Course Description

This course provides a survey of regression techniques for outcomes common in public health data including continuous, binary, count and survival data. Emphasis is on developing a conceptual understanding of the application of these techniques to solving problems, rather than to the numerical details. Extensive use of the computer will be made for analysis of datasets.

This course is designed for graduate and advanced undergraduate students who will be analyzing data with scientific colleagues and who want to develop a practical hands-on toolkit and gain experience in distilling complex statistical information into formats understandable to colleagues. This course will feature R programming elements. To make the most of R students will be expected to use . There are videos on the course’s R page to explain how to get set up and started in RStudio.

Prerequisites

Students should have courses in probability and statistical inference at the level of PHP 2510.

Course Objectives

After successful completion of this course you will understand and be able to develop and interpret regression models to describe how an outcome is related to one or more predictor variables. In particular these include the following capabilities:

  1. Recognize when data should be analyzed by regression
  2. Plan an appropriate analysis
  3. Bring in, Clean and Analyze dats with R.
  4. Coherently summarize results.

Overall Course Expectations

Students in this course will be expected to do the following:

  1. Attend all lectures and actively participate in discussion.

  2. Read all assigned material prior to coming to class and actively participate in class discussions.

  3. Complete and turn in all assignments on time. Solutions to homework must be clearly written with appropriate tables and figures included.

  4. Demonstrate an understanding on material on examinations.

  5. Respect each other, each others questions and each others discussion.

Evaluation

Students will be evaluated based on:

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Grade Category Percentage
Participation 10%
Homework 20%
Exam 1 (03/13/2017) 20%
Exam 2 (05/17/2017) 20%
Final Project 30%

Evaluation Category Details

Participation

This course will move very fast and it is crucial to success in the course that students attend and participate. Many classes will have polls or quizzes that will not be graded for having the most correct or best answer but for participating. Unexcused absences will result in a loss of percentage points.

Homework

Weekly assignments will be given out to students. Assignments will require data handling, data cleaning and interpretation of the results. It is expected that all assignments are completed on time. No late assignments will be accepted.

Students will also be graded on the conciseness and quality of work. Turning in many pages of just computer code and output will affect the grade in a negative fashion.

Exam 1 (March 13, 2017)

An in class exam will be given. Students will be expected to interpret and analyze regression models. Students will also be expected to understand conceptual ideas.

Exam 2 (May 17, 2017 at 2:00pm)

An in class exam will be given. Students will be expected to interpret and analyze regression models. Students will also be expected to understand conceptual ideas.

Final Project

Students will start working on a final project about half way through the semester. This project will require:

  1. Asking a relevant public Health question.
  2. Identify available data to answer this question.
  3. Model the question with appropriate statistical models.
  4. Write up a report with appropriate tables, graphs and results.

The project will consist of individual as well as group content. For the individual content you will complete the 4 requirements. For the group component. You will work in small groups to evaluate each others work. This will require:

  1. Constructive Criticism of Group members Projects based on Course Content.
  2. In depth review of group members work.

You will be graded on both individual and group aspects. It is important to learn not only how to ask a public health question and answer that question with a study or data but equally important to review others work and arguments.

Semester Hours

Over the course of the semester students will spend at least the amounts of time shown below:

Class Schedule

Students must read the following before Monday’s class session. Important: class readings are subject to change, contingent on mitigating circumstances and the progress we make as a class. Students are encouraged to attend lectures and check the course website for updates.

Week 01, 01/23 - 01/27: Syllabus Day / Introduction to RStudio and RMarkdown.

  • First Day of Class
  • Go over syllabus
  • Learn Use of Server.
  • Learn Basics of R and RMarkdown

Week 02, 01/30 - 02/03: Unit 1: Probability Distributions and Regression Outcomes

  • We will complete Unit 1 this week.
  • Monday
    • Notes: Unit 1 - Probability Distributions and Regression Outcomes
    • Required Reading: Andersen and Skovgaard 2.1
  • Wednesday
    • Notes: Unit 1 - Probability Distributions and Regression Outcomes
    • Required Reading: Andersen and Skovgaard 2.2

Week 03, 02/06 - 02/10: Unit 2: One Categorical Covariate

  • We will complete Unit 1 and begin Unit 2 this week.
  • Monday
    • Notes: Unit 1 - Probability Distributions and Regression Outcomes
    • Required Reading: Andersen and Skovgaard 2.3
  • Wednesday
    • Notes: Unit 2 - Binary Covariate
    • Required Reading: Andersen and Skovgaard 3.1

Week 04, 02/13 - 02/17: Unit 2: One Categorical Covariate

  • We will complete Unit 2 this week.
  • Monday
    • Notes: Unit 2: Categorical Covariate with more than 2 levels
    • Required Reading: Andersen and Skovgaard 3.2
  • Wednesday
    • Notes: Unit 2 -Further Examples

Week 05, 02/20 - 02/24: Unit 3: Quantitative Covariates

  • We will begin Unit 3 this week.
  • Monday
    • NO CLASS - LONG WEEKEND
  • Wednesday
    • Notes: Unit 3: Linear Effect
    • Required Reading: Andersen and Skovgaard 4.1

Week 06, 02/27 - 03/03: Unit 3: Quantitative Covariates

  • We will complete unit 3 and begin Unit 4 this week.
  • Monday
    • Notes: Unit 3: Nonlinear Effects
    • Required Reading: Andersen and Skovgaard 4.2
  • Wednesday
    • Notes: Unit 3 - Further Examples

Week 07, 03/06 - 03/10: Unit 4: Multiple Regressions

  • We will begin Unit 4 this week.
  • Monday
    • Notes: Unit 4: Two Covariates: Models without Interaction
    • Required Reading: Andersen and Skovgaard 5.1
  • Wednesday
    • Notes: Unit 4: Two Covariates: Models with Interaction
  • Required Reading: Andersen and Skovgaard 5.2

Week 08, 03/13 - 03/17: Midterm and Unit 4: Multiple Regressions

  • This week we will have a midterm and completing Unit 4.
  • Monday
    • Midterm - Units 1 - 4.2
  • Wednesday
    • Notes: Unit 4: Several Covariates
    • Required Reading: Andersen and Skovgaard 5.3

Week 09, 03/20 - 03/24: Unit 5: Linear Model Assumptions and Testing

  • We will begin Unit 5 this week.
  • Monday
    • Notes: Unit 5: Linear Regression Assumptions and Residuals
    • Required Reading: Sheather 2.2, 3.1
  • Wednesday
    • Notes: Unit 5: Residual and QQ-Plots
    • Required Reading: TBD

Week 10, 03/27 - 03/31: Spring Break

No Classes - Spring Break

Week 11, 04/03 - 04/07: Unit 5: Linear Model Assumptions and Testing

  • We will complete Unit 5 and begin Unit 6 this week.
  • Monday
    • Notes: Unit 5 - Multicollinearity
    • Required Reading: Sheather 6.4 and Andersen and Skovgaard 6.1
  • Wednesday
    • Notes: Unit 6 - Logistic Regression Diagnostics
    • Required Reading: Sheather 8.1-8.2

Week 12, 04/10 - 04/14: Unit 6 - Logistic Regression Diagnostics

  • We will complete Unit 6 and Unit 7 this week.
  • Monday
    • Notes: Unit 6 - Logistic Regression Diagnostics
    • Required Reading: Sheather 8.1-8.2
  • Wednesday
    • Notes: Unit 7: Survival Analysis Diagnostics
    • Required Reading: Andersen and Skovgaard 6.1, Sheather 7.1-7.2

Week 13, 04/17 - 04/21: Unit 8: Model Building and Selection

  • We will begin Unit 8 this week.
  • Monday
    • Notes: Unit 7: Model Building and Selection
    • Required Reading: Andersen and Skovgaard 6.1, Sheather 7.1-7.2
  • Wednesday
    • Notes: Unit 7: Model Building and Selection
    • Required Reading: Andersen and Skovgaard 6.1, Sheather 7.1-7.2

Week 14, 04/24 - 04/28: Unit 8: Putting it All together

  • We will begin Unit 8 this week.
  • Monday
    • Notes: Unit 8 - A Complete linear Regression
    • Required Reading: TBD
  • Wednesday
    • Notes: Unit 6 - A Complete Logistic Regression
    • Required Reading: TBD

Week 15, 05/01 - 05/05: Unit 8: Putting it All Together

  • We will finish Unit 8
    • Notes: Unit 8 - A Complete Poisson Regression
    • Required Reading: TBD
  • Wednesday
    • Notes: Unit 6 - A Complete Cox-PH Regression
    • Required Reading: TBD

Week 16, 05/08 - 05/12: Overflow and Project Time

With the final week of the course we will use as overflow from previous material. If we are up to date these classes will serve as time to work on your project.

Brown ScM/AM Competencies

Primary Competencies

  1. Identify and implement statistical techniques and models for analysis of data.
  2. Acquire knowledge and skills in research methodologies to collaborate with substantive investigators.
  3. Understand the advantages and disadvantages of randomized and non-randomized studies to measure effects of interventions.
  4. Apply programming skills to analyze data and develop simulation studies.

Refresher Competencies

  1. Demonstrate a foundation in statistical theory and methods for standard designs and analyses encountered with biomedical data.
  2. Recognize key research designs and be able to assist in developing plans for their implementation.
  3. Attain proficiency in management, documentation of study data for use in practical statistical analysis.
  4. Formulate a public health question in statistical terms.
  5. Develop proficiency in making oral, written and poster presentations of work to statistical and non-statistical colleagues.
  6. Review and evaluate the use of biostatistical methods in public health or biomedical field of study.
  7. Demonstrate proficiency in the language of the public health or biomedical field of studies.

Brown Undergraduate Competencies

Primary Competencies

  1. Apply, describe and assess the validity of statistical models (e.g., variety of linear and nonlinear parametric, semiparametric, and nonparametric regression models)

Refresher Competencies

  1. Explain the interplay between mathematical derivations and statistical applications.
  2. Perform exploratory data analysis approaches and graphical data analysis methods.
  3. Describe design of studies (e.g., random assignment, random selection, data collection, and efficiency) and issues of bias, causality, confounding, and coincidence.
  4. Be able to use of one or more professional statistical software environment.
  5. Be able to manipulate data (possibly “big”) using software in a well-documented and reproducible way.
  6. Communicate statistical results effectively.
  7. Identify and critique application of statistics in various fields

Students with Special Needs

Brown University is committed to full inclusion of all students. Students who, by nature of a documented disability, require academic accommodations should contact the professor during office hours. Students may also speak with Student and Employee Accessibility Services at 401-863-9588 to discuss the process for requesting accommodations.

Diversity Statement

This course is designed to support an inclusive learning environment where diverse perspectives are recognized, respected and seen as a source of strength. It is our intent to provide materials and activities that are respectful of various levels of diversity: mathematical background, previous computing skills, gender, sexuality, disability, age, socioeconomic status, ethnicity, race, and culture.

English Language Learners

Brown University welcomes students from around the world, and the unique perspectives international students bring enrich the campus community. To empower students whose first language is not English, an array of ELL support is available on campus including language and culture workshops and individual appointments. For more information about English Language Learning at Brown, contact the ELL Specialists at ellwriting@brown.edu.

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