Constrained Bayesian Estimation of Inverse Probability Weights for Nonmonotone Missing Data

Copyright c©2014 by the authors

Exact Approaches for Bias Detection and Avoidance with Small, Sparse, or Correlated Categorical Data

Every day, traditional statistical methodology are used world wide to study a variety of topics and provides insight regarding countless subjects. Each technique is based on a distinct set of assumptions to ensure valid results. Additionally, many statistical approaches rely on large sample behavior and may collapse or degenerate in the presence of small, spare, or correlated data. This dissertation details several advancements to detect these conditions, avoid their consequences, and analyze data in a different way to yield trustworthy results. One of the most commonly used modeling techniques for outcomes with only two possible categorical values (eg. live/die, pass/fail, better/worse, ect.) is logistic regression. While some potential complications with this approach are widely known, many investigators are unaware that their particular data does not meet the foundational assumptions, since they are not easy to verify. We have developed a routine for determining if a researcher should be concerned about potential bias in logistic regression results, so they can take steps to mitigate the bias or use a different procedure altogether to model the data. Correlated data may arise from common situations such as multi-site medical studies, research on family units, or investigations on student achievement within classrooms. In these circumstance the associations between cluster members must be included in any statistical analysis testing the hypothesis of a connection be-tween two variables in order for results to be valid. Previously investigators had to choose between using a method intended for small or sparse data while assuming independence between observations or a method that allowed for correlation between observations, while requiring large samples to be reliable. We present a new method that allows for small, clustered samples to be assessed for a relationship between a two-level predictor (eg. treatment/control) and a categorical outcome (eg. low/medium/high)

Analyzing Incomplete Categorical Data: Revisiting Maximum Likelihood Estimation (Mle) Procedure

Incomplete data poses formidable difficulties in the application of statistical techniques and requires special procedures to handle. The most common ways to solve this problem are by ignoring, truncating, censoring or collapsing those data, but these may lead to inappropriate conclusions because those data might contain important information. Most of the research for estimating cell probabilities involving incomplete categorical data is based on the EM algorithm. A likelihood approach is employed for estimating cell probabilities for missing values and makes comparisons between maximum likelihood estimation (MLE) and the EM algorithm. The MLE can provide almost the same estimates as that of the EM algorithm without any loss of properties. Results are compared for different distributional assumptions. Using clinical trial results from a group of 59 epileptics, results from the application of MLE and EM algorithm are compared and the advantages of MLE are highlighted

A methodology on how to create a real-life relevant risk profile for a given nanomaterial

With large amounts of nanotoxicology studies delivering contradicting results and a complex, moving regulatory framework, potential risks surrounding nanotechnology appear complex and confusing. Many researchers and workers in different sectors are dealing with nanomaterials on a day-to-day basis, and have a requirement to define their assessment/management needs. This paper describes an industry-tailored strategy for risk assessment of nanomaterials and nano-enabled products, which builds on recent research outcomes. The approach focuses on the creation of a risk profile for a given nanomaterial (e.g., determine which materials and/or process operation pose greater risk, where these risks occur in the lifecycle, and the impact of these risks on society), using state-of-the-art safety assessment approaches/tools (ECETOC TRA, Stoffenmanager Nano and ISO/TS 12901-2:2014). The developed nanosafety strategy takes into account cross-sectoral industrial needs and includes (i) Information Gathering: Identification of nanomaterials and hazards by a demand-driven questionnaire and on-site company visits in the context of human and ecosystem exposures, considering all companies/parties/downstream users involved along the value chain; (ii) Hazard Assessment: Collection of all relevant and available information on the intrinsic properties of the substance (e.g., peerreviewed (eco)toxicological data, material safety data sheets), as well as identification of actual recommendations and benchmark limits for the different nano-objects in the scope of this projects; (iii) Exposure Assessment: Definition of industry-specific and application-specific exposure scenarios taking into account operational conditions and risk management measures; (iv) Risk Characterisation: Classification of the risk potential by making use of exposure estimation models (i.e., comparing estimated exposure levels with threshold levels); (v) Refined Risk Characterisation and Exposure Monitoring: Selection of individual exposure scenarios for exposure monitoring following the OECD Harmonized Tiered Approach to refine risk assessment; (vi) Risk Mitigation Strategies: Development of risk mitigation actions focusing on risk prevention.This work was supported by ongoing projects that received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement no 646155 (INSPIRED), grant agreement no 646296 (Hi-Response) and grant agreement no 691095 (NANOGENTOOLS)

REPEATED MEANS MODELING: AN ALTERNATIVE FOR REPEATED MEASURES DESIGNS

The study presents a series of alternative ANOVA-based methods which offered a remedy to the traditional F test to accommodate violations of normality and sphericity assumptions. Specially Robust Means Modeling (RMM), developed from structured means modeling (SMM), a branch of structural equation modeling (SEM), is introduced to circumvent the sphericity assumption while alleviating the violation of normality assumption. Maximum likelihood, Satorra-Bentler scaled chi-square, asymptotic distribution-free (ADF) methods and its corrections, as well as residual-based ADF methods (RES) and its corrections, are included in this RMM category. A Monte Carlo simulation is designed to evaluate Type I error robustness and power of the ANOVA-based methods and the proposed RMM methods under the fully crossed conditions including degree of non-sphericity, degree of non-normality, sample size, and the number of levels of the repeated measures. The study gains strong ground for RMM methods to be recommended over ANOVA-based methods under almost all conditions except when the model was complex (i.e. 8 levels) and sample size was small (15, 30)

Robust mixture modeling

Doctor of PhilosophyDepartment of StatisticsWeixin Yao and Kun ChenOrdinary least-squares (OLS) estimators for a linear model are very sensitive to unusual values in the design space or outliers among y values. Even one single atypical value may have a large effect on the parameter estimates. In this proposal, we first review and describe some available and popular robust techniques, including some recent developed ones, and compare them in terms of breakdown point and efficiency. In addition, we also use a simulation study and a real data application to compare the performance of existing robust methods under different scenarios. Finite mixture models are widely applied in a variety of random phenomena. However, inference of mixture models is a challenging work when the outliers exist in the data. The traditional maximum likelihood estimator (MLE) is sensitive to outliers. In this proposal, we propose a Robust Mixture via Mean shift penalization (RMM) in mixture models and Robust Mixture Regression via Mean shift penalization (RMRM) in mixture regression, to achieve simultaneous outlier detection and parameter estimation. A mean shift parameter is added to the mixture models, and penalized by a nonconvex penalty function. With this model setting, we develop an iterative thresholding embedded EM algorithm to maximize the penalized objective function. Comparing with other existing robust methods, the proposed methods show outstanding performance in both identifying outliers and estimating the parameters