STAT 631Introduction to Statistacl Methods in Health Informatics0.50 units
Exploratory data analysis and data visualization. Confounding, censoring, selection bais, study designs and meta-analysis. Statistical modelling for continuous and binary data. Use of a statistics package, such as SAS, to analyze case studies will be imporant throughout. This is open only to students registered in the Masters of Health Informatics plan.
Review of experimental designs in a regression setting; analysis of variance; replication, balance, blocking, randomization, and interaction; one-way layout, two-way layout, and Latin square as special cases; factorial structure of treatments; covariates; treatment contrasts; two-level fractional factorial designs; fixed versus random effects; split-plot and repeated-measures designs; other topics.
STAT 831Generalized Linear Models and Applications0.50 units
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.
STAT 835Statistical Methods for Process Improvement0.50 units
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.
STAT 836Introduction to the Analysis of Spatial Data in Health Research0.50 units
The objective of this course is to develop understanding and working knowledge of spatial models and analysis of spatial data. The course provides an introduction to the rudiments of statistaical inference based on spatially correlated data. Methods of estimation and testing will be developed for geostatistical models based on variograms and spatial autoregressive models. Concepts and application of methods will be emphasized through case studies and projects with health applications.
STAT 837Analysis of Longitudinal Data in Health Research0.50 units
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.
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 including EM. Bootstrapping, Markov Chain Monte Carlo, and other computationally intensive methods.
STAT 841Statistical Learning - Classification0.50 units
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.
Visualization of high dimensional data including interactive methods directed at exploration and assessment of structure and dependencies in data. Methods for finding groups in data including traditional and modern methods of cluster analysis. Dimension reduction methods including multi-dimensional scaling, nonlinear and other methods.
STAT 844Statistical Learning - Function Estimation0.50 units
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.
STAT 850Estimation and Hypothesis Testing0.50 units
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.
Sources of survey error. Probability sampling designs, estimation and efficiency comparisons. Distribution theory and confidence intervals. Generalized regression estimation. Software for survey analysis.
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.
STAT 906Computer Intensive Methods for Stochastic Models in Finance0.50 units
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.
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.
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.
STAT 931Statistical Methods for the Design and Analysis of Epidemiological Studies0.50 units
This course covers a wide range of topics pertaining to the design and statistical analysis of observational health studies. The course is divided into three areas:
1) classical epidemiological study designs including cross-sectional, cohort, population and family-based case-control studies, and issues related to selection of controls;
2) advanced epidemiological study designs including case-cohort, nested case-control, and multiphase sampling designs;
3) causal inference using propensity scores with matching, stratification and regression adjustments, 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.
STAT 932Statistical Methods for the Design and Analysis of Randomized Intervention Trials0.50 units
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 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 is designed to teach students the appropriate techniques for analyzing data that is collected over time. This data could arise from biomedical, population public health studies as well as finance and actuarial science applications. The course will teach how to recognize the added complexity of longitudinal data versus the univariate response data which is typically seen in introductory and generalized linear model courses. The course emphasizes the importance of the covariance structure for longitudinal responses. The students will study the difference between subject-specific and population-averaged models and how to recognize problems where one or the other approach might be more appropriate. They will be expected to use statistical software in applications in order to analyze longitudinal data.
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.
The focus of this course is on the statistical modelling, estimation and inference and forecasting of nonlinear financial time series, with a special emphasis on volatility and correlation of asset prices and returns. Topics to be covered normally include: review on distribution and dynamic behaviour of financial time series, univariate and multivariate GARCH processes, long-memory time-series processes, stochastic volatility models, modelling of extreme values, copulas, realized volatility and correlation modelling for ultra high frequency data and continuous time models.