Course subject: Statistics (STAT)

This course will provide students with an overview of the rationale and stages involved in the conduct of a formal systematic review and meta-analysis of a well-defined clinical/health research question. The overarching aim is to provide students with the tools to critically appraise and conduct a systematic review and meta-analysis. Students will largely work in pairs to progress through each step involved (with feedback from instructors at each stage) and to produce a final systematic review and meta-analysis to be presented/submitted at the end of the course. Course Objectives: 1. To demonstrate an understanding of the rationale underlying a systematic review and meta-analysis and relevance to clinical care and health policy; 2. To critically appraise a systematic review; 3. To develop a focused research question amenable to a systematic review; 4. To develop and implement a comprehensive and systematic literature search strategy; 5. To determine and apply procedures for including/excluding potential studies for a systematic review and meta-analysis; 6. To develop and implement a data abstraction process and study database; 7. To demonstrate an understanding of the fundamental statistical/biostatistical issues relevant to the conduct of a formal systematic review and meta-analysis. 8. To perform statistical analyses for a systematic review and meta-analysis and complete/present a final report demonstrating all stages involved. Students will need to meet with Course Coordinators and provide of appropriate previous experience with linear and/or logistic regression techniques.

Review of normal linear regression and maximum likelihood estimation. Computational methods, including Newton-Raphson and iteratively reweighted least squares. Binomial regression; the role of the link function. Goodness-of-fit, goodness-of-link, leverage. Poisson regression models. Generalized linear models. Other topics in regression modelling.

Statistical methods for improving processes based on observational data. Assessment of measurement systems. Strategies for variation reduction. Process monitoring, control and adjustment. Clue generation techniques for determining the sources of variability. Variation transmission.

Introduction to and application of computational methods in statistical inference. Monte Carlo evaluation of statistical procedures, exploration of the likelihood function through graphical and optimization techniques. Topics include expectation-maximization, bootstrapping, Markov Chain Monte Carlo, and other computationally intensive methods.

Visualization methods applied to data. Both human perception and statistical properties inform the methods used to display and visually explore categorical, continuous, time-ordered, map, and high dimensional data. Order and layout effects on tables and graphics. Statistical concepts visually presented include variability, densities, quantiles, conditioning, and hypothesis testing. Interactive graphics include linking, brushing, motion, and the navigation of high dimensional spaces guided via projection indices. Glyphs (e.g. cartoon, statistical, or heatmap) and radial and parallel coordinates.

This is a foundational survey course designed for Data Science students who do not have an undergraduate degree in statistics. It provides an understanding and appreciation of the essential statistical concepts needed for Data Science. It has modular design with the following modules: probability for statistics, concepts of statistical inference, simulation and Monte Carlo methods, regression modelling, planning empirical studies, and drawing conclusions from data. Emphasis will be on exposing students to the core concepts and illustrating them largely through examples.

Discussion of inference problems under the headings of hypothesis testing and point and interval estimation. Frequentist and Bayesian approaches to inference. Construction and evaluation of tests and estimators. Large sample theory of point estimation.

Probability measures, random variables as measurable functions, expectation, independence, characteristic functions, limit theorems, applications.

Review of basic numerical methods. Simulation of random variables, stochastic processes and stochastic models in finance. Numerical solution of deterministic and stochastic differential equations. Valuation of complex financial instruments and derivative securities. Project and paper.

Multivariate normal and Wishart distributions, estimation and hypothesis testing of mean vectors and covariance matrices and their extensions to high-dimensional setting (n<p), principal component analysis (PCA), factor analysis, canonical analysis, discrimination, and classification with a focus on linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA). Precision matrices for high-dimensional data, high dimensional, and sparse PCA, Nonlinear PCA.

Multiple time series modeling including transfer function and intervention analysis. Various special topics in time series such as outliers, robustness, order determination methods, Kalman filtering, sampling and aggregation, seasonal adjustments.

In this course, we will cover classification and prediction in health research with a view to applications to screening and diagnosis of disease. This will lead to methods for evaluating the performance of various types of statistical models and learning techniques/algorithms. Cross-validation and bootstrap approaches will be introduced for model performance evaluation, and we will discuss discrimination and calibration as different components of prediction performance. We will cover variable selection techniques, including for high-dimensional data, with an emphasis on regularization techniques such as the LASSO and its variants. Model validation, both internal and external, and model updating will be covered, and we will also discuss post-model selection inference. An important focus will be on biomarker evaluation for a given disease, potentially connected to therapy, and leading to coverage of precision/personalized medicine. Finally, there will be coverage on the importance of reproducible and replicable research. Examples from different problems in health, including genetics, will be presented, and software (e.g. R or SAS) will be used throughout the course.

This course covers methods for analyzing data in which repeated measures have been obtained for individuals in health studies over time. Different methods will be discussed to handle both continuous and discrete longitudinal response data, with examples from biomedical and population health datasets. Some of the approaches covered will include linear, non-linear, and generalized linear mixed effects models, as well as generalized estimating equations and transition models, with distinctions drawn between subject-specific and population averaged approaches for generalized linear longitudinal response data. Also, there will be coverage of exploratory methods, evaluation of model assumptions and adapting to assumption violations, approaches for handling missing data, and treatment of advanced topics such as semiparametric and nonparametric models for longitudinal data. Software (e.g. R or SAS) will be used throughout the course.

Deep learning uses artificial neural networks to create representations of data with multiple levels of abstraction. Deep learning usually refers to a set of algorithms and computational models that are composed of multiple processing layers. These methods have significantly improved the state-of-the-art in many domains including Natural Language Processing (NLP), Natural Language Understanding (NLU), Speech Recognition, Computer Vision, Classification, Pattern Recognition and Bioinformatics. This course will cover the modern practice of deep networks, different architectures of deep networks including feed forward and convolutional models, methods for sequence modeling, variational and adversarial models, attention mechanism and optimization and regularization for deep models.

Topics of current interest