Curriculum

Curriculum Overview

Traditional features of the curriculum include parallel development of theory and applications as well as coverage of specific biostatistical topic areas and ethical issues in the conduct of statistical and medical research. The core curriculum covers the principles of epidemiologic studies in detail.  Embedded throughout the curriculum are examples of conflict of interest situations faced by biostatisticians, along with principles of reproducible research and strategies for implementation.

Required Knowledge in the Following Core Courses

For students with a Master's degree in Biostatistics, some of the required 700 level courses listed below may be waived if they have taken those courses or their equivalents previously. 

BIOSTAT 701. Introduction to Statistical Theory and Methods I
BIOSTAT 702. Applied Biostatistical Methods I
BIOSTAT 703. Introduction to the Practice of Biostatistics I
BIOSTAT 704. Introduction to Statistical Theory and Methods II
BIOSTAT 705. Applied Biostatistical Methods II
BIOSTAT 706. Introduction to the Practice of Biostatistics II
BIOSTAT 713. Survival Analysis
BIOSTAT 714. Categorical Data Analysis
BIOSTAT 718. Analysis of Correlated and Longitudinal Data
BIOSTAT 719. Generalized Linear Models
BIOSTAT 900. Current Problems in Biostatistics
BIOSTAT 905. Linear Models
BIOSTAT 906. Statistical Inference
BIOSTAT 910. Career Development and Prep
BIOSTAT 911. Advanced Inferential Techniques and Theory
STAT 711. Probability and Measure Theory

Approved Elective Courses

BIOSTAT 707 Statistical Methods for Learning and Discovery
BIOSTAT 708. Clinical Trial Design and Analysis
BIOSTAT 709. Observational Studies
BIOSTAT 710. Statistical Genetics and Genetic Epidemiology
BIOSTAT 902. Statistical Methods for Analysis with Missing Data
BIOSTAT 903. Advanced Survival Analysis
BIOSTAT 907. Early Phase Clinical Trials
BIOSTAT 908. Independent Study
BIOSTAT 909. Internship Course
BIOSTAT 914. Graphical Models for Biological Data
STA 561D. Probabilistic Machine Learning
STA 602. Bayesian and Modern Statistical Data Analysis
STA 640. Causal Inference
STA 663L. Statistical Computation

Timelines

The PhD program follows the Duke Graduate School Academic Calendar

Timeline and Curriculum for Students with an Applicable Quantitative Master's Degree 

Timeline and Curriculum for Students without an Applicable Quantitative Master's Degree

Course Descriptions

BIOSTAT 701: Introduction to Statistical Theory and Methods I: This course provides a formal introduction to the basic theory and methods of probability and statistics. It covers topics in probability theory with an emphasis on those needed in statistics, including probability and sample spaces, independence, conditional probability, random variables, parametric families of distributions, and sampling distributions. Core concepts are mastered through mathematical exploration and linkage with the applied concepts studied in BIOSTAT 704. Prerequisite(s): 2 semesters of calculus or its equivalent (multivariate calculus preferred). Familiarity with linear algebras is helpful. Corequisite(s): BIOSTAT 702, BIOSTAT 703. Credits: 3

BIOSTAT 702: Applied Biostatistical Methods I: This course provides an introduction to study design, descriptive statistics, and analysis of statistical models with one or two predictor variables. Topics include principles of study design, basic study designs, descriptive statistics, sampling, contingency tables, one- and two-way analysis of variance, simple linear regression, and analysis of covariance. Both parametric and non-parametric techniques are explored. Core concepts are mastered through team-based case studies and analysis of authentic research problems encountered by program faculty and demonstrated in practicum experiences in concert with BIOSTAT 703. Computational exercises will use the R and SAS packages. Prerequisite(s): 2 semesters of calculus or its equivalent (multivariate calculus preferred). Familiarity with linear algebras is helpful. Corequisites(s): BIOSTAT 701, BIOSTAT 703, BIOSTAT 721. Credits: 3

BIOSTAT 703: Introduction to the Practice of Biostatistics I: This course provides an introduction to biology at a level suitable for practicing biostatisticians and directed practice in techniques of statistical collaboration and communication. With an emphasis on the connection between biomedical content and statistical approach, this course helps unify the statistical concepts and applications learned in BIOSTAT 701 and BIOSTAT 702. In addition to didactic sessions on biomedical issues, students are introduced to different areas of biostatistical practice at Duke University Medical Center. Biomedical topics are organized around the fundamental mechanisms of disease from both evolutionary and mechanistic perspectives, illustrated using examples from infectious disease, cancer and chronic /degenerative disease. In addition, students learn how to read and interpret research and clinical trial papers. Core concepts and skills are mastered through individual reading and class discussion of selected biomedical papers, team-based case studies and practical sessions introducing the art of collaborative statistics. Corequisite(s): BIOSTAT 701, BIOSTAT 702. Credits: 3

BIOSTAT 703L: Introduction to the Practice of Biostatistics I Lab: The lab will be an extension of the course. The lab will be run like a journal club. The lab will instruct students how to dissect a research article from a statistical and scientific perspective. The lab will also give students the opportunity to present on material covered in the co-requisite course and to practice the communication skills that are a core tenant of the program. Corequisite(s): BIOSTAT 703 or permission of the Director of Graduate Studies. Credits: 0

BIOSTAT 704: Introduction to Statistical Theory and Methods II: This course provides formal introduction to the basic theory and methods of probability and statistics. It covers topics in statistical inference, including classical and Bayesian methods, and statistical models for discrete, continuous and categorical outcomes. Core concepts are mastered through mathematical exploration, simulations, and linkage with the applied concepts studied in BIOSTAT 705. Prerequisite(s): BIOSTAT 701 or its equivalent. Corequisite(s): BIOSTAT 705, BIOSTAT 706. Credits: 3

BIOSTAT 705: Applied Biostatistical Methods II: This course provides an introduction to general linear models and the concept of experimental designs. Topics include linear regression models, analysis of variance, mixed-effects models, generalized linear models (GLM) including binary, multinomial responses and log-linear models, basic models for survival analysis and regression models for censored survival data, and model assessment, validation and prediction. Core concepts are mastered through statistical methods application and analysis of practical research problems encountered by program faculty and demonstrated in practicum experiences in concert with BIOSTAT 706. Computational examples and exercises will use the SAS and R packages. Prerequisite(s): BIOSTAT 702 or its equivalent. Corequisite(s): BIOSTAT 704, BIOSTAT 706, BIOSTAT 722. Credits: 3

BIOSTAT 706: Introduction to the Practice of Biostatistics II: This course revisits the topics covered in BIOSTAT 703 in the context of high-throughput, high-dimensional studies such as genomics and transcriptomics. The course will be based on reading of both the textbook and research papers. Students will learn the biology and technology underlying the generation of “big data,” and the computational and statistical challenges associated with the analysis of such data sets. As with BIOSTAT 703, there will be strong emphasis on the development of communication skills via written and oral presentations. Prerequisite(s): BIOSTAT 703. Corequisite(s): BIOSTAT 704, BIOSTAT 705. Credits: 3

BIOSTAT 707: Statistical Methods for Learning and Discovery: This course surveys a number of techniques for high dimensional data analysis useful for data mining, machine learning and genomic applications, among others. Topics include principal and independent component analysis, multidimensional scaling, tree-based classifiers, clustering techniques, support vector machines and networks, and techniques for model validation. Core concepts are mastered through the analysis and interpretation of several actual high dimensional genomics datasets. Prerequisite(s): BIOSTAT 701, 702, 704, 705, and 721 or 722 or their equivalents, or permission of the Director of Graduate Studies. Credits: 3

BIOSTAT 708: Clinical Trial Design and Analysis: Topics include: history/background and process for clinical trial, key concepts for good statistics practice (GSP)/good clinical practice (GCP), regulatory requirement for pharmaceutical/clinical development, basic considerations for clinical trials, designs for clinical trials, classification of clinical trials, power analysis for sample size calculation, statistical analysis for efficacy evaluation, statistical analysis for safety assessment, implementation of a clinical protocol, statistical analysis plan, data safety monitoring, adaptive design methods in clinical trials (general concepts, group sequential design, dose finding design, and phase I/II or phase II/III seamless design) and controversial issues in clinical trials. Prerequisite(s): BIOSTAT 701, 702, 704, 705, and 721 or 722 or their equivalents, or permission of the Director of Graduate Studies. Credits: 3

BIOSTAT 709: Observational Studies: Methods for causal inference, including confounding and selection bias in observational or quasi-experimental research designs, propensity score methodology, instrumental variables, and methods for non-compliance in randomized clinical trials. Prerequisite(s): BIOSTAT 701, 702, 704, 705, and 721 or 722 or their equivalents, or permission of the Director of Graduate Studies. Credits: 3

BIOSTAT 710: Statistical Genetics and Genetic Epidemiology: Topics from current and classical methods for assessing familiality and heritability, linkage analysis of Mendelian and complex traits, family-based and population-based association studies, genetic heterogeneity, epistasis, and gene-environmental interactions. Computational methods and applications in current research areas. The course will include a simple overview of genetic data, terminology, and essential population genetic results. Topics will include sampling designs in human genetics, gene frequency estimation, segregation analysis, linkage analysis, tests of association, and detection of errors in genetic data. Prerequisite(s): BIOSTAT 701, 702, 704, 705, and 721 or 722 or their equivalents, or permission of the Director of Graduate Studies. Credits: 3

BIOSTAT 713: Survival Analysis: Introduction to concepts and techniques used in the analysis of time to event data, including censoring, hazard rates, estimation of survival curves, regression techniques, applications to clinical trials. Interval censoring, informative censoring, competing risks, multiple events and multiple endpoints, time dependent covariates; nonparametric and semi-parametric methods. Prerequisite(s): BIOSTAT 701, 702, 704, 705, and 721 or 722 or their equivalents, or permission of the Director of Graduate Studies. Credits: 3

BIOSTAT 714: Categorical Data Analysis: Topics in categorical modeling and data analysis/contingency tables; measures of association and testing; logistic regression; log-linear models; computational methods including iterative proportional fitting; models for sparse data; Poisson regression; models for ordinal categorical data, and longitudinal analysis. Prerequisite(s): BIOSTAT 701, 702, 704, 705, and 721 or 722 or their equivalents, or permission of the Director of Graduate Studies. Credits: 3

BIOSTAT 718: Analysis of Correlated and Longitudinal Data: Topics include linear and nonlinear mixed models; generalized estimating equations; subject specific versus population average interpretation; and hierarchical model. Prerequisite(s): BIOSTAT 701, 702, 704, 705, and 721 or 722 or their equivalents, or permission of the Director of Graduate Studies. Credits: 3

BIOSTAT 719: Generalized Linear Models: The class introduces the concept of exponential family of distributions and link function, and their use in generalizing the standard linear regression to accommodate various outcome types. Theoretical framework will be presented but detailed practical analyses will be performed as well, including logistic regression and Poisson regression with extensions. Majority of the course will deal with the independent observations framework. However, there will be substantial discussion of longitudinal/clustered data where correlations within clusters are expected. To deal with such data the Generalized Estimating Equations and the Generalized Linear Mixed models will be introduced. An introduction to a Bayesian analysis approach will be presented, time permitting.Prerequisite(s): BIOSTAT 701, 702, 704, 705, and 721 or 722 or their equivalents, or permission of the Director of Graduate Studies. Credits: 3

BIOSTAT 721: Introduction to Statistical Programming I (R): This class is an introduction to programming in R, targeted at statistics majors with minimal programming knowledge, which will give them the skills to grasp how statistical software works, tweak it to suit their needs, recombine existing pieces of code, and when needed create their own programs. Students will learn the core of ideas of programming (functions, objects, data structures, input and output, debugging, and logical design) through writing code to assist in numerical and graphical statistical analyses. Students will learn how to write maintainable code, and to test code for correctness. They will then learn how to set up stochastic simulations and how to work with and filter large data sets. Since code is also an important form of communication among scientists, students will learn how to comment and organize code to achieve reproducibility. Programming techniques and their application will be closely connected with the methods and examples presented in the co-requisite course. The primary programming package used in this course will be R. Prerequisite(s): None; familiarity with linear algebras is helpful. Corequisite(s): BIOSTAT 702. Credits: 3

BIOSTAT 722: Introduction to Statistical Programming II (SAS): This class is an introduction to programming in SAS, targeted at statistics majors with minimal programming knowledge, which will give them the skills to grasp how statistical software works, tweak it to suit their needs, recombine existing pieces of code, and when needed create their own programs. Students will learn the core of ideas of programming (data step, procedures, macros, ODS, input and output, debugging, and logical design) through writing code to assist in numerical and graphical statistical analyses. Students will learn how to write maintainable code, and to test code for correctness. They will then learn how to set up stochastic simulations and how to work with and filter large data sets. Since code is also an important form of communication among scientists, students will learn how to comment and organize code to achieve reproducibility. Programming techniques and their application will be closely connected with the methods and examples presented in the co-requisite course. The primary programming package focus used in this course will be SAS. Prerequisite(s): None; familiarity with linear algebra is helpful. Corequisite(s): BIOSTAT 705. Credits: 3

BIOSTAT 732: Independent Study: Independent Study is a semester long course focused on mentored research in the practice of biostatistics. Students work with an assigned mentor. This course is only open to students by permission of the Director of Graduate Studies. Credits: 1, 2, or 3

BIOSTAT 740: Continuation: Continuation is a semester-based, noncredit-bearing enrollment status used when a student is continuing scholarly activities with the same mentor. This course is only open to students by permission of the Director of Graduate Studies. Credits: 0

BIOSTAT 821: Software Tools for Data Science: A data scientist needs to master several different tools to obtain, process, analyze, visualize and interpret large biomedical data sets such as electronic health records, medical images, and genomic sequences. It is also critical that the data scientist masters the best practices associated with using these tools, so that the results are robust and reproducible. The course covers foundational tools that will allow students to assemble a data science toolkit, including the Unix shell, text editors, regular expressions, relational and NoSQL databases, and the Python programming language for data munging, visualization and machine learning. Best practices that students will learn include the Findable, Accessible, Interoperable and Reusable (FAIR) practices for data stewardship, as well as reproducible analysis with literate programming, version control and containerization. Prerequisite: BIOSTAT 721 and permission of the Director of Graduate Studies. Credits: 3

BIOSTAT 822: R for Data Science: This course will build on the foundation laid in software tools for data science. The course will explore the flow of a typical data science project from importing, cleaning, transforming and visualizing datasets to modeling and communicating results, within the context of R programming. While the course will include best practices, syntax and idioms specific to R, the focus will be on the process of conducting analysis in a reproducible fashion, writing readable, well-documented code and creating a coherent presentation of results.
Prerequisite: BIOSTAT 722 or BIOSTAT 821 or permission of the Director of Graduate Studies. Credits: 3

BIOSTAT 823: Statistical Program for Big Data: This course describes the challenges faced by analysts with the increasing importance of large data sets, and the strategies that have been developed in response to these challenges. The core topics are how to manage data and how to make computation scalable. The data management module covers guidelines for working with open data, and the concepts and practical skills for working with in-memory, relational and NoSQL databases. The scalable computing module focuses on asynchronous, concurrent, parallel and distributed computing, as well as the construction of effective workflows following DevOps practices. Applications to the analysis of structured, semi-structured and unstructured data, especially from biomedical contexts, will be interleaved into the course. The course examples are primarily in Python and fluency in Python is assumed. Prerequisite(s): BIOSTAT 821 or permission of the Director of Graduate Studies. Credits: 3

BIOSTAT 824: Case Studies in Biomedical Data Science: This course will highlight how biomedical data science blends the field of biostatistics with the field of computer science through the introduction of 3 to 5 case studies. Students will be introduced to analytic programs typically encountered in biomedical data science and will implement the data science and statistical skills introduced in their previous course work. Prerequisite(s): BIOSTAT 707, 821, 822, and 823 or permission of the Director of Graduate Studies. Credits: 3

BIOSTAT 900. Current Problems in Biostatistics. Advanced seminar on topics at the research frontiers in biostatistics. Readings of current biostatistical research and presentations by faculty and advanced students of current research in their area of specialization. Instructor: O’Brien. 1 unit.

BIOSTAT 902. Missing Data Analysis: Theory and Application. Theory and application of missing data methodology, ad hoc methods, missing data mechanism, selection models, pattern mixture models, likelihood-based methods, multiple imputation, inverse probability weighting, sensitivity analysis. Prerequisites: Statistical Science 711, 721, and 732, or consent of instructor. Instructor: Allen. 3 units.

BIOSTAT 903. Advanced Survival Analysis. Designed for PhD students in Biostatistics or DSS departments who may be interested in conducting methodological research in the area of Survival Data Analysis. Applications of counting process and martingale theory to right censored survival data. Applications of empirical process theory to more general and possibly more complex statistical models using nonparametric analysis of interval-censored data as illustrating examples. After completion, students are anticipated to understand the statistical method papers on survival analysis appearing in top tier statistical journals. Prerequisites: BIOSTAT 701, 704, and 713, or equivalent, or consent of instructor. Instructor: Wu. 3 units.

BIOSTAT 905. Linear Models and Inference. Introduction to linear models and linear inference from the coordinate-free viewpoint. Topics: identifiability and estimability, key properties of and results for finite-dimensional vector spaces, linear transformations, self-adjoint transformations, spectral theorem, properties and geometry of orthogonal projectors, Cochran's theorem, estimation and inference for normal models, distributional properties of quadratic forms, minimum variance linear unbiased estimation, Gauss-Markov theorem and estimation, calculus of differentials, analysis of variance and covariance. Prerequisite: Biostatistics 906. Instructor: O’Brien. 3 units.

BIOSTAT 906. Statistical Inference. Introduce decision theory and optimality criteria, sufficiency, methods for point estimation, confidence interval and hypothesis testing methods and theory. Prerequisite: Biostatistics 704 or equivalent. Instructor consent required. Instructor: Xie. 3 units.

BIOSTAT 907. Phase II Clinical Trials. Introduction to diverse statistical design and analytical methods for randomized phase II clinical trials. Topics: Minimax, optimal, and admissible clinical trials Inference methods for phase II clinical trials; clinical trials with a survival endpoint; clinical trials with heterogeneous patient populations; and randomized phase II clinical trials. Instructor consent required. Instructor: Jung. 3 units.

BIOSTAT 908. Independent Study (Rotations). Faculty directed statistical methodology research. Instructor consent required. Instructor: O’Brien. 1 unit.

BIOSTAT 909. Internship Course. Student gains practical experience by taking an internship in industry/government and writes a report about this experience. Requires prior consent from the student's advisor and from the Director of Graduate Studies. May be repeated with consent of the advisor and the Director of Graduate Studies. Credit/no credit grading only. Instructor: O’Brien. 1 unit.

BIOSTAT 910. Career Development and Prep. Student gains a holistic view of career choices and individual development plans including tools they will need to succeed as professionals in the world of work. The curriculum focuses on the unique challenges of PhD candidates and tools needed for successful careers in academia or in industry. May be repeated with consent of the advisor and the Director of Graduate Studies. Instructor: Baker. 1 unit.

BIOSTAT 911. Advanced Inferential Techniques and Theory. The theory for M- and Z- estimators and applications. Semiparametric models, geometry of efficient score functions and efficient influence functions, construction of semiparametric efficient estimators. Introduction to the bootstrap: consistency, inconsistency and remedy, correction for bias, and double bootstrap. U statistics and rank and permutation tests. Prerequisites: Statistical Sciences 711 and Biostatistics 906. Instructor: Li. 3 units.

BIOSTAT 914. Graphical Models for Biological Data. Introduction to probabilistic graphical models and structured prediction, with applications in genetics and genomics.  Hidden Markov Models, conditional random fields, stochastic grammars, Bayesian hierarchical models, neural networks, and approaches to integrative modeling.  Algorithms for exact and approximate inference.  Applications in DNA/RNA analysis, phylogenetics, sequence alignment, gene expression, allelic phasing and imputation, genome/epigenome annotation, and gene regulation. Department consent required. Instructor: Majoros. 3 units. C-L: Computational Biology and Bioinformatics 914.

BIOSTAT 990. Biostatistics Special Topics. Advanced course on topics at the research frontiers in biostatistics. Readings of current biostatistical research and presentations by faculty and advanced students of current research in their area of specialization. Department consent required. Instructor: Staff. 3 units.

STA 561D. Probabilistic Machine Learning. Introduction to concepts in robabilistic machine learning with a focus on discriminative and hierarchical generative models. Topics include directed and undirected graphical models, kernel methods, exact and approximate parameter estimation methods, and structure learning. Prerequisites: Linear algebra, Statistical Science 250 or Statistical Science 611. Instructor: Heller, Mukherjee, or Reeves. 3 units. 

STA 602. Bayesian and Modern Statistical Data Analysis. Principles of data analysis and modern statistical modeling. Exploratory data analysis. Introduction to Bayesian inference, prior and posterior distributions, predictive distributions, hierarchical models, model checking and selection, missing data, introduction to stochastic simulation by Markov Chain Monte Carlo using a higher level statistical language such as R or Matlab. Applications drawn from various disciplines. Not open to students with credit for Statistical Science 360. Prerequisite: Statistical Science 210, 230 and 250, or close equivalents. Instructor: Clyde, Dunson, Reiter, or Volfovsky. 3 units.

STA 640. Causal Inference. Statistical issues in causality and methods for estimating causal effects. Randomized designs and alternative designs and methods for when randomization is infeasible: matching methods, propensity scores, longitudinal treatments, regression discontinuity, instrumental variables, and principal stratification. Methods are motivated by examples from social sciences, policy and health sciences. Instructor: Li or VolfovskyStatistical issues in causality and methods for estimating causal effects. Randomized designs and alternative designs and methods for when randomization is infeasible: matching methods, propensity scores, longitudinal treatments, regression discontinuity, instrumental variables, and principal stratification. Methods are motivated by examples from social sciences, policy and health sciences. Instructor: Li or Volfovsky

STA 663L. Statistical Computation. Statistical modeling and machine learning involving large data sets and challenging computation. Data pipelines and data bases, big data tools, sequential algorithms and subsampling methods for massive data sets, efficient programming for multi-core and cluster machines, including topics drawn from GPU programming, cloud computing, Map/Reduce and general tools of distributed computing environments. Intense use of statistical and data manipulation software will be required. Data from areas such as astronomy, genomics, finance, social media, networks, neuroscience. Instructor consent required. Prerequisites: Statistics 521L, 523L; Statistics 531, 532 (or co-registration). (3 units)

STA 711. Probability and Measure Theory. Introduction to probability spaces, the theory of measure and integration, random variables, and limit theorems. Distribution functions, densities, and characteristic functions; convergence of random variables and of their distributions; uniform integrability and the Lebesgue convergence theorems. Weak and strong laws of large numbers, central limit theorem. Prerequisite: elementary real analysis and elementary probability theory. Instructor: Staff. 3 units.