The well-documented problems associated with mapping raw rates of disease have resulted in an increased use of Bayesian hierarchical models to produce maps of "smoothed'' estimates of disease rates. Two statistical problems arise in using Bayesian hierarchical models for disease mapping. The first problem is in comparing goodness of fit of various models, which can be used to test different hypotheses. The second problem is in identifying outliers/divergent regions with unusually high or low residual risk of disease, or those whose disease rates are not well fitted. The results of outlier detection may generate further hypotheses as to what additional covariates might be necessary for explaining the disease. Leave-one-out cross-validatory (LOOCV) model assessment has been used for these two problems. However, actual LOOCV is time-consuming. This thesis introduces two methods, namely iIS and iWAIC, for approximating LOOCV, using only Markov chain samples simulated from a posterior distribution based on a full data set. In iIS and iWAIC, we first integrate the latent variables without reference to holdout observation, then apply IS and WAIC approximations to the integrated predictive density and evaluation function. We apply iIS and iWAIC to two real data sets. Our empirical results show that iIS and iWAIC can provide significantly better estimation of LOOCV model assessment than existing methods including DIC, Importance Sampling, WAIC, posterior checking and Ghosting methods.

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This research examines public health mapping over two time periods, 1944-1954 and 2000-2004 and explores how mapping disease shaped scientific knowledge about disease. During World War II, the Atlas of Diseases was produced by cartographers and geographers well versed in the subjectivity of maps. Today professionals in a variety of disciplines use digital mapping software to produce maps of disease. This research takes a look at how public health maps and mapping of disease have changed over time and discusses the political implications of public health mapping as an aspect of geographic governance.

The use of the local likelihood method (Tibshirani and Hastie, 1987; Loader, 1996) in the presence of interval-censored or aggregated data leads to a natural consideration of an EM-type strategy, or rather a local EM algorithm. In the thesis, we consider local EM to analyze the point process data that are either interval-censored or aggregated into regional counts. We specifically formulate local EM algorithms for density, intensity and risk estimation and implement the algorithms using a piecewise constant function. We demonstrate that the use of the piecewise constant function at the E-step explicitly results in an iteration that involves an expectation, maximization and smoothing step, or an EMS algorithm considered in Silverman, Jones, Wilson and Nychka (1990). Consequently, we reveal a previously unknown connection between local EM and the EMS algorithm. From a theoretical perspective, local EM and the EMS algorithm complement each other. Although the statistical methodology literature often characterizes EMS methods as ad hoc, local likelihood suggests otherwise as the EMS algorithm arises naturally from a local likelihood consideration in the context of point processes. Moreover, the EMS algorithm not only serves as a convenient implementation of the local EM algorithm but also provides a set of theoretical tools to better understand the role of local EM. In particular, we present results that reinforce the suggestion that the pair of local EM and penalized likelihood are analogous to that of EM and likelihood. Applications include the analysis of bivariate interval-censored data as well as disease mapping for a rare disease, lupus, in the Greater Toronto Area.

The use of the local likelihood method (Tibshirani and Hastie, 1987; Loader, 1996) in the presence of interval-censored or aggregated data leads to a natural consideration of an EM-type strategy, or rather a local EM algorithm. In the thesis, we consider local EM to analyze the point process data that are either interval-censored or aggregated into regional counts. We specifically formulate local EM algorithms for density, intensity and risk estimation and implement the algorithms using a piecewise constant function. We demonstrate that the use of the piecewise constant function at the E-step explicitly results in an iteration that involves an expectation, maximization and smoothing step, or an EMS algorithm considered in Silverman, Jones, Wilson and Nychka (1990). Consequently, we reveal a previously unknown connection between local EM and the EMS algorithm. From a theoretical perspective, local EM and the EMS algorithm complement each other. Although the statistical methodology literature often characterizes EMS methods as ad hoc, local likelihood suggests otherwise as the EMS algorithm arises naturally from a local likelihood consideration in the context of point processes. Moreover, the EMS algorithm not only serves as a convenient implementation of the local EM algorithm but also provides a set of theoretical tools to better understand the role of local EM. In particular, we present results that reinforce the suggestion that the pair of local EM and penalized likelihood are analogous to that of EM and likelihood. Applications include the analysis of bivariate interval-censored data as well as disease mapping for a rare disease, lupus, in the Greater Toronto Area.

The statistical analysis based on the quantile method is more comprehensive, flexible, and not sensitive against outliers compared to the mean methods. The study of the joint disease mapping has usually focused on the mean regression. This means they study the correlation or the dependence between the means of the diseases by using standard regression. However, sometimes one disease limits the occurrence of another disease. In this case, the dependence between the two diseases will not be in the means but in the different quantiles; thus, the analyzes will consider a joint disease mapping of high quantile for one disease with low quantile of the other disease. In the proposed joint quantile model, the key idea is to link the diseases with different quantiles and estimate their dependence instead of connecting their means. The various components of this formulation are modeled by using the latent Gaussian model, and the parameters were estimated via R-INLA. Finally, we illustrate the model by analyzing the malaria and G6PD deficiency incidences in 21 African countries.

This research explores the ways in which communities can connect their experiential knowledge of space and place with observed spatial patterns of disease to increase our abilities to both understand underlying processes and implement effective interventions. We develop and test new methods for integrating observed patterns of disease with community knowledge, validate these methods through generation of new knowledge and hypotheses about processes that have produced cancer patterns, begin to translate this new knowledge into potential interventions, generate much needed recommendations for best practices in research that integrates Geographic Information Science (GISc) and community engagement, and generate new hypotheses for future research. Methods include the creation of continuous surface representation maps of cancer burdens and selected behaviors related to health risks, using adaptive spatial filtering, and a community-based project in which community members generate hypotheses regarding high rates of cancer in their community and explore and annotate cancer burden map layers in a GIS environment. We partner with community and public health practice partners in order to increase the likelihood of translation of research results into evidence-based intervention. Methods of spatial data analysis, community mapping and concept mapping are used.

Haemoglobinopathies, which include sickle-cell anaemia (SCA) and α- and β-thalassaemia, represent some of our few unequivocal examples of human evolution. The underlying genetic mutations reflect a recurring adaptation against one of the biggest infectious disease killers of humans, Plasmodium falciparum malaria. Inheritance of one copy of a sickle-cell or thalassaemic allele leads to protection against death from malaria, while two copies can result in a severe blood disorder. As a result, haemoglobinopathies have risen in frequency through balancing selection and pose a significant public health problem in parts of the world with a history of malaria transmission. Their study therefore lies at the interface between evolutionary biology and public health. In this thesis, I explore different aspects of the epidemiology and population genetics of haemoglobinopathies around the world. Using pre-existing epidemiological data, statistical and geostatistical methods and Geographic Information System tools, I develop detailed evidence-based maps of the α-thalassaemia allele frequency distribution and genetic diversity in Southeast Asia and sickle-cell allele frequency in India. Pairing these with birth data, I generate sub-national estimates of the number of newborns born with severe forms of α-thalassaemia and SCA in Thailand and India, respectively, together with uncertainty estimates. In addition, I use a flexible population genetic simulation model to explore evolutionary explanations for the contrasting spatial haplotype patterns observed for SCA and the severe form of β-thalassaemia (β0-thalassaemia) in sub-Saharan Africa and the Middle East, and resurrect a 20-year old question surrounding the genetic origin of sickle-cell. Understanding the fine-scale geographical heterogeneities in the distributions of malaria-protective haemoglobinopathies is critical for addressing basic science questions and applied public health queries. Working at the interface between evolutionary biology and public health has provided me with the opportunity to build a more complete overview of the neglected increasing public health burden that this group of human disorders represents.

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In my dissertation, I will present my research which contributes to solve the following three open problems from biomedical informatics: (1) Multi-task approaches for microarray classification; (2) Multi-label classification of gene and protein prediction from multi-source biological data; (3) Spatial scan for movement data. In microarray classification, samples belong to several predefined categories (e.g., cancer vs. control tissues) and the goal is to build a predictor that classifies a new tissue sample based on its microarray measurements. When faced with the small-sample high-dimensional microarray data, most machine learning algorithm would produce an overly complicated model that performs well on training data but poorly on new data. To reduce the risk of over-fitting, feature selection becomes an essential technique in microarray classification. However, standard feature selection algorithms are bound to underperform when the size of the microarray data is particularly small. The best remedy is to borrow strength from external microarray datasets. In this dissertation, I will present two new multi-task feature filter methods which can improve the classification performance by utilizing the external microarray data. The first method is to aggregate the feature selection results from multiple microarray classification tasks. The resulting multi-task feature selection can be shown to improve quality of the selected features and lead to higher classification accuracy. The second method jointly selects a small gene set with maximal discriminative power and minimal redundancy across multiple classification tasks by solving an objective function with integer constraints. In protein function prediction problem, gene functions are predicted from a predefined set of possible functions (e.g., the functions defined in the Gene Ontology). Gene function prediction is a complex classification problem characterized by the following aspects: (1) a single gene may have multiple functions; (2) the functions are organized in hierarchy; (3) unbalanced training data for each function (much less positive than negative examples); (4) missing class labels; (5) availability of multiple biological data sources, such as microarray data, genome sequence and protein-protein interactions. As participants in the 2011 Critical Assessment of Function Annotation (CAFA) challenge, our team achieved the highest AUC accuracy among 45 groups. In the competition, we gained by focusing on the 5-th aspect of the problem. Thus, in this dissertation, I will discuss several schemes to integrate the prediction scores from multiple data sources and show their results. Interestingly, the experimental results show that a simple averaging integration method is competitive with other state-of-the-art data integration methods. Original spatial scan algorithm is used for detection of spatial overdensities: discovery of spatial subregions with significantly higher scores according to some density measure. This algorithm is widely used in identifying cluster of disease cases (e.g., identifying environmental risk factors for child leukemia). However, the original spatial scan algorithm only works on static spatial data. In this dissertation, I will propose one possible solution for spatial scan on movement data. / Computer and Information Science