Course Team

Instructor

• Chris Slaughter
  • james.c.slaughter@vumc.org (best)
  • james.c.slaughter@vanderbilt.edu (checked ~ weekly)
  • Office: 2525 West End, 11-127

TA

• Chih-Ting Yang
• Haoyang Yi

Course website(s)

• https://chrissl789.github.io/modern-regression/

  • Course notes
    • HTML, PDF, Quarto (.qmd)
  • Daily schedule
  • Links to course tools

• Brightspace

  • Announcements
  • Submit homework and manage grades
  • FERPA compliance
    • The Family Educational Rights and Privacy Act (FERPA) is a federal law enacted in 1974 that protects the privacy of student education records.

Course Timetable

• Lectures (weekly)
  • Tuesdays, 10:30 - 11:50 am - 2525 WEA, Room 11105
  • Thursdays, 10:30 - 11:50 am - 2525 WEA, Room 11105

• Labs (weekly)
  • Mondays, 1:00 to 1:50 pm - 2525 WEA, Room 11105

Software – R

• Primary software package will be R
  • Free
  • Most adaptable statistical package
  • Used by the majority of academic Biostatisticians
  • Rstudio IDE used to work with R
  • Rstudio includes Quarto, the latest and greatest tool for rendering markdown documents

Software – Rstudio and Quarto

• Course notes rendered using Quarto with R code integrated
  • Quarto allows for creating dynamic content using embedded R (or other software) code
  • Will allow you to see all code used to generate notes
    • I will highlight important R code
  • I am still learning Quarto and it is evolving, so it has more features than I will likely use
• Quarto introduction covered tomorrow

Software – Stata

• Secondary software package will be Stata
  • My second favorite statistical package
  • Relatively easy syntax
  • Designed for people who know statistics, but don’t want to write basic functions
  • Not integrated with Quarto
    • I will provide a list of equivalent Stata commands in labs and lectures, but usually not produce the output

Generative AI (e.g. ChatGPT, Claude)

• See syllabus for complete statement on the permitted uses of generative AI in this course
• If any questions, ask the instructor for clarifications
• As with any tool, use with caution
  • Help with generating code, or converting code between languages
  • Help with editing interpretations in more easily understood language
  • The prompt that you use matters. Also, identical prompts at different times can give different answers

My views on generative AI

• Rapidly evolving with many potential applications
• Best used when you are the expert and AI is the assistant
  • If prompted correctly, AI can help you think through a problem, but you have to know the right prompts to use and evaluate critically
  • “Is my regression model good” vs “I am concerned about heteroskedasticity in my linear regression model. What diagnostic tests and remedies should I consider? What are the problems with using a p-value to test for heteroskedasticity like you said to do?”
• We work with highly confidential data in Biostatistics
  • Never upload data to AI platforms

Key limitations of AI

• No true uncertainty quantification. Generated text is confidently stated as being accurate.

• Training data is a frozen snapshot. Models do not learn new information after training.

• No reasoning from first principles for complex problems. Pattern recognition provides median responses.

• AI lowers barriers to performing analysis, but doing the right analysis remains complex.

  • This course is designed to build foundation for right-tail analytical ability - understanding why methods work and when standard approaches fail.

Key skills for effective statistical practice (essential foundations for AI use)

• Specification: Translating scientific questions into appropriate statistical approaches

• Verification: Recognizing when output is wrong or incomplete, knowing what diagnostics to check

• Assumption evaluation: Judging whether a method is appropriate given study design

• Interpretation: Understanding what results mean in scientific context

• In this course, assignments will systematically build these fundamental skills, positioning you as the expert in evaluating and improving AI-generated outputs

AI collapse

• AI “thinks” differently than people do. Iteration often makes things worse, unlike human refinement.
• Shumailov, I., Shumaylov, Z., Zhao, Y. et al. AI models collapse when trained on recursively generated data. Nature 631, 755–759 (2024).

AI Collapse

Guiding Principles

• Alternative course title: How to Use Statistics to Answer Scientific Questions (part 2)
  • Put science before statistics
  • Emphasize parameter estimates and confidence intervals (credible intervals, likelihood intervals) over hypothesis testing and p-values
    • The End of Statistical Significance (Jonathan Sterne)
    • What’s Wrong with P-Values (Bland, Altman)
    • Key difference between scientific/clinical significance and statistical significance
• This is a course in Biostatistics, not coding in R/Stata
  • I will show you how to get an interpret the key statistics, but not interpret every number on output
  • Often there is more than one way to arrive at identical final answers

Example: Clinical vs Scientific significance

• 5 clinical trials conducted to determine if drug A, B, or C lowers cholesterol
• Assume that a decrease of 10 mg/dl or more is important to clinicians
• Study design
  • Cholesterol measured at baseline, subjects take drug for 1 month, Cholesterol measured at 1 month
  • Change in cholesterol is the outcome of interest

Evaluation components and grade percentages

• Midterm (25%)
• Take Home Exam (25%)
• Final Exam (25%)
• Homework (25%)
• Class participation
• This is a 4-credit course. Your lab and lecture grades will be the same

Homework

• Up to 1 per week (probably 6 or 7 total)
• Will focus on real data analysis and interpretation with some mathematical derivations of important quantities
• Questions will focus on specific analyses, with questions stated in as scientific terms as possible
• Work handed in should address the scientific questions
  • Format Table and Figures
• Keys will be provided shortly after the homework is turned in
  • No late homework accepted after the key is posted
• Answers in keys may go beyond what is expected of your homework and present concepts in more detail. You are responsible for any material in the keys for exams.
• You may discuss the homework with others in the class, but the work you turn in should be your own
• Use Brightspace to turn in homeworks and receive feedback and grade

In Class Exams

• Midterm and Final in class
  • Focus on understanding concepts, not memorizing formulas
  • I will provide an example midterm and final
  • For midterm, you will be allowed 1 page of your own notes
  • For final, you will be allowed 2 pages of your own notes
• All output will be provide for you to interpret

Take Home Exam

• Will be given approximately mid point between Midterm and Final
• Demonstrate ability to obtain results through software and interpret findings
• One day to complete and turn in
  • Likely will be a Monday with no lab scheduled for that day
• Practice for applied portion of first year comprehensive exams
• Similar to Homework, but work should be your own

Course notes

• Course notes will be the primary source
• Available on web page
• Daily class schedule will indicate notes being covered
• Notes will be updated throughout semester

Recommended Textbook: Regression Methods in Biostatistics

• Vittinghoff, Glidden, Shiboski, and McCulloch
• Pros
  • Covers applied linear, logistic, survival, and repeated measures regression
  • Biomedical orientation
• Cons
  • Does not discuss robust standard errors, which I will use almost exclusively
  • Emphasizes model diagnostics more that I will
  • Does not cover Bayesian approaches
  • Does not cover matrix algebra
  • Little theory and mathematical derivation

Additional textbooks

• Weisberg, Applied Linear Regression
  • Uses matrix notation and appropriate level of statistical theory for this course
  • Poor for applied data analysis. Earlier version limited to linear models, no Bayesian approaches. Newer version is more comprehensive.
• Wakefield, Bayesian and Frequentist Regression Methods
  • Newer text that I am still evaluating
  • Provides a Bayesian approach to fitting the models we discuss
• I will give recommended readings throughout the semester
• If the course notes and book differ, go with the notes

Supplemental Material

• As needed, I will post supplemental material on the course web page or on Brightspace

  • I prefer the course web page, if possible

  • Brightspace will be used if necessary

• Relevant supplemental material will be noted on course schedule

Getting started

• To do on your own by Tuesday

  • Download and install new versions of R and Rstudio

    • Details on course web page, computing

• I would like everyone (including Stata users) to be able to Render a basic Quarto document

• Plan to discuss Quarto intro on Tuesday

  • It is difficult to anticipate all issues that might arise, so I would like to resolve any major software issues before then