This is a Public Health Course. Public Health classes are offered on the Health Services Campus at 168th Street. For more detailed course information, please go to Mailman School of Public Health Courses website at http://www.mailman.hs.columbia.edu/academics/courses
Prerequisite: Public Health P6103 or P6104. The study of linear statistical models. Regression and correlation with one independent variable. Partial and multiple correlation. Multiple and polynomial regression. Single factor analysis of variance. Simple logistic regression
Prerequisite: Public Health P6104 and working knowledge of calculus. Fundamentals, random variables, and distribution functions in one or more dimensions: moments, conditional probabilities, and densities; Laplace transforms and characteristic functions. Infinite sequences of random variables, weak and strong large numbers: central limit theorem
The first portion of this course provides an introductory-level mathematical treatment of the fundamental principles of probability theory, providing the foundations for statistical inference. Students will learn how to apply these principles to solve a range of applications. The second portion of this course provides a mathematical treatment of (a) point estimation, including evaluation of estimators and methods of estimation; (b) interval estimation; and (c) hypothesis testing, including power calculations and likelihood ratio testing.
Prerequisite: Public Health P8104 and P8109 or the equivalent. Clinical trials concerning chronic disease, comparison of survivorship functions, parametric models for patterns of mortality and other kinds of failures, and competing risks.
Prerequisite: Public Health P6104, P8100 and a working knowledge of calculus. An introduction to the application of statistical methods in survival analysis, generalized linear models, and design of experiments. Estimation and comparison of survival curves, regression models for survival data, log-linear models, logit models, analysis of repeated measurements, and the analysis of data from blocked and split-plot experiments. Examples drawn from the health sciences.
This is a Public Health Course. Public Health classes are offered on the Health Services Campus at 168th Street. For more detailed course information, please go to Mailman School of Public Health Courses website at http://www.mailman.hs.columbia.edu/academics/courses
Substantive questions in empirical scientific and policy research are often causal. This class will introduce students to both statistical theory and practice of causal inference. As theoretical frameworks, we will discuss potential outcomes, causal graphs, randomization and model-based inference, causal mediation, and sufficient component causes. We will cover various methodological tools including randomized experiments, matching, inverse probability weighting, instrumental variable approaches, dynamic causal models, sensitivity analysis, statistical methods for mediation and interaction. We will analyze the strengths and weaknesses of these methods. The course will draw upon examples from social sciences, public health, and other disciplines. The instructor will illustrate application of the approaches using R/SAS/STATA software. Students will be evaluated and will deepen the understanding of the statistical principles underlying the approaches as well as their application in homework assignments, a take home midterm, and final take home practicum.
This is a course at the intersection of statistics and machine learning, focusing on graphical models. In complex systems with many (perhaps hundreds or thousands) of variables, the formalism of graphical models can make representation more compact, inference more tractable, and intelligent data-driven decision-making more feasible. We will focus on representational schemes based on directed and undirected graphical models and discuss statistical inference, prediction, and structure learning. We will emphasize applications of graph-based methods in areas relevant to health: genetics, neuroscience, epidemiology, image analysis, clinical support systems, and more. We will draw connections in lecture between theory and these application areas. The final project will be entirely “hands on,” where students will apply techniques discussed in class to real data and write up the results.
Prerequisite: Public Health P6104 or the equivalent. Fundamental methods and concepts of the randomized clinical trial; protocol development, randomization, blindedness, patient recruitment, informed consent, compliance, sample size determination, cross-overs, collaborative trials. Each student prepares and submits the protocol for a real or hypothetical clinical trial.
Prerequisites: At least one course each in probability and genetics and the instructor's permission. Fundamental principles of population genetics, with emphasis on human populations. Genetic drift; natural selection; nonrandom mating; quantitave genetics; linkage analysis; and applications of current technology (e.g. SNPs). Students will master basic principles of population genetics and will be able to model these principles mathematically/statistically.
Prerequisite: Public Health P8111. Features of repeated measurements studies; balance in time, time-varying covariates, and correlation structure. Examination of the models for continuous repeated measures based on normal theory; random effects models, mixed models, multivariate analysis of variance, growth curve models, and autoregressive models. Non-parametric approaches and models for repeated binary data. Applications of generalized linear models to repeated data. Empirical Bayes approaches are discussed as time allows.
Prerequisites: Public Health P6104. Introduction to the principles of research data management and other aspects of data coordination using structured, computer-based exercises. Targeted to students with varying backgrounds and interests: (1) established and prospective investigators, scientists, and project leaders who want to gain a better understanding of the principles of data management to improve the organization of their own research, make informed decisions in assembling a data management team, and improve their ability to communicate with programmers and data analysts; and (2) students considering a career in data management, data analysis, or the administration of a data coordinating center.
The biostatistical field is changing with new directions emerging constantly. Doing research in these new directions, which often involve large data and complex designs, requires advanced probability and statistics tools. The purpose of this new course is to collect these important probability methods and present them in a way that is friendly to a biostatistics audience. This course is designed for PhD students in Biostatistics. Its primary objective is to help the students achieve a solid understanding of these probability methods and develop strong analytical skills that are necessary for conducting methodological research in modern biostatistics. At the completion of this course, the students will a) have a working knowledge in Law of Large Numbers, Central Limit Theorems, martingale theory, Brownian motions, weak convergence, empirical process, and Markov chain theory; b) be able to understand the biostatistical literature that involves such methods; c) be able to do proofs that call for such knowledge.
Prerequisite: Statistics G6105 (real analysis and probability theory), or the equivalent. A general introduction to mathematical statistics and statistical decision theory. Elementary decision theory, Bayes inference, Neyman-Pearson theory, hypothesis testing, uniformity, most powerful unbiased tests, confidence sets. Estimation: methods, theory, and asymptotic properties. Likelihood ratio tests, multivariate distribution. Elements of general linear hypothesis, invariance, nonparametric methods, sequential analysis.
This is an advanced course for first-year Ph.D. students in Biostatistics. The aim is to provide a solid foundation of the theory behind linear models and generalized linear models. More emphasis will be placed on concepts and theory with mathematical rigor. Topics covered including linear regression models, logistic regression models, generalized linear regression models and methods for the analysis contingency tables.
In this course, students will apply the concepts and methods introduced in Statistical Practices and Research for Interdisciplinary Science (SPRIS) I to a real research setting. Each student will be paired with a Biostatistics faculty member. The student will participate in one of the mentor’s collaborative projects to learn how to be an effective member of an interdisciplinary team. The relationship will mimic that between a medical resident and an attending physician. The SPRIS II experience will vary depending on the assigned faculty member, but all students will gain exposure to preparing collaborative grant applications, designing research studies, analyzing real data, interpreting and presenting results, and writing manuscripts. Mentors will help to develop the student’s data intuition skills, ability to ask good research questions, and leadership qualities. Where necessary, students may replicate projects already completed by the faculty mentor to gain experience.
For appropriately qualified students wishing to enrich their programs by undertaking literature reviews, special studies, or small group instruction in topics not covered in formal courses.