Physical Sciences and Mathematics Commons^™

Deriving Optimal Composite Scores: Relating Observational/Longitudinal Data With A Primary Endpoint, Rhonda Ellis

Theses and Dissertations

In numerous clinical/experimental studies, multiple endpoints are measured on each subject. It is often not clear which of these endpoints should be designated as of primary importance. The desirability function approach is a way of combining multiple responses into a single unitless composite score. The response variables may include multiple types of data: binary, ordinal, count, interval data. Each response variable is transformed to a 0 to1 unitless scale with zero representing a completely undesirable response and one representing the ideal value. In desirability function methodology, weights on individual components can be incorporated to allow different levels of importance to …

A Sequential Algorithm To Identify The Mixing Endpoints In Liquids In Pharmaceutical Applications, Akriti Saxena

Theses and Dissertations

The objective of this thesis is to develop a sequential algorithm to determine accurately and quickly, at which point in time a product is well mixed or reaches a steady state plateau, in terms of the Refractive Index (RI). An algorithm using sequential non-linear model fitting and prediction is proposed. A simulation study representing typical scenarios in a liquid manufacturing process in pharmaceutical industries was performed to evaluate the proposed algorithm. The data simulated included autocorrelated normal errors and used the Gompertz model. A set of 27 different combinations of the parameters of the Gompertz function were considered. The results …

Comparing Bootstrap And Jackknife Variance Estimation Methods For Area Under The Roc Curve Using One-Stage Cluster Survey Data, Allison Dunning

Theses and Dissertations

The purpose of this research is to examine the bootstrap and jackknife as methods for estimating the variance of the AUC from a study using a complex sampling design and to determine which characteristics of the sampling design effects this estimation. Data from a one-stage cluster sampling design of 10 clusters was examined. Factors included three true AUCs (.60, .75, and .90), three prevalence levels (50/50, 70/30, 90/10) (non-disease/disease), and finally three number of clusters sampled (2, 5, or 7). A simulated sample was constructed for each of the 27 combinations of AUC, prevalence and number of clusters. Estimates of …

Tolerance Intervals In Random-Effects Models, Kakotan Sanogo

Theses and Dissertations

In the pharmaceutical setting, it is often necessary to establish the shelf life of a drug product and sometimes suitable to assess the risk of product failure at the desired expiry period. The current statistical methodology use confidence intervals for the predicted mean to establish the expiry period and prediction intervals for a predicted new assay value or a tolerance interval for a proportion of the population for use in a risk assessment. A major concern is that most methodology treat a homogeneous subpopulation, say batch, either as a fixed effect and therefore uses a fixed-effects regression model (Graybill, 1976) …

Applications Of The Bivariate Gamma Distribution In Nutritional Epidemiology And Medical Physics, Jolene Barker

Theses and Dissertations

In this thesis the utility of a bivariate gamma distribution is explored. In the field of nutritional epidemiology a nutrition density transformation is used to reduce collinearity. This phenomenon will be shown to result due to the independent variables following a bivariate gamma model. In the field of radiation oncology paired comparison of variances is often performed. The bivariate gamma model is also appropriate for fitting correlated variances. A method for simulating bivariate gamma random variables is presented. This method is used to generate data from several bivariate gamma models and the asymptotic properties of a test statistic, suggested for …

Variable Selection In Competing Risks Using The L1-Penalized Cox Model, Xiangrong Kong

Theses and Dissertations

One situation in survival analysis is that the failure of an individual can happen because of one of multiple distinct causes. Survival data generated in this scenario are commonly referred to as competing risks data. One of the major tasks, when examining survival data, is to assess the dependence of survival time on explanatory variables. In competing risks, as with ordinary univariate survival data, there may be explanatory variables associated with the risks raised from the different causes being studied. The same variable might have different degrees of influence on the risks due to different causes. Given a set of …

Probe Level Analysis Of Affymetrix Microarray Data, Richard Ellis Kennedy

Theses and Dissertations

The analysis of Affymetrix GeneChip® data is a complex, multistep process. Most often, methodscondense the multiple probe level intensities into single probeset level measures (such as RobustMulti-chip Average (RMA), dChip and Microarray Suite version 5.0 (MAS5)), which are thenfollowed by application of statistical tests to determine which genes are differentially expressed. An alternative approach is a probe-level analysis, which tests for differential expression directly using the probe-level data. Probe-level models offer the potential advantage of more accurately capturing sources of variation in microarray experiments. However, this has not been thoroughly investigated, since current research efforts have largely focused on the …

Phase Ii Trials Powered To Detect Activity In Tumor Subsets With Retrospective (Or Prospective) Use Of Predictive Markers, Grishma S. Sheth

Theses and Dissertations

Classical phase II trial designs assume a patient population with a homogeneous tumor type and yield an estimate of a stochastic probability of tumor response. Clinically, however, oncology is moving towards identifying patients who are likely to respond to therapy using tumor subtyping based upon predictive markers. Such designs are called targeted designs (Simon, 2004). For a given phase I1 trial predictive markers may be defined prospectively (on the basis of previous results) or identified retrospectively on the basis of analysis of responding and non-responding tumors. For the prospective case we propose two Phase I1 targeted designs in which a) …

An Adaptive Dose Finding Design (Dosefind) Using A Nonlinear Dose Response Model, James Michael Davenport

Theses and Dissertations

First-in-man (FIM) Phase I clinical trials are part of the critical path in the development of a new compound entity (NCE). Since FIM clinical trials are the first time that an NCE is dosed in human subjects, the designs used in these trials are unique and geared toward patient safety. We develop a method for obtaining the desired response using an adaptive non-linear approach. This method is applicable for studies in which MTD, NOEL,NOAEL, PK, PD effects or other such endpoints are evaluated to determine the desired dose. The method has application whenever a measurable PD marker is an indicator …

Statistical Methods And Experimental Design For Inference Regarding Dose And/Or Interaction Thresholds Along A Fixed-Ratio Ray, Sharon Dziuba Yeatts

Theses and Dissertations

An alternative to the full factorial design, the ray design is appropriate for investigating a mixture of c chemicals, which are present according to a fixed mixing ratio, called the mixture ray. Using single chemical and mixture ray data, we can investigate interaction among the chemicals in a particular mixture. Statistical models have been used to describe the dose-response relationship of the single agents and the mixture; additivity is tested through the significance of model parameters associated with the coincidence of the additivity and mixture models.It is often assumed that a chemical or mixture must be administered above an unknown …

Optimal Clustering: Genetic Constrained K-Means And Linear Programming Algorithms, Jianmin Zhao

Theses and Dissertations

Methods for determining clusters of data under- specified constraints have recently gained popularity. Although general constraints may be used, we focus on clustering methods with the constraint of a minimal cluster size. In this dissertation, we propose two constrained k-means algorithms: Linear Programming Algorithm (LPA) and Genetic Constrained K-means Algorithm (GCKA). Linear Programming Algorithm modifies the k-means algorithm into a linear programming problem with constraints requiring that each cluster have m or more subjects. In order to achieve an acceptable clustering solution, we run the algorithm with a large number of random sets of initial seeds, and choose the solution …

A Normal-Mixture Model With Random-Effects For Rr-Interval Data, Jessica Mckinney Ketchum

Theses and Dissertations

In many applications of random-effects models to longitudinal data, such as heart rate variability (HRV) data, a normal-mixture distribution seems to be more appropriate than the normal distribution assumption. While the random-effects methodology is well developed for several distributions in the exponential family, the case of the normal-mixture has not been dealt with adequately in the literature. The models and the estimation methods that have been proposed in the past assume the conditional model (fixing the random-effects) to be normal and allow a mixture distribution for the random effects (Xu and Hedeker, 2001, Xu, 1995). The methods proposed in this …

Design And Analysis Methods For Cluster Randomized Trials With Pair-Matching On Baseline Outcome: Reduction Of Treatment Effect Variance, Misook Park

Theses and Dissertations

Cluster randomized trials (CRT) are comparative studies designed to evaluate interventions where the unit of analysis and randomization is the cluster but the unit of observation is individuals within clusters. Typically such designs involve a limited number of clusters and thus the variation between clusters is left uncontrolled. Experimental designs and analysis strategies that minimize this variance are required. In this work we focus on the CRT with pre-post intervention measures. By incorporating the baseline measure into the analysis, we can effectively reduce the variance of the treatment effect. Well known methods such as adjustment for baseline as a covariate …

Assessing, Modifying, And Combining Data Fields From The Virginia Office Of The Chief Medical Examiner (Ocme) Dataset And The Virginia Department Of Forensic Science (Dfs) Datasets In Order To Compare Concentrations Of Selected Drugs, Amy Elizabeth Herrin

Theses and Dissertations

The Medical Examiner of Virginia (ME) dataset and the Virginia Department of Forensic Science Driving Under the Influence of Drugs (DUI) datasets were used to determine whether people have the potential to develop tolerances to diphenhydramine, cocaine, oxycodone, hydrocodone, methadone, and morphine. These datasets included the years 2000-2004 and were used to compare the concentrations of these six drugs between people who died from a drug-related cause of death (of the drug of interest) and people who were pulled over for driving under the influence. Three drug pattern groups were created to divide each of the six drug-specific datasets in …

Quantifying The Effects Of Correlated Covariates On Variable Importance Estimates From Random Forests, Ryan Vincent Kimes

Theses and Dissertations

Recent advances in computing technology have lead to the development of algorithmic modeling techniques. These methods can be used to analyze data which are difficult to analyze using traditional statistical models. This study examined the effectiveness of variable importance estimates from the random forest algorithm in identifying the true predictor among a large number of candidate predictors. A simulation study was conducted using twenty different levels of association among the independent variables and seven different levels of association between the true predictor and the response. We conclude that the random forest method is an effective classification tool when the goals …

A Comparison For Longitudinal Data Missing Due To Truncation, Rong Liu

Theses and Dissertations

Many longitudinal clinical studies suffer from patient dropout. Often the dropout is nonignorable and the missing mechanism needs to be incorporated in the analysis. The methods handling missing data make various assumptions about the missing mechanism, and their utility in practice depends on whether these assumptions apply in a specific application. Ramakrishnan and Wang (2005) proposed a method (MDT) to handle nonignorable missing data, where missing is due to the observations exceeding an unobserved threshold. Assuming that the observations arise from a truncated normal distribution, they suggested an EM algorithm to simplify the estimation.In this dissertation the EM algorithm is …

Meta-Analysis Of Open Vs Closed Surgery Of Mandibular Condyle Fractures, Marcy Lauren Nussbaum

Theses and Dissertations

A review of the literature reveals a difference of opinion regarding whether open or closed reduction of condylar fractures produces the best results. It would be beneficial to critically analyze past studies that have directly compared the two methods in an attempt to answer this question. A Medline search for articles using the key words 'mandibular condyle fractures' and 'mandibular condyle fractures surgery' was performed. The articles chosen for the meta-analysis contained data on at least one of the following: postoperative maximum mouth opening, lateral excursion, protrusion, deviation on opening, asymmetry, and joint pain or muscle pain. Several common statistical …

Normal Mixture Models For Gene Cluster Identification In Two Dimensional Microarray Data, Eric Scott Harvey

Theses and Dissertations

This dissertation focuses on methodology specific to microarray data analyses that organize the data in preliminary steps and proposes a cluster analysis method which improves the interpretability of the cluster results. Cluster analysis of microarray data allows samples with similar gene expression values to be discovered and may serve as a useful diagnostic tool. Since microarray data is inherently noisy, data preprocessing steps including smoothing and filtering are discussed. Comparing the results of different clustering methods is complicated by the arbitrariness of the cluster labels. Methods for re-labeling clusters to assess the agreement between the results of different clustering techniques …

Power Analysis For The Mixed Linear Model, Cheryl Annette Dixon

Theses and Dissertations

Power analysis is becoming standard in inference based research proposals and is used to support the proposed design and sample size. The choice of an appropriate power analysis depends on the choice of the research question, measurement procedures, design, and analysis plan. The "best" power analysis, however, will have many features of a sound data analysis. First, it addresses the study hypothesis, and second, it yields a credible answer.

Power calculations for standard statistical hypotheses based on normal theory have been defined for t-tests through the univariate and multivariate general linear models. For these statistical methods, the approaches to power …

The Standardized Influence Matrix And Its Applications To Generalized Linear Models, Jiandong Lu

Theses and Dissertations

The standardized influence matrix is a generalization of the standardized influence function and Cook’s approach to local influence. It provides a general and unified approach to judge the suitability of statistical inference based on parametric models. It characterizes the local influence of data deviations from parametric models on various estimators, including generalized linear models. Its use for both robustness measures and diagnostic procedures has been studied. With global robust estimators, diagnostic statistics are proposed and shown to be useful in detecting influential points for linear regression and logistic regression models. Robustness of various estimators is compared via. the standardized influence …

Missing Data In Repeated Measurement Studies, Kejian Niu

Theses and Dissertations

Repeated measurement data or longitudinal data occur often in statistical applications. For example, in a clinical trial comparing the efficacy of a new treatment with that of a standard treatment, rather than measuring the main response variable only once on each patient, or subject, we can take several measurements over time on each subject.

A Repeated measurement study differs from a longitudinal study. The latter generally refers to any study in which one or more response variables are repeatedly measured over time. The former usually imposes some restrictions on the data. One common restriction is that each response variable must …

Classification Of Newborns Based On Maturity Rating And Intrauterine Growth At The Medical College Of Virginia Hospitals, Lydia Holmes Sund

Theses and Dissertations

Nurses at the Medical College of Virginia Hospitals (MCVH) in Richmond, Virginia, use the Newborn Maturity Rating and Classification Tool to identify high risk infants. An estimate of gestational age is made and using this estimate, weight, length, and head circumference measurements are plotted on graphs on the tool to determine if the infant achieves intrauterine growth smaller, larger or equal to gestational age.

The data used to generate the graphs on the Newborn Maturity Rating and Classification Tool were collected in Colorado during the 1950's. Two nurses at MCVH questioned the use of these graphs. They wanted to know …

False Positive Rates Encountered In The Detection Of Changes In Periodontal Attachment Level, John C. Gunsolley

Theses and Dissertations

This thesis demonstrates that the assumption of normality used by Goodson results in the underestimation of the type I error rate of the tolerance method by a factor of 10. This underestimation is due to the positive kurtosis demonstrated in the distribution of replicate differences. Therefore, the assumption of normality does not seem warranted. It is shown here that a resampling technique more accurately estimates the type I error rate.

The estimates of false positive rates have important implications in the field of periodontics. When diagnostic decisions are based on single measurements, false positive rates are high. Even when thresholds …

An Easy Access Interactive Statistical System For Use And Training In Biometry, Amos Addison Slaymaker Jr.

Theses and Dissertations

One of the most important tools of the applied statistician is the digital computer. It is natural, therefore, for the instructor in applied statistics to want his students to become familiar with the use of computers. If his students are going to get actual experience in using a computer for statistical analysis, he often has only two alternatives. The students can be required to write their own statistical programs or they can use programs already available through a computer facility.

If the course is to be taught such that each student is responsible for his own programs, the instructor must …

Group Sequential Methods For Clinical Trials Applied To The Logistic Regression Model, Joy Duci Mele

Theses and Dissertations

The objectives of this thesis are

1. to provide a comprehensive guide to using Pocock's group sequential method for clinical trials and

2. to show by computer simulations that the group sequential method is appropriate when using the logistic regression model.

In section 1.2, clinical trials are defined with an emphasis on Phase III clinical trials. The primary intent of sections 1.2 and 1.3 is to describe clinical trial characteristics which suggest that interim analyses are desirable. In section 1.4, it is shown that interim analyses should not consist of performing the usual significance tests. Chapter 1, then, describes the …