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.

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 problems as extensions of univariate problems, discriminant analysis, canonical correlation and principle component analysis.

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.

This course covers topics relevant for the design, conduct and analysis of clinical intervention trials. The statistical theory behind the methodology as well as practical issues will be discussed. The course is divided into three areas: 1) important methods for the design of randomized controlled trials including randomization techniques, sample size and power calculations, factorial designs, crossover designs, cluster-randomized trials, non-inferiority trials, adaptive designs, group sequential trials, and ethical issues in design and conduct of clinical trials; 2) topics of predictive modeling including ROC curves, explained variation, and biomarker analyses; 3) dealing with missing data in randomized trials through imputation and inverse weighting, missing covariates, non-compliance, contamination, unplanned crossover, and surrogate outcomes. Clinical trials from the medical literature and other sources in the public domain will be used as case studies for illustration. Simulations and data analyses will be carried out using statistical 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 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