PUBH 3415 Introduction to Clinical Trials (3 credits / Fall, Summer)
Phases of trials, hypotheses/endpoints, choice of intervention/control, ethical considerations, blinding/randomization, data collection/monitoring, sample size, analysis strategies. Protocol development/implementation, interactive discussion boards.

Prerequisites: PUBH 3415 enrollees must have one semester of undergraduate level introductory biostatistics or statistics (STAT 3011, EPSY 3264, SOC 3811, BIOL 3272, or instr consent) AND junior or senior standing or instructor consent.

PUBH 6414 Biostatistical Literacy (3 credits / Fall, Spring, Summer)
Develop ability to read/interpret statistical results in primary literature. Minimal calculation. No formal training in any statistical programming software. Biostatistical Literacy will cover the fundamental concepts of study design, descriptive statistics, hypothesis testing, confidence intervals, odds ratios, relative risks, adjusted models in multiple linear, logistic and Poisson regression, and survival analysis. The focus will be when to use a given method and how to interpret the results, not the actual computation or computer programming to obtain results from raw data.

Prerequisites: MPH or certificate student or environmental health or instructor consent

PUBH 6420 Introduction to SAS Programming (1 credit / Fall, Summer)
Use of SAS for analysis of biomedical data. Data manipulation/description. Basic statistical analyses (t-tests, chi-square, simple regression).

PUBH 6431 Topics in Hierarchical Bayesian Analysis (1 credit / May Session)
Hierarchical Bayesian methods combine information from various sources and are increasingly used in biomedical and public health settings to accommodate complex data and produce readily interpretable output. This course will introduce students to Bayesian methods, emphasizing the basic methodological framework, real-world applications, and practical computing.

PUBH 6432 Biostatistical Methods in Translational and Clinical Research (1 credit / May Session)
This short course on translational and clinical research will focus on the topics of diagnostic medicine and designing clinical research methods, application of regression models and early phase clinical trials.

Prerequisites: Students will benefit from having taken one or two semester courses in biostatistics or applied statistics covering up to and including multiple regression and introductory logistic regression.

PUBH 6450 Biostatistics I (4 credits / Fall, Spring)
Descriptive statistics. Gaussian probability models, point/interval estimation for means/proportions. Hypothesis testing, including t, chi-square, and nonparametric tests. Simple regression/correlation. ANOVA. Health science applications using output from statistical packages.

Prerequisites: [College-level algebra, health sciences grad student] or instructor consent

PUBH 6451 Biostatistics II (4 credits / Fall, Spring)
Two-way ANOVA, interactions, repeated measures, general linear models. Logistic regression for cohort and case-control studies. Loglinear models, contingency tables, Poisson regression, survival data, Kaplan-Meier methods, proportional hazards models.

Prerequisites: [[[6420, 6450] with grade of at least B, health sciences grad student] or instructor consent

PUBH 6470 SAS Procedures and Data Analysis (3 credits / Fall)
SAS procedures, how they are used in various health-related datasets to answer specific problems regarding estimation, testing, or prediction.

Prerequisites: [6450, 6451] or [7405, 7406] or [Stat 5101, Stat 5102]

PUBH 7401 Fundamentals of Biostatistical Inference (4 credits / Fall)
Part of two-course sequence intended for PhD students in School of Public Health who need rigorous approach to probability/statistics/statistical inference with applications to research in public health.

Prerequisites: Background in calculus; intended for PhD students in public health and other health sciences who need rigorous approach to probability/statistics and statistical inference with applications to research in public health

PUBH 7402 Biostatistics Modeling and Methods (4 credits / Spring)
Second of two-course sequence. Rigorous approach to probability/statistics, statistical inference. Applications to research in public health.

Prerequisites: 7401; intended for PhD students in health sciences

PUBH 7415 Introduction to Clinical Trials (3 credits / Fall, Summer)
Hypotheses/endpoints, choice of intervention/control, ethical considerations, blinding/randomization, data collection/monitoring, sample size, analysis, writing. Protocol development, group discussions.

Prerequisites: 6414 or 6450 or one semester graduate-level introductory biostatistics or statistics or instructor consent

PUBH 7405 Biostatistics: Regression (4 credits / Fall)
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.

Prerequisites: [[Stat 5101 or concurrent registration is required (or allowed) in Stat 5101], biostatistics major] or instructor consent

PUBH 7406 Advanced Regression and Design (4 credits / Spring)
Topics include maximum likelihood estimation, single and multifactor analysis of variance, logistic regression, log-linear models, multinomial logit models, proportional odds models for ordinal data, gamma and inverse-Gaussian models, over-dispersion, analysis of deviance, model selection and criticism, model diagnostics, and an introduction to non-parametric regression methods. R is used.

Prerequisites: [7405, [STAT 5102 or concurrent registration is required (or allowed) in STAT 5102], biostatistics major] or instructor consent

PUBH 7420 Clinical Trials: Design, Implementation, and Analysis (3 credits / Spring)
Introduction to and methodology of randomized clinical trials. Design issues, sample size, operational details, interim monitoring, data analysis issues, overviews.

Prerequisites: 6451 or concurrent registration is required (or allowed) in 6451 or 7406 or instructor consent

PUBH 7430 Statistical Methods for Correlated Data (3 credits / Fall)
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.

PUBH 7440 Introduction to Bayesian Analysis (3 credits / Spring)
Introduction to Bayesian methods. Comparison with traditional frequentist methods. Emphasizes data analysis via modern computing methods: Gibbs sampler, WinBUGS software package.

Prerequisites: [[7401 or STAT 5101 or equiv], [public health MPH or biostatistics or statistics] grad student] or instructor consent

PUBH 7445 Statistics for Human Genetics and Molecular Biology (3 credits / Fall)
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.

Prerequisites: [6450, [6451 or equiv]] or instructor consent; background in molecular biology recommended

PUBH 7450 Survival Analysis (3 credits / Fall)
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.

Prerequisites: 7406, [STAT 5102 or STAT 8102]

PUBH 7460 Advanced Statistical Computing (3 credits / Fall)
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.

Prerequisites: [7405, biostatistics major, [C or FORTRAN]] or instructor consent

PUBH 7465 Biostatistics Consulting (3 credits / Spring)
Professional roles/responsibilities of practicing biostatistician as consultant/collaborator in health science research. Discussion, written assignments, student presentations, meeting notes, interviews, guests.

Prerequisites: [[[7405, 7406, 7407] or [STAT 8051, STAT 8052]], [[STAT 5101, STAT 5102] or [STAT 8101, STAT 8102]], biostatistics major] or instructor consent

PUBH 7470 Statistics for Translational and Clinical Research (3 credits / Fall)
Diagnostic medicine, including methods for ROC curve. Bioassays. Early-phase clinical trials, methods including dose escalation, toxicity, and monitoring. Quality of life.

Prerequisites: [[6450, 6451] or equiv], [grad student in biostatistics or statistics or clinical research], familiarity with SAS

PUBH 7475 Statistical Learning and Data Mining (3 credits / Spring)
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.

Prerequisites: [[[6450, 6452] or equiv], programming background in [FORTRAN or C/C++ or JAVA or Splus/R]] or instructor consent; 2nd year MS recommended

PUBH 8401 Linear Models (4 credits / Fall)
Theory/application of statistical techniques for regression analysis. Computing for linear models. Modeling, computation, data analysis.

Prerequisites: [[7405, concurrent registration is required (or allowed) in STAT 8101] or instructor consent], calculus, familiar with matrix/linear algebra

PUBH 8403 Research Skills in Biostatistics (1 credit / Fall)
Introduces research skills necessary for writing/defending dissertation, career in research.

Prerequisites: Stat 8101-02 and admission to PhD program in Biostatistics. The course is meant to be taken the fall before PhD written exam is attempted, so Schedule 2 students typically wait to enroll until second year in program.

PUBH 8412 Advanced Statistical Inference (3 credits / Spring)
Overview of inferential methods needed for biostatistical research. Topics without overt reliance on measure-theoretic concepts. Classic likelihood inference, asymptotic distribution theory, robust inferential methods (M-estimation).

Prerequisites: Stat 8101-8102 or equivalent, students should be comfortable with multivariate normal distribution/have some introduction to convergence concepts

PUBH 8422 Modern Nonparametrics (3 credits / Fall)
Classical nonparametric inference, exact tests, and confidence intervals. Robust estimates. The jackknife. Bootstrap and cross-validation. Nonparametric smoothing and classification trees. Models/applications. Formal development sufficient for understanding statistical structures/properties. Substantial computing.

Prerequisites: [7406, STAT 5102, [public health or grad student]] or instructor consent

PUBH 8432 Probability Models (3 credits / Fall)
Three basic models used for stochastic processes in the biomedical sciences: point processes (emphasizes Poisson processes), Markov processes (emphasizes Markov chains), and Brownian motion. Probability structure and statistical inference studied for each process.

Prerequisites: [7450, 7407, Stat 5102, [advanced biostatstics or statistics] major] or instructor consent

PUBH 8442 Bayesian Decision Theory and Data Analysis (3 credits / Spring)
Theory/application of Bayesian methods. Bayesian methods compared with traditional, frequentist methods.

Prerequisites: [[7460 or experience with FORTRAN or with [C, S+]], Stat 5101, Stat 5102, Stat 8311, grad student in [biostatistics or statistics]] or instructor consent

PUBH 8445 Statistics for Human Genetics and Molecular Biology (3 credits / Fall)
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.

Prerequisites: [[[Stat 8101, Stat 8102] or equiv], PhD student] or instructor consent; some background with molecular biology desirable

PUBH 8446 Advanced Statistical Genetics and Genomics (3 credits / Spring)
Genetic mapping of complex traits in humans, modern population genetics with an emphasis on inference based observed molecular genetics data, association studies; statistical methods for low/high level analysis of genomic/proteomic data. Multiple comparison and gene network modeling.

Prerequisites: [7445, statistical theory at level of STAT 5101-2; college-level molecular genetics course is recommended] or instructor consent

PUBH 8452 Advanced Longitudinal Data Analysis (3 credits / Fall)
Methods of inference for outcome variables measured repeatedly in time or space. Linear/nonlinear models with either normal or non-normal error structures. Random effects. Transitional/marginal models with biomedical applications.

Prerequisites: [Stat 5102, Stat 8311, experience with [SAS or S+], advanced [biostats or stat] student] or instructor consent

PUBH 8462 Advanced Survival Analysis (3 years / Spring)
Statistical methods for counting processes. Martingale theory (transforms, predictable processes, Doob decomposition, convergence, submartingales). Applications to nonparametric intensity estimation. Additive/relative risk models. Inference for event history data, recurrent events, multivariate survival, diagnostics.

Prerequisites: [7450, 8432, Stat 5102, advanced [biostatistics or statistics] major] or instructor consent

PUBH 8472 Spatial Biostatistics (3 credits / Spring)
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.

Prerequisites: [[STAT 5101, STAT 5102] or [STAT 8101, STAT 8102]], some experience with S-plus; STAT 8311 recommended

PUBH 8482 Sequential and Adaptive Methods for Clinical Trials (3 credits / Fall)
Statistical methods for design/analysis of sequential experiments. Wald theorems, stopping times, martingales, Brownian motion, dynamic programming. Compares Bayesian/frequentist approaches. Applications to interim monitoring of clinical trials, medical surveillance.

Prerequisites: Stat 8101-8102 or equivalent, [students should be comfortable with the multivariate normal distribution or instr consent]

PUBH 8492 Theories of Hierarchical and Other Richly Parametrized Linear Models (3 credits / Spring)
Linear richly-parameterized models. Hierarchical/dynamic/linear/linear mixed models. Random regressions. Smoothers, longitudinal models. Schemes for specifying/fitting models. Theory/computing for mixed-linear-models. Richly parameterized models and the odd/surprising/undesirable results in applying them to data sets. Lectures, class project.

Prerequisites: [[8401 or STAT 8311], [[STAT 8101, STAT 8102] or equiv], [biostatistics or statistics] PhD student] or instructor consent