Physical Sciences and Mathematics Commons^™

Novel Methods For Characterizing Conditional Quantiles In Zero-Inflated Count Regression Models, Xuan Shi

Theses and Dissertations--Statistics

Despite its popularity in diverse disciplines, quantile regression methods are primarily designed for the continuous response setting and cannot be directly applied to the discrete (or count) response setting. There can also be challenges when modeling count responses, such as the presence of excess zero counts, formally known as zero-inflation. To address the aforementioned challenges, we propose a comprehensive model-aware strategy that synthesizes quantile regression methods with estimation of zero-inflated count regression models. Various competing computational routines are examined, while residual analysis and model selection procedures are included to validate our method. The performance of these methods is characterized through …

Estimating And Testing Treatment Effects With Misclassified Multivariate Data, Zi Ye

Theses and Dissertations--Statistics

Clinical trials are often used to assess drug efficacy and safety. Participants are sometimes pre-stratified into different groups by diagnostic tools. However, these diagnostic tools are fallible. The traditional method ignores this problem and assumes the diagnostic devices are perfect. This assumption will lead to inefficient and biased estimators. In this era of personalized medicine and measurement-based care, the issues of bias and efficiency are of paramount importance. Despite the prominence, only few researches evaluated the treatment effect in the presence of misclassifications in some special cases and most others focus on assessing the accuracy of the diagnostic devices. In …

Innovative Statistical Models In Cancer Immunotherapy Trial Design, Jing Wei

Theses and Dissertations--Statistics

A challenge arising in cancer immunotherapy trial design is the presence of non-proportional hazards (NPH) patterns in survival curves. We considered three different NPH patterns caused by delayed treatment effect, cure rate and responder rate of treatment group in this dissertation. These three NPH patterns would violate the proportional hazard model assumption and ignoring any of them in an immunotherapy trial design will result in substantial loss of statistical power.

In this dissertation, four models to deal with NPH patterns are discussed. First, a piecewise proportional hazards model is proposed to incorporate delayed treatment effect into the trial design consideration. …

Novel Nonparametric Testing Approaches For Multivariate Growth Curve Data: Finite-Sample, Resampling And Rank-Based Methods, Ting Zeng

Theses and Dissertations--Statistics

Multivariate growth curve data naturally arise in various fields, for example, biomedical science, public health, agriculture, social science and so on. For data of this type, the classical approach is to conduct multivariate analysis of variance (MANOVA) based on Wilks' Lambda and other multivariate statistics, which require the assumptions of multivariate normality and homogeneity of within-cell covariance matrices. However, data being analyzed nowadays show marked departure from multivariate normal distribution and homoscedasticity. In this dissertation, we investigate nonparametric testing approaches for multivariate growth curve data from three aspects, i.e., finite-sample, resampling and rank-based methods.

The first project proposes an approximate …

Dimension Reduction Techniques In Regression, Pei Wang

Theses and Dissertations--Statistics

Because of the advances of modern technology, the size of the collected data nowadays is larger and the structure is more complex. To deal with such kinds of data, sufficient dimension reduction (SDR) and reduced rank (RR) regression are two powerful tools. This dissertation focuses on these two tools and it is composed of three projects. In the first project, we introduce a new SDR method through a novel approach of feature filter to recover the central mean subspace exhaustively along with a method to determine the dimension, two variable selection methods, and extensions to multivariate response and large p …