# Biostatistics Graduate Program

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# General Course Descriptions

Preliminary course descriptions follow. Staff is denoted in parentheses after course descriptions.

301. Introduction to Statistical Computing

This course is designed for students who seek to develop skills in statistical computing. Students will learn to use R and STATA for data manipulation, database querying, reporting generating, data presentation, and data tabulation and summarization. Topics will include organization and documentation of data, input and export of data sets, methods of cleaning data, tabulation and graphing of data, programming capabilities, and an introduction to simulations and bootstrapping. Students will also be introduced to LaTeX and Sweave for report writing. Students will also be briefly introduced to SAS and SQL programming. FALL. [2] (Fonnesbeck)

311. Principles of Modern Biostatistics

This is the first in a two-course series (311-312) designed for students who seek to develop skills in modern biostatistical reasoning and data analysis. Students will learn the statistical principles that govern the analysis of data in the health sciences and biomedical research. Traditional probabilistic concepts and modern computational techniques will be integrated with applied examples from biomedical and health sciences. Statistical computing uses the software packages STATA and R; prior familiarity with these packages is helpful but not required. Topics include: types of data, tabulation of data, methods of exploring and presenting data, graphing techniques (boxplots, q-q plots, histograms), indirect and direct standardization of rates, axioms of probability, probability distributions and their moments, properties of estimators, the Law of Large numbers, the Central Limit Theorem, theory of confidence intervals and hypothesis testing (one sample and two sample problems), paradigms of statistical inference (Frequentist, Bayesian, Likelihood), introduction to non-parametric techniques, bootstrapping and simulation, sample size calculations and basic study design issues. One-hour lab required; Students are required to take 311L concurrently. Prerequisite: Calculus I. Fall. [3] Greevy

311L. Principles of Modern Biostatistics Lab

This is a discussion section/lab for Principles of Modern Biostatistics. Students will review relevant theory and work on applications as a group. Computing solutions and extensions will be emphasized. Students are required to take 311 concurrently. Fall. [1] Greevy

312. Modern Regression Analysis

This is the second in a two-course series (311-312) designed for students who seek to develop skills in modern biostatistical reasoning and data analysis. Students learn modern regression analysis and model building techniques from an applied perspective. Theoretical principles will be demonstrated with real-world examples from biomedical studies. This course requires substantial statistical computing in the software packages STATA and R; familiarity with at least one of these packages is required. The course covers regression modeling for continuous outcomes, including simple linear regression, multiple linear regression, and analysis of variance with one-way, two-way, three-way and analysis of covariance models. This is a brief introduction to models for binary outcomes (logistic models), ordinal outcomes (proportional odds models), count outcomes (Poisson/Negative-Binomial models), and time-to-event outcomes (Kaplan-Meier curves, Cox proportional hazard modeling). Incorporated into the presentation of these models are subtopic topics such as regression diagnostics, nonparametric regression, splines, data reduction techniques, model validation, parametric bootstrapping, and a very brief introduction to methods for handling missing data. One-hour lab required; Students are required to take 312L concurrently. Prerequisite: Biostatistics 311 or equivalent; familiarity with STATA and R software packages. Spring. [3] Johnson

312L. Modern Regression Analysis Lab

This is a discussion section/lab for Modern Regression Analysis. Students will review relevant theory and work on applications as a group. Computing solutions and extensions will be emphasized. Students are required to take 312 concurrently. Spring. [1] Johnson

321. Clinical Trials and Experimental Design

This course covers the statistical aspects of study designs, monitoring and analysis. Emphasis is on studies of human subjects, i.e. clinical trials. Topics include: principles of measurement, selection of endpoints, bias, masking, randomization and balance, blocking, study designs, sample size projections, study conduct, interim monitoring of accumulating results, flexible and adaptive designs, sequential analysis, analysis principles, adjustment techniques, compliance, data and safety monitoring boards (DSMB), Institutional Review Boards (IRB), the ethics of animal and human subject experimentation, history of clinical trials, and the Belmont report. Spring (3) (Koyama)

323. Applied Survival Analysis

This course provides an introduction to methods for time-to-event data with censoring mechanisms. Topics include: life tables, nonparametric approaches (e.g., Kaplan-Meir, log-rank), semi-parametric approaches (e.g., Cox model), parametric approaches (e.g., Weibull, gamma, frailty), competing Risks (Introduce Poisson regression as connection to Cox model), and time-dependent covariates. Focus is on fitting the models and the relevance of those models for the biomedical application. Fall (4) (Chen, Q.)

330. Regression Modeling Strategies

The first part of the course presents the following elements of multivariable predictive modeling for a single response variable: using regression splines to relax linearity assumptions, perils of variable selection and over-fitting, where to spend degrees of freedom, shrinkage, imputation of missing data, data reduction, and interaction surfaces. Then a default overall modeling strategy will be described. This is followed by methods for graphically understanding models (e.g., using nomograms) and using re-sampling to estimate a model’s likely performance on new data. Then, the R rms package, which facilitates most steps of the modeling process, will be overviewed. Next, statistical methods related to binary logistic models and ordinal logistic and survival models will be covered. Five comprehensive case studies will be presented: an exploration of voting tendencies over U.S. counties in the 1992 presidential election, an exploration of the survival of Titanic passengers, developing a survival time model for critically ill patients, developing a Cox model in chronic disease, and developing a model for a longitudinal data analysis for serially collected data in a clinical trial, using generalized least squares. In the hands-on computer lab students themselves will develop, validate, and graphically describe multivariable regression models. Spring (3) (Harrell)

334. Statistical Genetics and Bioinformatics

This course provides an introduction to, and discusses, the statistical methodology of, genomics-inspired techniques and bioinformatics tools, including genome sequencing, DNA microarrays, proteomics, publicly available databases and software tools. Statistical topics include multiple hypothesis testing, clustering and classification, variable selection, hidden Markov model, and Bayesian networks. Methods for high-dimensional data analysis will also be illustrated and discussed.

336. Principles of Graphics

This course discusses the underlying goals in presenting and visualizing data, and how best to achieve those goals using different graphical techniques. Topics include: nomograms, principles of scaling, data summarization, theories of graphical perception and principles of graph construction.

338. Accommodating Missing Data

This course provides an in-depth exploration of methods for handling missing data. Topics include last observation carried forward, complete case analysis, pattern mixture models, predictive mean methods, MAR and MCAR assumptions, missingness in the response and covariates, and sensitivity analysis.

341. Fundamentals of Probability

This is the first in a two-course series (341-342) designed to teach the fundamental probabilistic and inferential framework in statistical probability and inference. Students learn probability theory and its application to everyday statistical concepts and analysis methods. Students will validate analytical solutions and explore limit theorems using R software. This course covers probability axioms, probability and sample space, events and random variables, probability inequalities, independence, discrete and continuous distributions,  expectations and variances, conditional expectation, moment generating functions, random vectors, convergence  concepts (in probability, in law, almost surely), Central Limit Theorem, weak and strong Law of Large Numbers, extreme value distributions, order statistics, exponential family. Fall (4) ( Shepherd)

342. Contemporary Statistical Inference

This is the second in a two-course series (341-342) designed to teach the fundamental probabilistic and inferential framework in statistical probability and inference. Students also learn classical methods of inference (hypothesis testing), and modes of inference (Frequentist, Bayesian and Likelihood approaches) and their surrounding controversies. Topics include: delta method, sufficiency, minimal sufficiency, ancillarity, completeness, conditionality principle, Fisher’s Information, Cramer-Rao inequality, hypothesis testing (likelihood ratios test, most powerful test, optimality, Neyman-Pearson lemma, inversion of test statistics), Likelihood principle, Law of Likelihood, Bayesian posterior estimation, Interval estimation (confidence intervals, support intervals, credible intervals), basic asymptotic and large sample theory, maximum likelihood estimation, re-sampling techniques (e.g., bootstrap). Spring (4) ( Blume)

345. Advanced Regression Analysis I (Linear & General Linear Models)

Students are exposed to a theoretical framework for linear and generalized models. First half of the semester covers linear models: multivariate normal theory, least squares estimation, limiting chi-square and F-distributions, sum of squares (partial, sequential) and expected sum of squares, weighted least squares, orthogonality, Analysis of Variance (ANOVA). Second half of the semester focuses on generalized linear models: binomial, Poisson, multinomial errors, introduction to categorical data analysis, conditional likelihoods, quasi-likelihoods, model checking, matched pair designs. Fall (4) (Kang)

346. Advanced Regression Analysis II (General Linear Models & Longitudinal Data Analysis)

Covers classic repeated measures model, random effect models, generalized estimating equations (GEEs), hierarchical models, and transitional models for binary data, marginal vs. mixed effects models, model fitting, model checking, clustering, and implication for study design. Also includes discussion of missing data techniques, Bayesian and Likelihood methods for GLMs, and various fitting algorithms such as maximum likelihood and generalized least squares. Spring (4) (Schildcrout)

351. Statistical Collaboration in Health Sciences I

First course of two on collaboration in statistical science. Students are exposed to a variety of problems that arise in collaborative arrangements. The course’s goal is to sharpen students’ consulting skills while exposing them to the application of advanced statistical techniques in routine health science applications. The importance of understanding and learning the science underlying collaborations will be emphasized. Students will role‐play with real investigators, discuss real consulting projects that have gone awry, and face real life problems such as opaque scientific direction, poor scientific formulation, lack of time, and ill‐formulated messy data. Students will engage in several consulting projects that will involve the use of a wide range of biostatistics methods from design to analysis. Course content will also make use of departmental clinics that are run concurrently.Fall (3) (Davidson, Shotwell)

352. Statistical Collaboration in Health Sciences II

Second course of a year-long sequence in collaboration in statistical science. Students are exposed to a variety of problems that arise in collaborative arrangements. The course’s goal is to sharpen students’ consulting skills while exposing them to the application of advanced statistical techniques in routine health science applications. The importance of understanding and learning the science underlying collaborations will be emphasized. Students will role-play with real investigators, discuss real consulting projects that have gone awry, and face real-life problems such as opaque scientific direction, poor scientific formulation, lack of time, and ill-formulated messy data. Students will engage in several consulting projects that will involve the use of a wide range of biostatistics methods from design to analysis. Course content will also make use of departmental clinics that are run concurrently. Prerequisite: 351 Spring (3) (Davidson, Shotwell)

355. Statistical Learning and Multivariate Methods

With rapidly growing warehouses of medical data and the emergence of technologies that output massive amounts of data, new methods of analysis are necessary to turn these resource outputs into information that can be translated into medical practice.  This course will broadly cover methods such as data mining, machine learning, and bioinformatics.  Even though the language in these statistical settings differ; there are common underpinnings to these methods and course’s primary goal will be to demonstrate their common framework.  Specific topics to be addressed in this course include supervised and unsupervised learning, neural networks, support vector machines, and classification trees. Methods for high-dimensional data analysis will also be covered.

361. Advanced Probability and Real Analysis Concepts

Covers advanced probabilistic concepts such as characteristic functions, Brownian motion, classical limit theorems, Lp spaces, projection, sigma-algebras and RVs, martingales, random walks, Markov chains,  probabilistic asymptotics, Wald’s SPRT. Fall (3) (Johnson)

362. Advanced Statistical Inference

This course provides a detailed survey of modern inferential tools. Topics include nonparametric statistics, quasi-likelihood, estimating equations, re-sampling techniques, statistical learning, methods for high-dimensional data, estimation-maximization (EM) algorithms, and Gibbs sampling. Spring (3) (Li)

370. Foundations of Statistical Inference

Examines the foundations of statistical inference as viewed from Frequentist, Bayesian, and Likelihood approaches. Famous papers and controversies are discussed along with statistical theories of evidence and decision theory, and their historic significance.

372. Bayesian Methods

This course covers the methodology and rationale for Bayesian methods and their applications. Statistical topics include the historical development of Bayesian method such as hierarchical models, Markov Chain Monte Carlo (MCMC) and related sampling methods, specification of priors, sensitivity analysis, model specification and selection. This course features applications of Bayesian methods to biomedical research. Fall (3) (Choi)

366. Advanced Statistical Computing

Course covers numerical optimization, Markov Chain Monte Carlo (MCMC), estimation-maximization (EM) algorithms, Gaussian processes, Hamiltonian Monte Carlo, and data augmentation algorithms with applications for model fitting and techniques for dealing with missing data. Prerequisite: BIOS 301 or permission of instructor (3) Fall (Fonnesbeck)

368. Analysis of Failure time Data

Advanced survival course. Content to be determined.

375. Causal Inference

This course provides an introduction to the framework for causal modeling in observational data. Topics include propensity score adjustment, inverse probability weighting, instrumental variables, and sensitivity analysis. Methods are applied to a variety of biomedical examples.

398. Topics in Biostatistics

Special topics in Biostatistics like sequential analysis or nonparametric methods. Topics will be set by the faculty instructor. (Staff)

399. PhD Dissertation Research

Credit hours for students engaging in dissertation research. (Staff)

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