This course will provide an introduction to the basics of regression analysis. The class will proceed systematically from the examination of the distributional qualities of the measures of interest, to assessing the appropriateness of the assumption of linearity, to issues related to variable inclusion, model fit, interpretation, and regression diagnostics. We will primarily use scalar notation (i.e. we will use limited matrix notation, and will only briefly present the use of matrix algebra).
The main objective of this course is to provide Columbia University's Clinical & Translational Science award trainees, students, and scholars with skills and knowledge that will optimize their chances of entering into a satisfying academic career. The course will emphasize several methodological and practical issues related to the development of a science career. The course will also offer support and incentives by facilitating timely use of CTSA resources, obtaining expert reviews on writing and curriculum vitae, and providing knowledge and resources for the successful achievement of career goals.
With the explosion of “Big Data” problems, statistical learning has become a very hot field in many scientific areas. The goal of this course is to provide the training in practical statistical learning. It is targeted to MS students with some data analysis experience.
This course covers a review of mathematical statistics and probability theory at the Masters level. Students will be exposed to theory of estimation and hypothesis testing, confidence intervals and Bayesian inference. Topics include population parameters, sufficient statistics, basic distribution theory, point and interval estimation, introduction to the theory of hypothesis testing, and nonparametric procedures.
This course will introduce the statistical methods for analyzing censored data, non-normally distributed response data, and repeated measurements data that are commonly encountered in medical and public health research. Topics include estimation and comparison of survival curves, regression models for survival data, logit models, log-linear models, and generalized estimating equations. Examples are drawn from the health sciences.
A comprehensive overview of methods of analysis for binary and other discrete response data, with applications to epidemiological and clinical studies. It is a second level course that presumes some knowledge of applied statistics and epidemiology. Topics discussed include 2 × 2 tables, m × 2 tables, tests of independence, measures of association, power and sample size determination, stratification and matching in design and analysis, interrater agreement, logistic regression analysis.
Regression analysis is widely used in biomedical research. Non-continuous (e.g., binary or count-valued) responses, correlated observations, and censored data are frequently encountered in regression analysis. This course will introduce advanced statistical methods to address these practical problems. Topics include generalized linear models (GLM) for non-Gaussian response, mixed-effects models and generalized estimating equations (GEE) for correlated observations, and Cox proportional hazards models for survival data analysis. Examples are drawn from biomedical sciences.
This course explores the theoretical foundations underlying the models and techniques used in mathematical genetics and genetic epidemiology. Topics include use and interpretation of likelihood methods, formulation of mathematical models, segregation analysis, ascertainment bias, linkage analysis, genetic heterogeneity, and complex genetic models. The course includes lectures, discussions, homework problems, and a final exam. My single most important objective for this course is for students to be able to break down any mathematical modeling problem logically into all its component parts, to express each part" accurately, and to know how to "add" all the pieces back up and to check the accuracy of their result."
Students in this course will learn and practice the fundamental methods and concepts of the randomized clinical trial: protocol development, randomization, blindedness, patient recruitment, informed consent, compliance, sample size determination, crossovers, collaborative trials. Each student prepares and submits the protocol for a real or hypothetical clinical trial.
As statistical models become increasingly complex, it is often the case that exact or even asymptotic distributions of estimators and test statistics are intractable. With the continuing improvement of processor speed, computationally intensive methods have become invaluable tools for statisticians to use in practice. This course will cover the basic modern statistical computing techniques and how they are applied in a variety of practical situations. Topics to be covered include numerical optimization, random number generation, simulation, Monte Carlo integration, permutation tests, jackknife and bootstrap procedures, Markov chain Monte Carlo methods in Bayesian settings, and the EM algorithm.
In this course students will synthetize knowledge from the core with knowledge from both specific department required courses and from certificate required courses. The course deliverable is a written paper combining analyses of a student’s selected data set that uses two of the following methods: (linear regression, logistic regression, nonlinear modeling, mixed effect modeling, machine learning, survival analyses). Students will demonstrate understanding of summarizing (numerically and graphically) data for purposes of specific analyses, presenting results, and interpreting them in the context of public health. Finally, students will also demonstrate the ability to present various stages of the analyses, to ask questions in large collaborative settings, and to troubleshoot their work.
In this course, you will learn to design and build relational databases in MySQL and to write and optimize queries using the SQL programming language. Application of skills learned in this course will be geared toward research and data science settings in the healthcare field; however, these skills are transferable to many industries and application areas. You will begin the course examining the pitfalls of using Excel spreadsheets as a data storage tool and then learn how to build properly-designed relational databases to eliminate the issues related to spreadsheets and maintain data integrity when storing and modifying data. You will then learn two aspects of the SQL programming language: 1) the data manipulation language (DML), which allows you to retrieve data from and populate data into database tables (e.g., SELECT, INSERT INTO, DELETE, UPDATE, etc.), and 2) the data definition language (DDL), which allows you to create and modify tables in a database (e.g., CREATE, ALTER, DROP, etc.). You will additionally learn how to optimize SQL queries for best performance, use advanced SQL functions, and utilize SQL within common statistical software programs: R and SAS.
This course provides a general introduction to mathematical statistics and statistical decision theory for doctoral students in biostatistics. It covers elementary decision theory, Bayes rules, Neyman-Pearson theory, uniformly most power tests, similar tests, uniformly most powerful unbiased tests, confidence sets; basic asymptotic criteria, estimation methods and their asymptotic properties, M-estimators, U-statistics, statistical functionals; likelihood ratio tests, Wald tests, Rao's score tests, and their asymptotic properties, Pitman efficiency. This course will prepare students to their theory qualifying exam.
This course serves as the cumulative experience for those in the Clinical Research Methods (CRM) Track in the Department of Biostatistics. By the end of the semester, students are expected to produce a submission ready manuscript to a journal appropriate to their field of study.
The Statistical Practices and Research for Interdisciplinary Sciences (SPRIS, P9185) is a required course for the PhD and DrPH students in the Department of Biostatistics. The goal is to prepare doctoral students to be effective statisticians to collaborate in an interdisciplinary team and to identify novel statistical research problems with important public health and medical applications. The course aims to provide guidelines and insights of the arts and sciences of consulting, collaboration, and translation of statistical methods to medical studies. Practically useful technical skills acquired from previous coursework will be enhanced and illustrated through applications to real world problems in class projects. Important statistical issues currently undergoing extensive debate will be introduced. Examples of conducting original statistical research to develop new methods addressing real world challenges will be discussed. Career-development related topics will be covered to prepare students to become effective independent and interdisciplinary researchers. Class projects will showcase examples of how to analyze real world data.