Indiana University-Purdue University Indianapolis (IUPUI) / Epidemiologic and clinical studies routinely collect longitudinal measures of multiple outcomes. These longitudinal outcomes can be used to establish the temporal order of relevant biological processes and their association with the onset of clinical symptoms. In the first part of this thesis, we proposed to use bivariate change point models for two longitudinal outcomes with a focus on estimating the correlation between the two change points. We adopted a Bayesian approach for parameter estimation and inference. In the second part, we considered the situation when time-to-event outcome is also collected along with multiple longitudinal biomarkers measured until the occurrence of the event or censoring. Joint models for longitudinal and time-to-event data can be used to estimate the association between the characteristics of the longitudinal measures over time and survival time. We developed a maximum-likelihood method to joint model multiple longitudinal biomarkers and a time-to-event outcome. In addition, we focused on predicting conditional survival probabilities and evaluating the predictive accuracy of multiple longitudinal biomarkers in the joint modeling framework. We assessed the performance of the proposed methods in simulation studies and applied the new methods to data sets from two cohort studies. / National Institutes of Health (NIH) Grants R01 AG019181, R24 MH080827, P30 AG10133, R01 AG09956.

Wang, Zexi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 63-64). / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 0 --- Introduction --- p.1 / Chapter 1 --- The Design of the Experiments --- p.4 / Chapter 1.1 --- Flies and the Devices --- p.5 / Chapter 1.2 --- Parameter Settings and Interested Information --- p.8 / Chapter 2 --- Video Processing --- p.11 / Chapter 2.1 --- "Videos, Computer Vision and Image Processing" --- p.11 / Chapter 2.2 --- Details in Video Processing --- p.14 / Chapter 3 --- Data Analysis --- p.20 / Chapter 3.1 --- Background --- p.20 / Chapter 3.2 --- Outline of Data Analysis in Our Project --- p.22 / Chapter 4 --- Effect of the Medicine --- p.25 / Chapter 4.1 --- Hypothesis Testing --- p.26 / Chapter 4.2 --- Two-sample t Test --- p.28 / Chapter 5 --- Significance of the Two Factors --- p.32 / Chapter 5.1 --- Background of ANOVA --- p.33 / Chapter 5.2 --- The Model of ANOVA --- p.35 / Chapter 5.3 --- Two-way ANOVA in Our Data Analysis --- p.42 / Chapter 6 --- Regression Model --- p.45 / Chapter 6.1 --- Background of Regression Analysis --- p.47 / Chapter 6.2 --- Polynomial Regression Models --- p.52 / Chapter 6.2.1 --- Background --- p.52 / Chapter 6.2.2 --- R2 and adjusted R2 --- p.53 / Chapter 6.3 --- Model Verification --- p.58 / Chapter 6.4 --- A Simpler Model As the Other Choice --- p.59 / Chapter 6.5 --- Conclusions --- p.60 / Chapter 7 --- Further Studies --- p.61 / Bibliography --- p.62

The last two decades have seen several large-scale epidemics of international impact, including human, animal and plant epidemics. Policy makers face health challenges that require epidemic predictions based on limited information. There is therefore a pressing need to construct models that allow us to frame all available information to predict an emerging outbreak and to control it in a timely manner. The aim of this thesis is to develop an early-warning modelling approach that can predict emerging disease outbreaks. Based on Bayesian techniques ideally suited to combine information from different sources into a single modelling and estimation framework, I developed a suite of approaches to epidemiological data that can deal with data from different sources and of varying quality. The SEIR model, particle filter algorithm and a number of influenza-related datasets were utilised to examine various models and methodologies to predict influenza outbreaks. The data included a combination of consultations and diagnosed influenza-like illness (ILI) cases for five influenza seasons. I showed that for the pandemic season, different proxies lead to similar behaviour of the effective reproduction number. For influenza datasets, there exists a strong relationship between consultations and diagnosed datasets, especially when considering time-dependent models. Individual parameters for different influenza seasons provided similar values, thereby offering an opportunity to utilise such information in future outbreaks. Moreover, my findings showed that when the temperature drops below 14°C, this triggers the first substantial rise in the number of ILI cases, highlighting that temperature data is an important signal to trigger the start of the influenza epidemic. Further probing was carried out among Maltese citizens and estimates on the under-reporting rate of the seasonal influenza were established. Based on these findings, a new epidemiological model and framework were developed, providing accurate real-time forecasts with a clear early warning signal to the influenza outbreak. This research utilised a combination of novel data sources to predict influenza outbreaks. Such information is beneficial for health authorities to plan health strategies and control epidemics.

Statistical research can be more difficult to plan than other kinds of projects, since the research must adapt as knowledge is gained. This dissertation establishes a formal language and methodology for designing experimental research strategies with limited resources. It is a mathematically rigorous extension of a sequential and adaptive form of statistical research called response surface methodology. It uses sponsor-given information, conditions, and resource constraints to decompose an overall project into individual stages. At each stage, a "parent" decision-maker determines what design of experimentation to do for its stage of research, and adapts to the feedback from that research's potential "children", each of whom deal with a different possible state of knowledge resulting from the experimentation of the "parent". The research of this dissertation extends the real-world rigor of the statistical field of design of experiments to develop an deterministic, adaptive algorithm that produces deterministically generated, reproducible, testable, defendable, adaptive, resource-constrained multi-stage experimental schedules without having to spend physical resource.

The Bayesian network (BN) formalism is a powerful representation for encoding domains characterised by uncertainty. However, before it can be used it must first be constructed, which is a major challenge for any real-life problem. There are two broad approaches, namely the hand-crafted approach, which relies on a human expert, and the data-driven approach, which relies on data. The former approach is useful, however issues such as human bias can introduce errors into the model. We have conducted a literature review of the expert-driven approach, and we have cherry-picked a number of common methods, and engineered a framework to assist non-BN experts with expert-driven construction of BNs. The latter construction approach uses algorithms to construct the model from a data set. However, construction from data is provably NP-hard. To solve this problem, approximate, heuristic algorithms have been proposed; in particular, algorithms that assume an order between the nodes, therefore reducing the search space. However, traditionally, this approach relies on an expert providing the order among the variables --- an expert may not always be available, or may be unable to provide the order. Nevertheless, if a good order is available, these order-based algorithms have demonstrated good performance. More recent approaches attempt to ''learn'' a good order then use the order-based algorithm to discover the structure. To eliminate the need for order information during construction, we propose a search in the entire space of Bayesian network structures --- we present a novel approach for carrying out this task, and we demonstrate its performance against existing algorithms that search in the entire space and the space of orders. Finally, we employ the hand-crafting framework to construct models for the task of diagnosis in a ''real-life'' medical domain, dementia diagnosis. We collect real dementia data from clinical practice, and we apply the data-driven algorithms developed to assess the concordance between the reference models developed by hand and the models derived from real clinical data.