BIOS 6100 Biostatistical Methods I. 4 Credits
Three hours of lecture and two hours of lab per week. General introduction to descriptive and inferential statistics: techniques and principles for summarizing data, estimation, hypothesis testing and decision-making. Students are instructed on the proper use of statistical software to manage, manipulate, and analyze data and to prepare summary reports and graphical displays. Examples and problems from the health sciences are used throughout. Laboratory sessions will be held in the SPH computing lab and are designated to closely follow the lecture material. (Non-biostatistics majors only)

BIOS 6102 Biostatistical Methods II. 4 Credits
Three hours of lecture and two hours of lab per week. General introduction to descriptive and inferential statistics: techniques and principles for summarizing data, estimation, hypothosis testing and decision-making. Students are instructed on the proper use of statistical software to manage, manipulate, and analyze data and to prepare summary reports and graphical displays. Examples and problems from the health sciences are used throughout. Laboratory sessions will be conducted in the SPH computer lab and will provide hands-on instruction to students on the proper use of statistical software to analyze data arising from linear and logistic regression models and multi-way ANOVA models. Non-Biostatistics majors only. Prerequisite: BIOS 6100.

BIOS 6200 Principles of Applied Statistics. 4 Credits
Three hours lecture and two hours of lab per week. Broad coverage of methods of applied statistics, designed for students who want to take advantage of their good math backgrounds for better understanding. Data description; elementary probability, random variables, distributions; principles of statistical inference; methods for one-, two-, and multi-sample settings, including ANOVA and multiple regression; methods for categorical responses. Use of SAS and other software for analysis, simulations, graphics, and report writing. Some cases will use large national databases, such as NHANES and CPS. Laboratory sessions will be held in the SPH computing lab and are designed to closely follow the lecture material. Prerequisites: multi-variable calculus and linear algebra.

BIOS 6202 Applied Linear Models. 3 Credits
Three hours of lecture per week. This is a practical course on the use of general linear models. Topics include a review of relevant matrix algebra; general linear models including multiple regression, analysis of variance, analysis of covariance, multivariate response, and logistic regression models; methods for estimation, hypothesis testing and diagnostics; model specification for designed experiments and for observational studies; applications are in the health sciences. Prerequisites: BIOS 6100 or BIOS 6200.

BIOS 6204 Statistical Theory I. 3 Credits
Three hours of lecture per week. Elementary concepts of probability; conditional probability, Bayes’ theorem; random variables and probability distributions, transformations of random variables; moments and moment generating functions; discrete and continuous random variables, common families of distributions; essential inequalities and identities; multivariate distributions, joint, conditional and marginal distributions; covariance and correlation, conditional expectation; basic concepts of random samples; convergence concepts, convergence in probability and in distribution, the law of large numbers, and the central limit theorem. Prerequisite: Calculus I-III and linear algebra.

BIOS 6206 Statistical Theory II. 3 Credits
Three hours of lecture per week. Principles of data reduction, sufficiency and completeness, minimal sufficient statistics; the likelihood principle; point estimation, method of moments, maximum likelihood estimation; methods of evaluating estimators, unbiased estimation, Fisher information, hypotheses testing, likelihood ratio tests, methods of evaluating tests, most powerful tests; interval estimation, methods of evaluating interval estimators Prerequisite: BIOS 6204.

BIOS 6210 Categorical Data Analysis. 3 Credits
Three hours of lecture per week. Model formulation, parameter estimation, and hypothesis testing for categorical data from different types of experimental and survey research situations: Characterization of interaction in multidimensional contingency tables, stepwise regression procedures for proportions, and exact inference. Prerequisite: BIOS 6102 or BIOS 6202.

BIOS 6212 Survival Analysis. 3 Credits
Three hours of lecture per week. This course provides students with statistical methodology for the analysis of time-to-event data and trains students in the appropriate analysis of survival data, by both parametric and nonparametric methods. Emphasis will be placed on methods and models most useful in clinical research with attention to proper interpretation of statistical packages output. Prerequisite: BIOS 6102 or BIOS 6202.

BIOS 6300 Statistical Computing. 3 Credits
Three hours of lecture per week, summer semester. An introductory programming course oriented toward statistical applications using SAS (including IML) and the R programming languages. Topics include data types, assignment statements, operators, sequential control, conditional control, iteration, subprograms, arrays, character manipulation, manipulating and processing SAS output from SAS procedures, Gibbs sampler, and Markoff Chain Monte-Carlo methods. Prerequisite: BIOS 6202 or permission of the instructor.

BIOS 6302 Longitudinal Data Analysis. 3 Credits
Three hours of lecture per week. This course will emphasize analysis and interpretation of data obtained from subjects measured repeatedly over time. Coverage will begin with traditional approaches to analysis of longitudinal data such as multivariate repeated measures and the univariate analysis of repeated measures as a split-plot model and will quickly lead into models for mean response such as the analysis of response profiles and parametric curve fitting including linear splines. Models for the covariance matrix will be then be considered. Linear mixed models and generalized estimation equations will be covered in detail. Other topics will be covered as time allows. Examples from the health and biomedical sciences will be presented to motivate the material. Prerequisites: BIOS 6102 or BIOS 6202.

BIOS 6304 Design and Analysis of Experiments. 3 Credits
Three hours of lecture per week. Principles of experimentation. Completely randomized designs, randomized complete block designs, factorial designs, Latin squares, crossover designs, blocking, response surface designs. Applications are in the health sciences. Prerequisite: BIOS 6100 or BIOS 6200, or permission of the instructor.

BIOS 6308 Multivariate Methods. 3 Credits
Three hours of lecture per week. Review of matrix algebra, multivariate normal distribution, multivariate general linear model, principal components, factor analysis, cluster analysis, discriminant analysis. Applications are in the health sciences. Prerequisites: BIOS 6202, BIOS 6206.

BIOS 6310 Applied Bayesian Methods. 3 Credits
Three hours of lecture per week. Introduction to Bayesian approach to statistical inference. Application oriented, but such theory as is necessary for a proper understanding of the Bayesian methodology will be covered. Topics covered include Bayesian Inference – prior determination, point and interval estimation, hypothesis testing, prediction, model assessment and model choice; Bayesian Computation – Markov Chain Monte Carlo (MCMC) methods, Gibbs Sampling and extensions; and Bayesian applications on real data sets from the biological or medical fields. Prerequisite: BIOS 6202, BIOS 6206, BIOS 6300, or permission of the instructor.

BIOS 6312 Sampling Methods. 3 Credits
Three hours of lecture per week. Methods for conducting sample surveys in the health sciences: Biases and non-sampling errors, probability and non-probability samples, simple random sampling, stratification, varying probabilities of selection, multi-stage sampling, systematic sampling, cluster sampling, double sampling, and ratio estimation. Prerequisite: Permission of the instructor.

BIOS 6314 Clinical Trials Methodology. 3 Credits
Three hours of lecture per week. Introduction to the conduct of clinical trials and clinical trials methodology. Topics covered include selection of primary and secondary research questions and hypotheses, use of surrogate variables, defining study population, generalizability of results, basic study design, randomization process, blinding, sample size estimation, using baseline assessments, recruitment of study participants, data collection and quality control, assessing and reporting adverse events, assessing quality of life, participant adherence, survival analysis techniques and issues, monitoring response variables, data analysis issues, study closeout, and reporting and interpreting results. Prerequisites: BIOS 6102 or BIOS 6202.

BIOS 6316 Stochastic Processes. 3 Credits
Three hours of lecture per week. Markov chains; birth-death processes; random walks; renewal theory; Poisson processes; Brownian motion; branching processes; martingales; with applications. Prerequisites: BIOS 6206.

BIOS 6318 Nonparametric Statistics, 3 Credits
Three hours of lecture per week. This course will cover methods based on ranks for one, two, and k sample inference, including Sign Test, Wilcoxon Rank-Sum Test, Kruskal-Wallis Test, Tests for Trends and Association and Multivariate Tests, Analysis of Censored Data, Bootstrap Methods, Expectation-Maximization Algorithm. The advantages and disadvantages of each of these methods when compared to the parametric counterpart will be discussed. Prerequisites: BIOS 6100, 6102 (or BIOS 6200, 6202), BIOS 6204

BIOS 6320 Time Series Analysis, 3 Credits
The course will cover both time and frequency domain methods in time series analysis and their applications to biomedical, public health and other scientific data collected over time. The real-life examples and implementation of the methods in statistical software (SAS/R) will be discussed.

BIOS 6400 Independent Study. 1-3 Credits
This course provides the student an opportunity to study a topic in depth while under the guidance of a faculty member. The focus of the course will be a specific aspect of a public health discipline, which is not the primary focus of exiting public health courses. The course will involve directed readings and may require completion of a paper or study project that provides evidence of comprehension and professional proficiency in the area studied. Independent Study may only be taken for a maximum of 3 credit hours toward the MPH Degree.

BIOS 6450 Design and Analysis of Expression Studies. 3 Credits
Three hours of lecture per week. Design and analysis of differential gene expression studies using microarrays. Design and analysis of differential protein expression studies. Analysis of RT-PCR gene expression data. Design and analysis of tissue array studies. Current statistical issues. Applications in biomedical research, e.g. expression and survival times of patients by tumor grade. Data mining approaches for expression data: clustering and classification algorithms. Prerequisites: BIOS 6202.

BIOS 6500 Special Topics in Biostatistics. 1-4 Credits
Hours and credits to be arranged depending on the particular topic. This course is designed, depending upon the students’ interest and faculty availability, to cover advanced topics such as stochastic processes, time series analysis, analysis of survival distributions, experimental design, multivariate analysis, etc. Prerequisite: Permission of the instructor.

BIOS 6600 Culminating Experience/Capstone in Biostatistics. 3 Credits
All professional degree programs identified in the instructional matrix shall assure that each student demonstrates skills and integration of knowledge through a culminating experience. A culminating experience is one that requires a student to synthesize and integrate knowledge acquuired in coursework and other learning experiences and ato apply theory and principles in a situation that approximates some aspect of professional practice. Prerequisite: BIOS 6200 Principles of Applied Statistics; EPID 6210 Principles of Epidemiology or EPID 6209 Principles of Epidemiology – Online; ENHS 6238 Principles of Environmental Health; BCHS 6212 Behavioral Science Theories in Public Health; and HPSM 6268 Health Services Administration and Management.

BIOS 6610 Biostatistical Consulting. 2 Credits
A practical course designed to expose students to real-life consulting situations and the statistical problems that arise in the health sciences. The student will work on a consulting project under the supervision of a faculty member and will present a progress report each week. Prerequisites: BIOS 6202.

BIOS 6611 Biostatistical Consulting II. 2 Credits
A course designed to expose students to realistic facets of biostatistical consulting practice. The course draws on cumulated knowledge on the biostatistics curriculum for use on actual applications in public health and  biomedical sciences. Data analysis/reporting and grant proposal development using using techniques beyond BIOS 6202 will be illustrated. Applications in public health, clinical trials, and OMICS will be covered. This course is intended for biostatistics majors after the first year of master’s level coursework.

BIOS 6700 Research Seminar in Biostatistics. 1 Credit
Reports on research progress in current literature. Students attend colloquium and give an oral presentation in their second year.

BIOS 6900 Thesis Research. 1-6 Credits
Registration by permission of the school. Amount of credit must be stated at time of registration.

BIOS 7200 Theory of Linear Models. 3 Credits
Three hours of lecture per week. This course presents the essentials of statistical inference theory for general linear models. Topics include a review of relevant matrix algebra; distributions of quadratic forms; theoretical aspects of estimation, hypothesis testing and diagnostics. Prerequisites: BIOS 6202, BIOS 6206, or permission of the instructor.

BIOS 7202 Generalized Linear Models. 3 Credits
Three hours of lecture per week. Study of parametric models in the exponential family of distributions including the normal, binomial, Poisson, and gamma. Parameter estimation with Iterative re-weighted least squares and quasi-likelihood methods. Modeling of correlated data or data with non-constant variance via mixed models (e.g., GLIMMIX). In-depth coverage of generalized estimating equations (GEE1 and GEE2) and quadratic estimating equations (QEE). Applications with be presented from a variety of settings such as the basic sciences, medicine, dental, and public health. Prerequisite: BIOS 6202, BIOS 6206, or permission of the instructor.

BIOS 7204 Advanced Statistical Theory I. 3 Credits
Three hours of lecture per week. A mathematical study of the classical theory of statistical inference. Moment generating functions and characteristic functions, distributions of order statistics, exponential family of distributions, models of convergence, the Cramer-Rao inequality, efficiency, best unbiased estimation, completeness, minimal sufficiency, maximum likelihood estimators; monotone likelihood ratio, unbiased and invariant hypothesis tests, generalized likelihood ratio tests, Bayes’ and minimax procedures. Prerequisite: BIOS 6206 or permission of the instructor.

BIOS 7205 Advanced Statistical Theory II. 3 Credits
Three hours of lecture per week. A mathematically rigorous survey of selected topics in the theory of statistical inference such as: Bayesian inference, decision theory, information theory, large sample theory, multivariate distributions, nonparametric inference, sequential analysis, stochastic processes, time series, components of variance. Prerequisite: BIOS 7204.

BIOS 7302 Mixed Models. 3 Credits
Three hours of lecture per week. Rigorous course on the theory of mixed models. Essentials of relevant matrix algebra; distribution of quadratic forms; models with variance-covariance components; one-way, two-way random and mixed models with fixed effects; methods of estimation of variance components; ML, REML, ANOVA; estimation of fixed effects; testing hypotheses about fixed effects; repeated measures design methods; choices of covariance structures; generalized linear mixed models. Prerequisite: BIOS 7200.

BIOS 7318 Statistical Learning. 3 Credits
Statistical learning or machine learning methodology explores various ways of estimating functional dependencies between a response variable (e.g., a disease outcome) and a large set of explanatory variables (e.g., gene expression data). This course will provide an overview of supervised learning methods used in bioinformatics and high-dimensional data research. The topics include regularization in linear models, tree and related methods, support vector machines, and boosting. Practical uses of these algorithms will be illustrated in biological research. Prerequisites: BIOS 6202, BIOS 6206

BIOS 7320 Robust Inference. 3 Credits
Three hours of lecture per week. This course will provide a general introduction to robust statistical inference. The aim is to provide specific techniques for handling outliers and small deviations from model assumptions in linear models, generalized linear models, and survey sampling. Prerequisites: BIOS 7200, BIOS 7202 (or BIOS 6210), BIOS 7204

BIOS 7410 Teaching Practicum in Biostatistics. 1-3 Credits
Advanced PhD students in Biostatistics working under the supervision of a faculty member will have the opportunity to gain valuable in-class teaching experience. Students will be intensively involved in all aspects of course teaching and administration. Working closely with a faculty member, the student will prepare a syllabus, lectures, handouts, quizzes, and exams. The student will also be responsible for all grading of homework, quizzes and exams. The faculty member will evaluate each of the lectures, providing direction, advice and feedback to the student. A written evaluation detailing the student’s performance will be provided as feedback to the student and will be the basis for the (Pass/Fail) grade. Each PhD student in Biostatistics is required to successfully complete at least 3 hours of supervised teaching before graduation. Prerequisites: Successful completion of the qualifying exam at the PhD level.

BIOS 7900 Dissertation Research.1-9Credits
Registration by permission of the program. Amount of credit must be stated at time of registration.