Fellowships and Student Programs.

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Case studies will illustrate regulatory science in action and practice and will include content publically available from the FDA's website that can be used in conjunction with FDA science-based guidance and decision precedents. This course will provide a basic, yet thorough introduction to the probability theory and mathematical statistics that underlie many of the commonly used techniques in public health research.

Topics to be covered include probability distributions normal, binomial, Poisson , means, variances and expected values, finite sampling distributions, parameter estimation method of moments, maximum likelihood , confidence intervals, hypothesis testing likelihood ratio, Wald and score tests. All theoretical material will be motivated with problems from epidemiology, biostatistics, environmental health and other public health areas.

This course is aimed towards second year doctoral students in fields other than Biostatistics. Background in algebra and calculus required. Topics will include types of censoring, hazard, survivor, and cumulative hazard functions, Kaplan-Meier and actuarial estimation of the survival distribution, comparison of survival using log rank and other tests, regression models including the Cox proportional hazards model and the accelerated failure time model, adjustment for time-varying covariates, and the use of parametric distributions exponential, Weibull in survival analysis.

Methods for recurrent survival outcomes and competing risks will also be discussed, as well as design of studies with survival outcomes.

## Modelling of discrete spatial variation in epidemiology with SAS using GLIMMIX

Class material will include presentation of statistical methods for estimation and testing along with current software SAS, Stata for implementing analyses of survival data. Applications to real data will be emphasized. BST may be taken concurrently. This course covers modern methods for the analysis of repeated measures, correlated outcomes and longitudinal data, including the unbalanced and incomplete data sets characteristic of biomedical research.

Topics include an introduction to the analysis of correlated data, analysis of response profiles, fitting parametric curves, covariance pattern models, random effects and growth curve models, and generalized linear models for longitudinal data, including generalized estimating equations GEE and generalized linear mixed effects models GLMMs.

## Summer Workshop Series - Epidemiology and Biostatistics - Western University

Course Note: Lab or section times will be announced at first meeting. This course introduces students to the diverse statistical methods used throughout the process of statistical genetics, from familial aggregation and segregation studies to linkage scans and association studies. Topics covered include basic principles from population genetics, multipoint and model-free linkage analysis, family-based and population-based association testing, and Genome Wide Association analysis.

Instructors use ongoing research into the genetics of respiratory disease, psychiatric disorders and cancer to illustrate basic principles. Weekly homework supplements reading, course lectures, discussion and section. Relevant concepts in genetics and molecular genetics will be reviewed in lectures and labs. The emphasis of the course is fundamental principles and concepts. Course Prerequisites: BST concurrent enrollment allowed Course Note: There will be a weekly lab section; the time will be scheduled at first meeting.

This course is a practical introduction to the Bayesian analysis of biomedical data. It is an intermediate Master's level course in the philosophy, analytic strategies, implementation, and interpretation of Bayesian data analysis. Specific topics that will be covered include: the Bayesian paradigm; Bayesian analysis of basic models; Bayesian computing: Markov Chain Monte Carlo; STAN R software package for Bayesian data analysis; linear regression; hierarchical regression models; generalized linear models; meta-analysis; models for missing data.

Programming and case studies will be used throughout the course to provide hands-on training in these concepts. Axiomatic foundations of probability, independence, conditional probability, joint distributions, transformations, moment generating functions, characteristic functions, moment inequalities, sampling distributions, modes of convergence and their interrelationships, laws of large numbers, central limit theorem, and stochastic processes.

A fundamental course in statistical inference. Discusses general principles of data reduction: exponential families, sufficiency, ancillarity and completeness. Describes general methods of point and interval parameter estimation and the small and large sample properties of estimators: method of moments, maximum likelihood, unbiased estimation, Rao-Blackwell and Lehmann-Scheffe theorems, information inequality, asymptotic relative efficiency of estimators.

Describes general methods of hypothesis testing and optimality properties of tests: Neyman-Pearson theory, likelihood ratio tests, score and Wald tests, uniformly and locally most powerful tests, asymptotic relative efficiency of tests.

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Introduction to the data structures and computer algorithms that are relevant to statistical computing. The implementation of data structures and algorithms for data management and numerical computations are discussed. An advanced course in linear models, including both classical theory and methods for high dimensional data.

Topics include theory of estimation and hypothesis testing, multiple testing problems and false discovery rates, cross validation and model selection, regularization and the LASSO, principal components and dimensional reduction, and classification methods. Background in matrix algebra and linear regression required. A foundational course in measure theoretic probability.

Topics include measure theory, Lebesgue integration, product measure and Fubini's Theorem, Radon-Nikodym derivatives, conditional probability, conditional expectation, limit theorems on sequences of random stochastic processes, and weak convergence. Course Prerequisites: BST or permission from the instructor required. Sequel to BIO Considers several advanced topics in statistical inference.

Topics include limit theorems, multivariate delta method, properties of maximum likelihood estimators, saddle point approximations, asymptotic relative efficiency, robust and rank-based procedures, resampling methods, and nonparametric curve estimation. Presents classical and modern approaches to the analysis of multivariate observations, repeated measures, and longitudinal data.

Topics include the multivariate normal distribution, Hotelling's T2, MANOVA, the multivariate linear model, random effects and growth curve models, generalized estimating equations, statistical analysis of multivariate categorical outcomes, and estimation with missing data. Discusses computational issues for both traditional and new methodologies. BST is a seminar style course with readings selected from the literature in areas of expertise of the participating faculty.

Content may vary from year to year. The specific objectives are 1 To train students to critically read foundational papers and current journal articles in Statistical Genetics, 2 To train students to present sophisticated ideas to an audience of peers, and 3 To prepare students to engage in doctoral level research in the area.

After the course, students are expected to have an in-depth and broad understanding on important topics of statistical genetics research. BIO may be taken concurrently. General principles of the Bayesian approach, prior distributions, hierarchical models and modeling techniques, approximate inference, Markov chain Monte Carlo methods, model assessment and comparison. Bayesian approaches to GLMMs, multiple testing, nonparametrics, clinical trials, survival analysis.

The course will build upon our existing course, BST Introduction to Data Science, in presenting a set of tools for modeling and understanding complex datasets. Specifically, the course will provide practical regression and tree-based techniques for big data. Specific topics that will be covered include: linear model selection and regularization: LASSO and regularization; principal component regression and partial least squares; tree-based methods: decision trees; bagging, random forests, and boosting; unsupervised learning: principal components analysis, cluster analysis.

Programming Python and R and case studies will be used throughout the course to provide hands-on training in these concepts. Prerequisites: BST or permission of instructor.

### Epidemiology Course Checklist

Many systems of scientific and societal interest consist of a large number of interacting components. The structure of these systems can be represented as networks where network nodes represent the components and network edges the interactions between the components. Network analysis can be used to study how pathogens, behaviors and information spread in social networks, having important implications for our understanding of epidemics and the planning of effective interventions. In a biological context, at a molecular level, network analysis can be applied to gene regulation networks, signal transduction networks, protein interaction networks, and more.

This introductory course covers some basic network measures, models, and processes that unfold on networks. The covered material applies to a wide range of networks, but we will focus on social and biological networks. To analyze and model networks, we will learn the basics of the Python programming language and its Network X module. The course contains a number of hands-on computer lab sessions.

There are five homework assignments and four reading assignments that will be discussed in class. In addition, each student will complete a final project that applies network analysis techniques to study a public health problem. This course is an introduction to modern statistical computing techniques used to characterize and interpret cancer genome sequencing datasets.

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This Master's level course will begin with a basic introduction to DNA, genes, and genomes for students with no biology background. It will then introduce cancer as an evolutionary process and review landmarks in the history of cancer genetics, and discuss the basics of sequencing technology and modern Next Generation Sequencing. By the end of the course, students will be able to apply state-of-the art analysis to cancer genome datasets and to critically evaluate papers employing cancer genome data. Epigenetics is a fast growing field, with increasing applicability in environmental and epidemiology studies, focusing on the alterations in chromatin structure that can stably and heritably influence gene expression.

Epigenetic changes can be as profound as those exerted by mutation, but, unlike mutations, are reversible and responsive to environmental influences. The course will focus on epigenetic mechanisms and laboratory methods for DNA methylamine, his tone modifications, small non-coding RNAs, and epigenomics. EPI introduces the principles and methods used in epidemiologic research.