This thesis focuses on assessing and improving statistical methods implemented in two areas of public health research. The first topic involves estimation of national influenza-associated mortality rates via mathematical modeling. The second topic involves the timely detection of infectious disease outbreaks using statistical process control monitoring. For over fifty years, the Centers for Disease Control and Prevention has been estimating annual rates of U.S. deaths attributable to influenza. These estimates have been used to determine costs and benefits associated with influenza prevention and control strategies. Quantifying the effect of influenza on mortality, however, can be challenging since influenza infections typically are not confirmed virologically nor specified on death certificates. Consequently, a wide range of ecologically based, mathematical modeling approaches have been applied to specify the association between influenza and mortality. To date, all influenza-associated death estimates have been based on mortality data first aggregated at the national level and then modeled. Unfortunately, there are a number of local-level seasonal factors that may confound the association between influenza and mortality - thus suggesting that data be modeled at the local level and then pooled to make national estimates of death. The first component of the thesis topic involving mortality estimation addresses this issue by introducing and implementing a two-stage hierarchical Bayesian modeling approach. In the first stage, city-level data with varying trends in mortality and weather were modeled using semi-parametric, generalized additive models. In the second stage, the log-relative risk estimates calculated for each city in stage 1 represented the “outcome” variable, and were modeled two ways: (1) assuming spatial independence across cities using a Bayesian generalized linear model, and (2) assuming correlation among cities using a Bayesian spatial correlation model. Results from these models were compared to those from a more-conventional approach. The second component of this topic examines the extent to which seasonal confounding and collinearity affect the relationship between influenza and mortality at the local (city) level. Disentangling the effects of temperature, humidity, and other seasonal confounders on the association between influenza and mortality is challenging since these covariates are often temporally collinear with influenza activity. Three modeling strategies with varying representations of background seasonality were compared. Seasonal covariates entered into the model may have been measured (e.g., ambient temperature) or unmeasured (e.g., time-based smoothing splines or Fourier terms). An advantage of modeling background seasonality via time splines is that the amount of seasonal curvature can be controlled by the number of degrees of freedom specified for the spline. A comparison of the effects of influenza activity on mortality based on these varying representations of seasonal confounding is assessed. The third component of this topic explores the relationship between mortality rates and influenza activity using a flexible, natural cubic spline function to model the influenza term. The conventional approach of fitting influenza-activity terms linearly in regression was found to be too constraining. Results show that the association is best represented nonlinearly. The second area of focus in this thesis involves infectious disease outbreak detection. A fundamental goal of public health surveillance, particularly syndromic surveillance, is the timely detection of increases in the rate of unusual events. In syndromic surveillance, a significant increase in the incidence of monitored disease outcomes would trigger an alert, possibly prompting the implementation of an intervention strategy. Public health surveillance generally monitors count data (e.g., counts of influenza-like illness, sales of over-the-counter remedies, and number of visits to outpatient clinics). Statistical process control charts, designed for quality control monitoring in industry, have been widely adapted for use in disease and syndromic surveillance. The behavior of these detection methods on discrete distributions, however, has not been explored in detail. For this component of the thesis, a simulation study was conducted to compare the CuSum and EWMA methods for detection of increases in negative binomial rates with varying amounts of dispersion. The goal of each method is to detect an increase in the mean number of cases as soon as possible after an upward rate shift has occurred. The performance of the CuSum and EWMA detection methods is evaluated using the conditional expected delay criterion, which is a measure of the detection delay, i.e., the time between the occurrence of a shift and when that shift is detected. Detection capabilities were explored under varying shift sizes and times at which the shifts occurred.

Changepoint analysis is a useful tool in environmental statistics in that it provides a methodology for threshold detection and modeling processes subject to periodic changes in the underlying model due to anthropogenic effects or natural phenomena. Several applications of changepoint analysis are investigated here. The use of inappropriate changepoint detection methods is first discussed and the need for a simple, flexible, correct method is established and such a method is proposed for the mean-shift model. Data from the Everglades, Florida, USA is used to showcase the methodology in a real-world setting. An extension to the case of time-series data represented via transition matrices is presented as a result of joint work with Matt Williams (Department of Statistics, Virginia Tech) and rainfall data from Kenya, Africa is presented as a case-study. Finally the multivariate changepoint problem is addressed by a two-stage approach beginning with dimension reduction via principal component analysis (PCA). After the dimension reduction step the location of the changepoint in principal component space is estimated and assuming at most one change in a mean-shift setting, all possible sub-models are investigated. / Ph. D.

Maximally selected statistics for the estimation of simple cutpoint models are embedded into a generalized conceptual framework based on conditional inference procedures. This powerful framework contains most of the published procedures in this area as special cases, such as maximally selected chi-squared and rank statistics, but also allows for direct construction of new test procedures for less standard test problems. As an application, a novel maximally selected rank statistic is derived from this framework for a censored response partitioned with respect to two ordered categorical covariates and potential interactions. This new test is employed to search for a high-risk group of rectal cancer patients treated with a neo-adjuvant chemoradiotherapy. Moreover, a new efficient algorithm for the evaluation of the asymptotic distribution for a large class of maximally selected statistics is given enabling the fast evaluation of a large number of cutpoints. / Series: Research Report Series / Department of Statistics and Mathematics

Data showing a trend that characterizes a change due to a shock to the system are a type of changepoint data, and may be referred to as shock-through data. As a result of the shock, this type of data may exhibit one of two types of transitions: gradual or abrupt. Although shock-through data are of particular interest in many areas of study such as biological, medical, health and environmental applications, previous research has shown that statistical inference from modeling the trend is challenging in the presence of discontinuous derivatives. Further complications arise when we have (1) longitudinal data, and/or (2) samples which come from two potential populations: one with a gradual transition, and the other abrupt. Bent-cable regression is an appealing statistical tool to model shock-through data due to the model's flexibility while being parsimonious with greatly interpretable regression coefficients. It comprises two linear segments (incoming and outgoing) joined by a quadratic bend. In this thesis, we develop extended bent-cable methodology for longitudinal data in a Bayesian framework to account for both types of transitions; inference for the transition type is driven by the data rather than a presumption about the nature of the transition. We describe explicitly the computationally intensive Bayesian implementation of the methodology. Moreover, we describe modeling only one type of transition, which is a special case of this more general model. We demonstrate our methodology by a simulation study, and with two applications: (1) assessing the transition to early hypothermia in a rat model, and (2) understanding CFC-11 trends monitored globally. Our methodology can be further extended at the cost of both theoretical and computational extensiveness. For example, we assume that the two populations mentioned above share common intercept and slopes in the incoming and outgoing phases, an assumption that can be relaxed for instances when intercept and slope parameters could behave differently between populations. In addition to this, we discuss several other directions for future research out of the proposed methodology presented in this thesis.

Data showing a trend that characterizes a change due to a shock to the system are a type of changepoint data, and may be referred to as shock-through data. As a result of the shock, this type of data may exhibit one of two types of transitions: gradual or abrupt. Although shock-through data are of particular interest in many areas of study such as biological, medical, health and environmental applications, previous research has shown that statistical inference from modeling the trend is challenging in the presence of discontinuous derivatives. Further complications arise when we have (1) longitudinal data, and/or (2) samples which come from two potential populations: one with a gradual transition, and the other abrupt. Bent-cable regression is an appealing statistical tool to model shock-through data due to the model's flexibility while being parsimonious with greatly interpretable regression coefficients. It comprises two linear segments (incoming and outgoing) joined by a quadratic bend. In this thesis, we develop extended bent-cable methodology for longitudinal data in a Bayesian framework to account for both types of transitions; inference for the transition type is driven by the data rather than a presumption about the nature of the transition. We describe explicitly the computationally intensive Bayesian implementation of the methodology. Moreover, we describe modeling only one type of transition, which is a special case of this more general model. We demonstrate our methodology by a simulation study, and with two applications: (1) assessing the transition to early hypothermia in a rat model, and (2) understanding CFC-11 trends monitored globally. Our methodology can be further extended at the cost of both theoretical and computational extensiveness. For example, we assume that the two populations mentioned above share common intercept and slopes in the incoming and outgoing phases, an assumption that can be relaxed for instances when intercept and slope parameters could behave differently between populations. In addition to this, we discuss several other directions for future research out of the proposed methodology presented in this thesis.

Scholarship shows that the social construction of crime is responsible for the public’s demand for tougher criminal justice policies. Yet, there remains disagreement over several key issues regarding the relationship between strategic communication and the punitiveness of the mass public. Little is known about the magnitude and direction of changes in punitive sentiment over the last 50 years. Moreover, there is disagreement over when the public began to demand punitive solutions to crime over alternative policies. Many scholars point the racial turmoil of the 1960s, but none have shown conclusive evidence of any fundamental change in punitive sentiment. Finally, there is disagreement over what type of strategic appeal is most effective at shaping public opinion. The argument of this research is that the democratic nature of American pol- itics creates an environment where the competition of ideas flourish. Political ac- tors can use several types of strategic communication (agenda-setting, persuasion, priming, framing) to shape political outcomes. The effectiveness of an appeal does not remain constant over time, but should evolve around systematic social changes— environmental conditions and social norms. Thus, there is a time varying relationship between various appeals and public opinion. A content analysis of crime news in the New York Times provides measures of four types of strategic messages. Instrumental factors such as the economy and public policy are also shown to influence the public’s desire for punitive criminal justice policies. A Bayesian changepoint model provides a means to test when, if any,fundamental change occurred in the public’s punitive sentiment. Contrary to most accounts, the changepoint model identifies 1972 as having the highest probability of a breakpoint suggesting a public backlash against the Supreme Court’s Furman vs. Georgia decision to abolish the death penalty. Estimates from a state-space model show that different types of messages in the media shape punitive sentiment and that the effectiveness of racial primes and presidential attention to crime changes over time. Moreover, these changes are shown to be a function of changes in social context and norms suggesting ways to improve political communication.

Mechanics and biological function of nucleic acids are intimately coupled. The DNA double helix must be opened to allow base pairing of RNA during transcription; RNA must bend and fold in its many cellular functions. Presented in this dissertation are two investigations of mechanical deformations of nucleic acids, conducted with optical tweezers.In the introduction, the mechanical properties of DNA and RNA and their relevance to their cellular functions are introduced, to give the reader context for the results presented in the Chapters 2 and 3. This is followed by an introduction to the theory of semiflexible polymer elasticity. The optical tweezers instruments used in conducting these investigations are then presented, along with calibration procedures and a short introduction to optical trapping physics.Chapter 2 presents an investigation of the effect of downstream DNA tension on initiation by T7 RNA polymerase. A hidden Markov model is fit to force-dependent lifetimes obtained from optical tweezers experiments, allowing us to identify which steps in initiation are force-dependent and estimate rates and transition state distances. We find that 1-2 pN of tension is sufficient to turn o gene expression by causing transcription bubble collapse and destabilizing the bound state. Our force-dependence scheme and estimated transition distances provide independent supportfor the \scrunching" model of initiation.The effects of cation binding and screening on single-stranded helix formation in poly(A) RNA are presented in Chapter 3. Magnesium and calcium bind to poly(A), stabilize the helix, and change its mechanical properties. A new model of helix-coil transitions is presented and used to estimate energetics and mechanical properties.Chapter 4 presents the first fully objective algorithm for use in analyzing the noisy staircaselike data that is often produced by single-molecule fluorescence experiments. A test based on the SIC (BIC) statistic is used in conjunction with a progressive step-placement scheme to locate changepoints (steps) in noisy data. Its performance is compared to other step detection algorithms in use by biophysicists by repeating tests performed in a recent review.Experimental protocols and computer codes used in these investigations are presentedin detail in the appendices.

We will propose a random changepoint model for the analysis of longitudinal CD4 and CD8 T-cell counts, as well as viral RNA loads, for HIV infected subjects following highly active antiretroviral treatment. The data was taken from two studies, one of the Aids Clinical Group Trial 398 and one performed by the Terry Beirn Community Programs for Clinical Research on AIDS. Models were created with the changepoint following both exponential and truncated normal distributions. The estimation of the changepoints was performed in a Bayesian analysis, with implementation in the WinBUGS software using Markov Chain Monte Carlo methods. For model selection, we used the deviance information criterion (DIC), a two term measure of model adequacy and complexity. DIC indicates that the data support a random changepoint model with the changepoint following an exponential distribution. Visual analyses of the posterior densities of the parameters also support these conclusions.

abstract: The emergence of new technologies as well as a fresh look at analyzing existing processes have given rise to a new type of response characteristic, known as a profile. Profiles are useful when a quality variable is functionally dependent on one or more explanatory, or independent, variables. So, instead of observing a single measurement on each unit or product a set of values is obtained over a range which, when plotted, takes the shape of a curve. Traditional multivariate monitoring schemes are inadequate for monitoring profiles due to high dimensionality and poor use of the information stored in functional form leading to very large variance-covariance matrices. Profile monitoring has become an important area of study in statistical process control and is being actively addressed by researchers across the globe. This research explores the understanding of the area in three parts. A comparative analysis is conducted of two linear profile-monitoring techniques based on probability of false alarm rate and average run length (ARL) under shifts in the model parameters. The two techniques studied are control chart based on classical calibration statistic and a control chart based on the parameters of a linear model. The research demonstrates that a profile characterized by a parametric model is more efficient monitoring scheme than one based on monitoring only the individual features of the profile. A likelihood ratio based changepoint control chart is proposed for detecting a sustained step shift in low order polynomial profiles. The test statistic is plotted on a Shewhart like chart with control limits derived from asymptotic distribution theory. The statistic is factored to reflect the variation due to the parameters in to aid in interpreting an out of control signal. The research also looks at the robust parameter design study of profiles, also referred to as signal response systems. Such experiments are often necessary for understanding and reducing the common cause variation in systems. A split-plot approach is proposed to analyze the profiles. It is demonstrated that an explicit modeling of variance components using generalized linear mixed models approach has more precise point estimates and tighter confidence intervals. / Dissertation/Thesis / Ph.D. Industrial Engineering 2010

This thesis provides a study on stochastic models of financial markets related to problems of asset pricing and hedging, optimal portfolio managing and statistical changepoint detection in trends of asset prices. Chapter 1 develops a general model of a system of interconnected stochastic markets associated with a directed acyclic graph. The main result of the chapter provides sufficient conditions of hedgeability of contracts in the model. These conditions are expressed in terms of consistent price systems, which generalise the notion of equivalent martingale measures. Using the general results obtained, a particular model of an asset market with transaction costs and portfolio constraints is studied. In the second chapter the problem of multi-period utility maximisation in the general market model is considered. The aim of the chapter is to establish the existence of systems of supporting prices, which play the role of Lagrange multipliers and allow to decompose a multi-period constrained utility maximisation problem into a family of single-period and unconstrained problems. Their existence is proved under conditions similar to those of Chapter 1.The last chapter is devoted to applications of statistical sequential methods for detecting trend changes in asset prices. A model where prices are driven by a geometric Gaussian random walk with changing mean and variance is proposed, and the problem of choosing the optimal moment of time to sell an asset is studied. The main theorem of the chapter describes the structure of the optimal selling moments in terms of the Shiryaev–Roberts statistic and the posterior probability process.