T-tests, confidence intervals, power, type I/II errors. Exploratory data analysis. Simple linear regression, regression in matrix notation, multiple regression, diagnostics. Ordinary least squares, violations, generalized least squares, nonlinear least squares regression. Introduction to General linear Model. SAS and S-Plus used. prereq: [[Stat 5101 or concurrent registration is required (or allowed) in Stat 5101], biostatistics major] or instr consent

This course introduces students to a variety of concepts, tools, and techniques that are relevant to the rigorous design and analysis of complex biomedical studies. Topics include ANOVA, sample-size calculations, multiple testing, missing data, prediction, diagnostic testing, smoothing, variable selection, the bootstrap, and nonparametric tests. R software will be used. Biostatistics students are strongly encouraged to typeset their work using LaTeX or in R markdown. prereq: [7405, [STAT 5102 or concurrent registration is required (or allowed) in STAT 5102], biostatistics major] or instr consent

Introduction to and methodology of randomized clinical trials. Design issues, sample size, operational details, interim monitoring, data analysis issues, overviews. prereq: 6451 or concurrent registration is required (or allowed) in 6451 or 7406 or instr consent

Statistical methodologies in analysis of survival data. Kaplan-Meier estimator, Cox's proportional hazards multiple regression model, time-dependent covariates, analysis of residuals, multiple failure outcomes. Typical biomedical applications, including clinical trials and person-years data. prereq: 7405, [STAT 5101 or STAT 8101]

Correlated data arise in many situations, particularly when observations are made over time and space or on individuals who share certain underlying characteristics. This course covers techniques for exploring and describing correlated data, along with statistical methods for estimating population parameters (mostly means) from these data. The focus will be primarily on generalized linear models (both with and without random effects) for normally and non-normally distributed data. Wherever possible, techniques will be illustrated using real-world examples. Computing will be done using R and SAS. prereq: Regression at the level of PubH 6451 or PubH 7405 or Stat 5302. Familiarity with basic matrix notation and operations (multiplication, inverse, transpose). Working knowledge of SAS or R (PubH 6420).

This course examines the professional roles, responsibilities and analytic skills of the practicing biostatistician as consultant and collaborator in health science research. The spectrum of roles will be explored through lecture, readings, discussion, written assignments, and participation in statistical consulting sessions with investigators at the University of Minnesota and in the community. prereq: PubH 7405-7406 (or Stat 8051-8052) and Stat 5101-5102 (or Stat 8101-8102); Biostatistics graduate student.

Logical development of probability, basic issues in statistics. Probability spaces. Random variables, their distributions and expected values. Law of large numbers, central limit theorem, generating functions, multivariate normal distribution. prereq: (MATH 2263 or MATH 2374 or MATH 2573H), (MATH 2142 or CSCI 2033 or MATH 2373 or MATH 2243)

Review of linear algebra. Introduction to probability theory. Random variables, their transformations/expectations. Standard distributions, including multivariate Normal distribution. Probability inequalities. Convergence concepts, including laws of large numbers, Central Limit Theorem. delta method. Sampling distributions. prereq: Statistics grad major or instr consent

Sampling, sufficiency, estimation, test of hypotheses, size/power. Categorical data. Contingency tables. Linear models. Decision theory. prereq: [5101 or Math 5651 or instr consent]

Statistical inference. Sufficiency. Likelihood-based methods. Point estimation. Confidence intervals. Neyman Pearson hypothesis testing theory. Introduction to theory of linear models. prereq: 8101, Statistics graduate major or instr consent

In this course we will examine values, contexts, principles, and frameworks of public health. We will provide an introduction to public health, consider the history of public health, social/political determinants, impact of health disparities on race, class and gender, moral and legal foundations, public health structures, historical trauma and cultural competence, health and human rights, advocacy and health equity, communication and financing, and the future of public health in the 21st century. Grounded in theory and concepts, we will incorporate core competencies and skills for public health professionals and will focus on developing problem solving and decision-making skills through critical analysis, reflection, case studies, readings, and paper assignments.

Use of SAS for analysis of biomedical data. Data manipulation/description. Basic statistical analyses (t-tests, chi-square, simple regression).

This course is intended for students, both within and outside the School of Public Health, who want to learn how to manipulate data, perform simple statistical analyses, and prepare basic visualizations using the statistical software R. While the tools and techniques taught will be generic, many of the examples will be drawn from biomedicine and public health.

This course is intended for students who are relatively proficient with R, and are looking to improve their coding and data analysis skills. The emphasis will be on learning tools and techniques which are useful to students who will be doing non-trivial programming and/or data analysis in either a research or production environment.

Statistical computing using SAS, Splus, and FORTRAN or C. Use of pseudo-random number generators, distribution functions. Matrix manipulations with applications to regression and estimation of variance. Simulation studies, minimization of functions, nonlinear regression, macro programming, numerical methods of integration. prereq: [7405, biostatistics major, [C or FORTRAN]] or instr consent

Various statistical techniques for extracting useful information (i.e., learning) from data. Linear discriminant analysis, tree-structured classifiers, feed-forward neural networks, support vector machines, other nonparametric methods, classifier ensembles, unsupervised learning. prereq: [[[6450, 6452] or equiv], programming backgroud in [FORTRAN or C/C++ or JAVA or Splus/R]] or instr consent; 2nd yr MS recommended

Introduction to Bayesian methods. Comparison with traditional frequentist methods. Emphasizes data analysis via modern computing methods: Gibbs sampler, WinBUGS software package. prereq: [[7401 or STAT 5101 or equiv], [public health MPH or biostatistics or statistics] grad student] or instr consent

Introduction to statistical problems arising in molecular biology. Problems in physical mapping (radiation hybrid mapping, DDP), genetic mapping (pedigree analysis, lod scores, TDT), biopolymer sequence analysis (alignment, motif recognition), and micro array analysis. prereq: [6450, [6451 or equiv]] or instr consent; background in molecular biology recommended

Diagnostic medicine, including methods for ROC curve. Bioassays. Early-phase clinical trials, methods including dose escalation, toxicity, and monitoring. Quality of life. prereq: [[6450, 6451] or equiv], [grad student in biostatistics or statistics or clinical research], familiarity with SAS

Although most of statistical inference focuses on associational relationships among variables, in many biomedical and health sciences contexts the focus is on establishing the causal effect of an intervention or treatment. Drawing causal conclusions can be challenging, particularly in the context of observational data, as treatment assignment may be confounded. The first part of this course focuses on methods to establish the causal effect of a point exposure, i.e., situations in which treatment is given at a single point in time. Methods to estimate causal treatment effects will include outcome regression, propensity score methods (i.e., inverse weighting, matching), and doubly robust approaches. The second half of the course focuses on estimating the effect of a series of treatment decisions during the course of a chronic disease such as cancer, substance abuse, mental health disorders, etc. Methods to estimate these time-varying treatments include marginal structural models estimated by inverse probability weighting, structural nested models estimated by G-estimation, and the (parametric) G-computation algorithm. We will then turn our attention to estimating the optimal treatment sequence for a given subject, i.e., how to determine “the right treatment, for the right patient, at the right time,” using dynamic marginal structural models and methods derived from reinforcement learning (e.g., Q-learning, A-learning) and classification problems (outcome weighted learning, C-learning). PubH 8485 is appropriate for Ph.D students in Biostatistics and Statistics. The homework and projects will focus more on the theoretical aspects of the methods to prepare students for methodological research in this area. PubH 7485 is appropriate for Masters students in Biostatistics and PhD students in other fields who wish to learn causal methods to apply them to topics in the health sciences. This course uses the statistical software of R, a freely available statistical software package, to implement many of the methods we discuss. However, most of the methods discussed in this course can be implemented in any statistical software (e.g., SAS, Stata, SPSS, etc.) and students will be free to use any software for homework assignments. prereq: Background in regression (e.g. linear, logistic, models) at the level of PubH 7405-7406, PubH 6450-6451, PubH 7402, or equiv. Background in statistical theory (Stat 5101-5102 or PubH 7401) is helpful.

Spatial data, spatial statistical models, and spatial inference on unknown parameters or unobserved spatial data. Nature of spatial data. Special analysis tools that help to analyze such data. Theory/applications. prereq: [[STAT 5101, STAT 5102] or [STAT 8101, STAT 8102]], some experience with S-plus; STAT 8311 recommended

MPH students complete an integrative learning experience (ILE) that demonstrates synthesis of foundational and concentration competencies. Students in consultation with faculty select foundational and concentration-specific competencies appropriate to the student?s educational and professional goals. prereq: Biostatistics program, instr consent