Course Descriptions

This reading and discussion-based course is based on the American Statistical Association’s Ethical Guidelines for Statistical Practice. Topics include professional integrity and accountability, integrity of data and methods, responsibilities to science/public/funder/client, responsibilities to research subjects, responsibilities to research team colleagues, responsibilities to other statisticians or statistics practitioners, responsibilities regarding allegations of misconduct, and responsibilities of employers, including organizations, individuals, attorneys, or other clients employing statistical practitioners. Prerequisites: None. Fall [0].

This course is the first in a two-course series on modern biostatistical reasoning and evaluation of data analysis methods. Students learn the statistical principles that govern the analysis of data in the health sciences and biomedical research. Traditional probabilistic concepts and modern computational techniques are integrated with applied examples from biomedical and health sciences. Topics include axioms of probability, probability distributions and their moments, properties of estimators, law of large numbers, central limit theorem, theory of confidence intervals and hypothesis testing (for one-sample and two-sample problems), paradigms of statistical inference (frequentist, Bayesian, likelihood), introduction to non-parametric techniques, bootstrapping and simulation, sample size projections, and basic study design issues. Prerequisites: Familiarity with calculus and probability concepts such as double integrals, partial derivatives, expectations, variances, cumulative density functions, and quantile functions is expected. Fall [3].

Participants must also enroll in BIOS 6311L, the laboratory and discussion session for this course, where students review relevant theory and work on applications as a group. Computing solutions and extensions using R software are emphasized. Fall [1].

This course is the second in a two-course series on modern biostatistical reasoning and evaluation of data analysis methods. Students learn modern regression analysis and model-building techniques from an applied perspective. Theoretical principles are demonstrated with applied examples from biomedical and health sciences. Topics include 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. There is a brief introduction to regression models for binary outcomes (logistic regression), ordinal outcomes (proportional odds models), count outcomes (Poisson and negative binomial models), and time-to-event outcomes (Kaplan-Meier curves, Cox proportional hazards models). Incorporated into the presentation of these models are topics such as regression diagnostics, non-parametric regression, splines, data-reduction techniques, model validation, parametric bootstrapping, and a brief introduction to methods for handling missing data. Prerequisites: BIOS 6311. Spring [3].

Participants must also enroll in BIOS 6312L, the laboratory and discussion session for this course, where students review relevant theory and work on applications as a group. Computing solutions and extensions using R software are emphasized. Spring [1].

This course is an introduction to statistical aspects of the design, monitoring, and analysis of experiments. Emphasis is on studies of human subjects (i.e., clinical trials). Topics include study designs, randomization and balance, selection of estimands and endpoints, sample size projections, data collection and quality control, data monitoring and interim analysis, principles of and issues in the analysis of trial data, and interpretation and reporting of results. Prerequisites: BIOS 6301 or equivalent, BIOS 6311 or equivalent. Spring [3].

This course is the first in a two-course series on probability and statistical inference that introduces and explores the probabilistic framework underling statistical theory. Students learn probability theory—the formal language of uncertainty—and its application to everyday statistical concepts and analysis methods. Topics include probability axioms, probability and sample space, events and random variables, transformation of random variables, probability inequalities, independence, discrete and continuous distributions, expectations and variances, conditional expectation, moment generating functions, random vectors, convergence concepts (in probability, in distribution, and almost surely), weak and strong law of large numbers, central limit theorem, delta method, order statistics, and exponential family. Prerequisites: Familiarity with infinite series, double integrals, integration by parts, and partial derivatives is expected. Fall [3].

Participants must also enroll in BIOS 6341L, the laboratory and discussion session for this course, where students review relevant theory and work on applications as a group. Collaborative work and problem solving as a group are emphasized. Students validate analytical solutions and explore limit theorems using R software. Fall [1].

This course is the second in a two-course series on probability and statistical inference that introduces and explores the fundamental inferential framework for parameter estimation, testing hypotheses, and interval estimation. Students learn classical methods of inference (hypothesis testing), and paradigms of statistical inference (frequentist, Bayesian, likelihood) and their surrounding controversies. Topics include sufficiency, minimal sufficiency, exponential family, ancillarity, completeness, conditionality principle, Fisher’s information, Cramer-Rao inequality, hypothesis testing (likelihood ratio 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, and maximum likelihood estimation. Prerequisites: BIOS 6341. Spring [3].

Participants must also enroll in BIOS 6342L, the laboratory and discussion session for this course, where students review relevant theory and work on applications as a group. Computing solutions and extensions using R software are emphasized. Spring [1].

This course provides an applied introduction to methods for time-to-event data with censoring mechanisms. Topics include life tables, non-parametric approaches (Kaplan-Meier curves, log-rank test), semi-parametric approaches (Cox proportional hazards model), parametric approaches (Weibull, gamma), competing risks, and time-dependent covariates. Focus is on fitting the models and the relevance of those models for the biomedical application. Prerequisites: BIOS 6312 or equivalent. Fall [3].

Participants must also enroll in BIOS 7323L, the laboratory and discussion session for this course, where students review relevant theory and work on applications as a group. Computing solutions and extensions using R software are emphasized. Fall [1].

This course presents strategies for, and a survey of current thinking on, building multivariable regression models primarily for the purpose of prediction, but also for estimation and inference. Topics include using regression splines to relax linearity assumptions, the perils of variable selection and over-fitting, where to spend degrees of freedom, shrinkage, imputation of missing data, data reduction, and interaction surfaces. There is also an emphasis placed on describing approaches for graphically understanding models and using resampling to estimate a model’s likely performance on new data. Statistical methods related to binary logistic models, ordinal logistic models, and survival models are covered. Students will develop, validate, and graphically describe multivariable regression models. Prerequisites: BIOS 6312 or equivalent. Spring [3].

Participants must also enroll in BIOS 7330L, the laboratory and discussion session for this course, where students review relevant theory and work on applications as a group. Computing solutions and extensions using R software are emphasized. Spring [1].

This course covers the methodology and rationale for Bayesian methods and their applications. Topics include the historical development of Bayesian methods such as hierarchical models, Markov chain Monte Carlo (MCMC) and related sampling methods, specification of priors, sensitivity analysis, and model checking and comparison. This course features applications of Bayesian methods to biomedical research. Prerequisites: BIOS 6301 or equivalent, BIOS 7345 or equivalent. Biennial [3].

Participants must also enroll in BIOS 7337L, the laboratory and discussion session for this course, where students review relevant theory and work on applications as a group. Computing solutions and extensions using R software are emphasized. Biennial [1].

This course is the first in a two-course series on advanced regression analysis that covers the underlying mechanics of linear and generalized linear models for independent data. Following a brief review of salient topics in linear algebra and multivariate normal theory, the first half of the course covers ordinary least squares in the cases of full rank and non-full rank design matrices, weighted least squares, optimality (the Gauss-Markov theorem), analysis of variance (ANOVA), hypothesis testing, confidence and prediction regions, model misspecification, diagnostics, and regularization. The second half of the course covers generalized linear models (e.g., binomial, Poisson, and gamma regression) from the likelihood and Z-estimation frameworks, overdispersion and quasi-likelihood, hypothesis testing, diagnostics, and negative binomial regression. As time permits, advanced topics will be covered such as matched pair designs, regression of nominal and ordinal outcomes, cumulative probability models, and receiver operating characteristic regression. Prerequisites: BIOS 6312 or equivalent, BIOS 6342 or equivalent. Fall [3].

Participants must also enroll in BIOS 7345L, the laboratory and discussion session for this course, where students review relevant theory and work on applications as a group. Computing solutions and extensions using R software are emphasized. Fall [1].

This course is the second in a two-course series on advanced regression analysis that extends linear and generalized linear models to the analysis of dependent (specifically, longitudinal) data. Parametric (generalized least squares, likelihood-based mixed-effects models) and semi-parametric (generalized estimating equations) regression-based methods are central to the course. Advanced topics include transition models, marginalized models, missing data, and joint models for longitudinal and survival data. Emphasis is placed on the theoretical framework for longitudinal data analysis, the statistical properties of longitudinal data analysis methods, and their development and application to modern biomedical research. Prerequisite: BIOS 7345. Spring [3].

Participants must also enroll in BIOS 7346L, the laboratory and discussion session for this course, which focuses on the illustrative application of longitudinal data analysis methods to biomedical research data using R software. Spring [1].

This course is the first in a two-course series on collaboration in statistical science. Students are exposed to a variety of challenges that arise in collaborative arrangements. The course’s goal is to develop the knowledge, skills, attitude, and behavior necessary to interact with research and statistical collaborators in routine health science applications. The importance of understanding and learning the science underlying collaborations is emphasized. Students experience various biostatistics roles while collaborating with real investigators and projects. Students gain experience that builds interpersonal, communication, professionalism, leadership, teaching, and presentation and interviewing skills. Real-world issues and challenges are discussed. There will be special guest lectures on grants, career choices, and collaboration satisfaction. Course content also makes use of departmental clinics that are run concurrently. Prerequisites: None. Fall [3].

This course is the second in a two-course series on collaboration in statistical science. Students are exposed to a variety of challenges that arise in collaborative arrangements. The course’s goal is to sharpen students’ collaborative 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 are emphasized. Students are exposed to real collaborative projects, and face real-life challenges such as opaque scientific direction, poor scientific formulation, lack of time, and ill-formulated messy data. Students engage in several projects that involve the use of a wide range of biostatistics methods from design to analysis. Course content may also make use of departmental clinics. Prerequisite: BIOS 7351. Spring [3].

Designed to allow the student to explore and/or master advanced or specialized topics in biostatistics under the guidance of faculty with relevant expertise. May be repeated. [1-3]

This course is the first in a two-course series on advanced probability and statistical inference. Topics include characteristic functions, modes of converge, uniform integrability, Brownian motion, classical limit theorems, L^p spaces, projections, sigma-algebras and RVs, martingales, random walks, Markov chains, and probabilistic asymptotics. Emphasis on measure theory is minimal. Concepts are illustrated in biomedical applications whenever possible. Prerequisites: BIOS 6342 or equivalent. Fall [3].

This course is the second in a two-course series on advanced probability and statistical inference. Through a combination of lectures, readings, hands-on exercises, and student-led discussions, the course offers an intricate blend of both theoretical and applied insights into probabilistic machine learning algorithms, excluding deep learning. Initial sessions provide a concise yet comprehensive review of linear models, which is then followed by an in-depth exploration of non-parametric methods such as KNN, kernel density estimation, and kernel methods. The latter part of the course introduces advanced topics such as learning with fewer labeled examples, including transfer and active learning, and concludes with a focus on dimensionality reduction, clustering, and recommender systems. Student participation in discussions is a significant part of the learning process. The course employs a variety of biomedical case studies to offer a nuanced understanding of how statistical learning algorithms are deployed in real-world scenarios. Prerequisite: BIOS 7361. Spring [3].

This course introduces advanced computing and analytical skills and concepts in biomedical data sciences. The course covers real-world data platforms, diverse analytics environments, statistical data analysis in Python, numerical methods, bioinformatics computing, cloud computing, and data visualization. The objective of the course is to enable students to adapt to the computational challenges required by today’s biomedical data sciences and big data computing, and to equip them with the knowledge and skills to solve real-world problems. Students are expected to analyze big complex data in cloud-based computing and data analysis environments. The course involves substantial programming in R, Python, SQL, and shell scripts. Prerequisites: BIOS 6301 and BIOS 6342 or equivalent. Biennial [3].

This advanced course introduces causal inference methods for observational data and randomized studies. Topics include the Rubin causal model, directed acyclic graphs, propensity scores, inverse probability weighting, instrumental variables, causal mediation analysis, marginal structural models, g-computation, and sensitivity analyses to examine robustness to untestable assumptions. Students learn the basic theory behind the methods and their application to biomedical data examples. Prerequisites: BIOS 7323 and BIOS 7346 or equivalent. Biennial [3].

This course presents advanced topics in design, analysis, and governance of clinical trials. Design topics include adaptive trials, pragmatic trials, sequential trials, cluster-randomized trials, and platform trials. Analysis topics include methods for handling missing data, estimand frameworks, Bayesian analysis methods, composite endpoints, and confirmatory and exploratory assessment of heterogeneous treatment effects. Governance topics include regulatory perspectives on advanced trial designs, informed consent in pragmatic trials, and other ethical and operational issues. Prerequisites: BIOS 6312, BIOS 6342, and BIOS 6321 or equivalent. Biennial [2].

This course covers standard and modern/advanced methods for neuroimage analysis from a biostatistical perspective. Students will learn to analyze and interpret common modalities such as fMRI, structural MRI, cortical thickness, diffusion-weighted imaging, and resting-state connectivity using popular neuroimaging analysis software and visualization tools. Advanced topics may include, site correction, first-level and group-level models, network analysis, AI/machine learning, circularity analysis, multivariate/spatial inference, confidence set methods, and centile methods. Upon completion of this course, students will be prepared to understand and contribute to statistical research in neuroimaging. Prerequisites: BIOS 6312 and BIOS 6342 or equivalent. Biennial [2].