Bayesian and pseudo-likelihood interval estimation for comparing two Poisson rate parameters using under-reported data.
(2009-04-01T15:56:04Z) Greer, Brandi A.; Young, Dean M.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.
We present interval estimation methods for comparing Poisson rate parameters from two independent populations with under-reported data for the rate difference and the rate ratio. In addition, we apply the Bayesian paradigm to derive credible intervals for both the ratio and the difference of the Poisson rates. We also construct pseudo-likelihood-based confidence intervals for the ratio of the rates. We begin by considering two cases for analyzing under-reported Poisson counts: inference when training data are available and inference when they are not. From these cases we derive two marginal posterior densities for the difference in Poisson rates and corresponding credible sets. First, we perform Monte Carlo simulation analyses to examine the effects of differing model parameters on the posterior density. Then we perform additional simulations to study the robustness of the posterior density to misspecified priors. In addition, we apply the new Bayesian credible intervals for the difference of Poisson rates to an example concerning the mortality rates due to acute lower respiratory infection in two age groups for children in the Upper River Division in Gambia and to an example comparing automobile accident injury rates for male and female drivers. We also use the Bayesian paradigm to derive two closed-form posterior densities and credible intervals for the Poisson rate ratio, again in the presence of training data and without it. We perform a series of Monte Carlo simulation studies to examine the properties of our new posterior densities for the Poisson rate ratio and apply our Bayesian credible intervals for the rate ratio to the same two examples mentioned above. Lastly, we derive three new pseudo-likelihood-based confidence intervals for the ratio of two Poisson rates using the double-sampling paradigm for under-reported data. Specifically, we derive profile likelihood-, integrated likelihood-, and approximate integrated likelihood-based intervals. We compare coverage properties and interval widths of the newly derived confidence intervals via a Monte Carlo simulation. Then we apply our newly derived confidence intervals to an example comparing cervical cancer rates.
Bayesian sample-size determination and adaptive design for clinical trials with Poisson outcomes.
(Elsevier., 2010) Hand, Austin L.; Stamey, James D.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.
Because of the high cost and time constraints for clinical trials, researchers often need to determine the smallest sample size that provides accurate inferences for a parameter of interest or need to adaptive design elements during the course of the trial based on information that is initially unknown. Although most experimenters have employed frequentist methods, the Bayesian paradigm offers a wide variety of methodologies and are becoming increasingly more popular in clinical trials because of their flexibility and their ease of interpretation. Recently, Bayesian approaches have been used to determine the sample size of a single Poisson rate parameter in a clinical trial setting. We extend these results to the comparison of two Poisson rates and develop methods for sample-size determination for hypothesis testing in a Bayesian context. Also, we propose a Bayesian predictive adaptive two-stage design for Poisson data that allows for sample-size adjustments by basing the second-stage sample size on the first-stage results. Lastly, we present a new Bayesian meta-analytic non-inferiority method for binomial data that allows researchers a more direct interpretation of their results. Our method uses MCMC methods to approximate the posterior distribution of the new treatment compared to a placebo rather than indirectly inferring a conclusion from the comparison of the new treatment to an active control.
Topics in dimension reduction and missing data in statistical discrimination.
(2010-02-02T20:15:04Z) Young, Phil D.; Tubbs, Jack Dale.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.
This dissertation is comprised of four chapters. In the first chapter, we define the concept of linear dimension reduction, review some popular linear dimension reduction procedures, discuss background research that we use in chapters two and three, and give a brief outline of the dissertation contents. In chapter two, we derive a linear dimension reduction (LDR) procedure for statistical discriminant analysis for multiple multivariate skew-normal populations. First, we define the multivariate skew-normal distribution and give several applications of its use. We also provide marginal and conditional properties of the MSN random vector. Then, we state and prove several lemmas used in a series of theorems that present our LDR procedure for the multivariate skew-normal populations using parameter configurations. Lastly, we illustrate our LDR method for multiple multivariate skew-normal distributions with three examples. In the third chapter, we define and rigorously prove the existence of the multivariate singular skew-normal (MSSN) distribution. Next, we state and prove distributional properties for linear combinations, marginal, and conditional random variables from a MSSN distribution. Then, we state and prove several lemmas used in deriving our LDR transformation for the multiple MSSN distributions with assorted parameter combinations. We then state and prove several theorems concerning the formulation of our LDR technique. Finally, we illustrate the effectiveness of our LDR technique for multiple multivariate singular skew-normal classes with two examples. In chapter four, we compare two statistical linear discrimination procedures when monotone missing training data exists in the training data sets from two different multivariate normally distributed populations with unequal means but equal covariance matrices. We derive the maximum likelihood estimators (MLEs) for the partitioned population means and the common covariance matrix in an appendix. Additionally, we contrast two classifiers: a linear combination discriminant function derived from Chung and Han (C-H) (2000) and a linear classifier based on the MLE of two multivariate normal training samples with identical monotone missing training-data in one or more features. We then perform two Monte Carlo simulations with various parameter configurations to compare the effectiveness of the MLE and C-H classifiers as the correlation between features for the population covariance matrix increases. Moreover, we compare the two competing classifiers using parametric bootstrap estimated expected error rates for a subset of the well-known Iris data.
Lectio divina.
(2010-06-23T12:18:33Z) Crites, Margaret.; McAllister, Scott.; Music.; Baylor University. School of Music.
Lectio Divina is a musical exploration of the contemplative prayer and scripture‐reading practice called "Lectio Divina". The work is written for a chamber ensemble: flute, clarinet, violin, cello, piano and percussion. Each instrument represents an individual that participates in this contemplative moment. There are three sections in the practice of Lectio Divina and thus three movements in its musical realization. As is intended in the contemplative practice, the three sections in this composition Lectio Divina progress from complexity and fullness to simplicity and understanding.
Count regression models with a misclassified binary covariate : a Bayesian approach.
(2010-06-23T12:28:43Z) Morgan-Cox, MaryAnn.; Stamey, James D.; Seaman, John Weldon, 1956-; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.
Mismeasurment, and specifically misclassification, are inevitable in a variety of regression applications. Fallible measurement methods are often used when infallible methods are either expensive or not available. Ignoring mismeasurement will result in biased estimates for the associated regression parameters. The models presented in this dissertation are designed to correct this bias and yield variance estimates reflecting the uncertainty that is introduced by flawed measurements. We consider a generalized linear model for a Poisson response. This model accounts for the misclassification associated with the binary exposure covariate. In the first portion of the analysis, diffuse priors are utilized for the regression coefficients and the effective prior sample size technique is implemented to construct informative priors for the misclassification parameters. In the second portion of the analysis we place informative priors on the regression parameters and diffuse priors on the misclassification parameters. We also present results of a simulation study that incorporates prior information for both the regression coefficients and the misclassification parameters. Next, we extend the Poisson model with a single binary covariate in various ways, including adding a continuous covariate and accounting for clustering through the use of random effects models. We also consider a zero-inflated version of the model. Simulation studies are summarized for each extension. Finally, we discuss an application in which frequentist and Bayesian logistic regression models are used to predict prevalence of high BMI-for-age among preschool-aged children in Texas.
Bayesian models for discrete censored sampling and dose finding.
(2010-06-23T12:29:00Z) Pruszynski, Jessica E.; Seaman, John Weldon, 1956-; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.
We first consider the problem of discrete censored sampling. Censored binomial data may lead to irregular likelihood functions and problems with statistical inference. We consider a Bayesian approach to inference for censored binomial problems and compare it to non-Bayesian methods. We include examples and a simulation study in which we compare point estimation, interval coverage, and interval width for Bayesian and non-Bayesian methods. The continual reassessment method (CRM) is a Bayesian design often used in Phase I cancer clinical trials. It models the toxicity response of the patient as a function of administered dose using a model that is updated as data accrues. The CRM does not take into consideration the relationship between the toxicity response and the proportion of the administered drug that is absorbed by targeted tissue. Not accounting for this discrepancy can yield misleading conclusions about the maximum tolerated dose to be used in subsequent Phase II trials. We will examine, through simulation, the effect that disregarding the level of bioavailability has on the performance of the CRM.

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