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.

This course will provide an introduction to principles and methods for the analysis of longitudinal data. Conditional and random effect of modeling approaches to regression analysis will be covered, as well as semiparametric methods based on generalized estimating equations. The importance of model assessment and parameter interpretation will be emphasized. Problems will be motivated by applications in epidemiology, clinical medicine, health services research, and disease natural history studies. Students will be required to think critically about appropriate strategies for data analysis. Analysis will be carried out with appropriate statistical software.

Given known group membership, methods which learn from data how to classify objects into the groups are treated. Review of likelihood and posterior based discrimination. Main topics include logistic regression, neural networks, tree-based methods and nearest neighbour methods. Model assessment, training and tuning.

Methods for finding surfaces in high dimensions from incomplete or noisy functional information. Both data adaptive and methods based on fixed parametric structure will be treated. Model assessment, training and tuning.

This course introduces Data Science students to exploratory data analysis with a focus on the concepts and tools necessary for understanding and successfully undertaking an end to end exploratory analysis of large and complex data. All stages of data collection, preparation and cleaning, importation into a statistical programming environment, data manipulation, as well as analysis and visualization will be treated. Material will be presented via case studies which will involve hands on programming and analysis. Methods and models (both statistical and computational) will be introduced as needed according to the nature of the data encountered in each case. The case studies will be chosen to give a breadth of experience to the student. A modern statistical programming language will be used throughout.

Sources of survey error. Probability sampling designs, estimation and efficiency comparisons. Distribution theory and confidence intervals. Generalized regression estimation. Software for survey analysis.

This course acts as a capstone on the coursework based part of the PhD program and as a stepping stone to the PhD proposal and to research. It is aimed at developing research skills: critically reading published research, summarizing and synthesizing areas of research, writing and orally presenting summaries of research problems, data sets and theoretical and applied results. The course is designed to be integrative across core areas of the student discipline.

Review of conditioning on sigma-fields; martingale theory (discrete and continuous-time) and applications; counting processes; Brownian motion; stochastic differential and integral equations and applications; general theory of Markov processes (including martingale problems and semigroup theory), diffusions; weak convergence of stochastic processes on function spaces; functional versions of the central limit theorem and strong laws; convergence of empirical processes.

Principles of Inference: sufficiency, conditionality, and likelihood; examples and counter examples; conditional inference and ancillarity. Theory of Hypothesis Testing: Neyman-Pearson lemma; similar tests; invariant tests. Asymptotic Theory: maximum likelihood and related theory; large-sample properties of parametric significance tests. Interval Estimation: confidence intervals and significance intervals; location and scale models, conditional intervals. Introduction to Decision Theory: loss and risk functions, admissibility; minimax and Bayes rules; prior and posterior analysis. The course content of Stat 850 is a presumed prerequisite for Stat 908.

Iterative model building. ARIMA models, application to forecasting, seasonal models, applications.

Causal inference in health research will be covered. Methods for the design and analysis of randomized controlled trials including randomization techniques, sample size and power calculations, and specialized additional topics including missing data, noncompliance, and ethics. The design and analysis of classical and modern epidemiological studies will then be discussed for settings in which randomization is not feasible. Causal inference methodologies for the analysis of observational data include propensity scores, marginal structural models and instrumental variables. Studies will be discussed from the epidemiological literature and other sources in the public domain. Simulations and data analyses will be carried out using software (e.g. R or SAS). Students will be trained and assessed in part based on the preparation of reports and delivery of presentations.

This course deals with methods of analyzing data on the time to failure with particular emphasis on the use of regression models for such data. Both parameteric and semi-parametric regression models will be considered.

This course will cover some of the basic tools of a statistical consultant. Topics will include the use of statistical packages, problem-solving techniques, discussion of common statistical consulting problems, effective communication of statistical concepts and management of consulting sessions.

Topics of current interest