BIOS6311: Principles of Modern Biostatistics
2023-08-19
Course information
This document includes all the course notes for Vanderbilt Biostatistics BIOS6311 Principles of Modern Biostatistics.
MIDTERM NOVEMBER 9TH 2023
From that Rice book above here are some good practice problems:
Section 4.7: 2, 16, 44, 47, 50, 54, 68 (not really that helpful)
Section 5.4: 11 (might be helpful), 17 (the equality should be approximate equality),
Section 7.7: 3, 8, 10, 16, 17, 18, 21
Syllabus
Schedule: Tuesdays/Thursdays 10:30am-12pm (in-person)
Lab: Tuesdays 4pm-5pm (in-person)
Instructor: Simon Vandekar (he/him/his)
TA: Yeji Kuo
Office hours: by appointment
Email: simon.vandekar@vumc.org. I do not check my vanderbilt.edu email address, regularly.
0.0.1 Overview
Biostatistics (and statistics) is a framework for learning about the world that is based on the theory of probability. The goal of this class is to teach the concepts of biostatistics through basic examples that form the content of the class using software tools for reproducible statistical research in R. The concepts are the basis for modern statistical research – i.e. the foundational concepts you learn here can be used to evaluate modern statistical methods. The objective content will cover basic statistical objects (e.g. means), with as much focus as possible on rigorous modern methods. My interests are in medical imaging in the fields of psychology, psychiatry, and cellular biology, so I will use examples from those fields, hoping to pique your interest in those research areas.
0.0.2 Goal
Upon completion of this course, you should be able to evaluate statistical methods based on their operating characteristics. While the concepts for methods evaluation we will learn are more general, they will be taught in the context of one and two-sample statistical methods within Frequentist, Likelihood, and Bayesian philosophies with as much focus as possible on rigorous modern methods. If the course is effective you will
- Strengthen mathematical tools for understanding and evaluating statistical methods
- Learn to analyze a dataset using basic statistical inference tools (e.g. one sample/two sample tests)
- Learn to program statistical evaluation tools in R
- Learn to use the goals and concepts of the three statistical philosophies
- Evaluate statistical methods using simulations and bootstrapping
- Understand how statisticians choose and design statistical methods
0.0.3 Datasets
Most of the course will be taught through applications with a dataset. I will make a couple datasets available for you to apply your statistical methods and evaluation tools.
0.0.4 Homework
Homework will be your primary grade for the course. It will also be the way that you will learn software tools through hands on experience: we will plan for you to submit most of homework assignments using Rmarkdown.
0.0.5 Exams and Quizzes
Previously, I just had fill-in-the-blank quizzes and a final exam. This time we will have an open-answer midterm and final to help prepare you for the first qualifying exam.
0.0.6 Class
This will be an in-person class, but I might record the lectures. We will meet in-person twice a week (Tues/Thurs 10:30am-12pm). In class meetings we’ll be working to solve math and programming problems together that will help you do your homework.
0.0.7 Lab
There will be as many lab activities as I have time to plan. Otherwise that time will be used to help debug code, catch up on missed classes, or learn the materials and work together or in groups on the homework.
Background necessary for the course: The official background for the course is Calculus 1. I will teach as if you have taken introductory probability, such as “A first course in probability,” by Ross. I assume novice level literacy in R statistical programming, but experience in another language will be helpful to learning R (in particular Matlab and Python). I will use some linear algebra if the class as a whole seems to have sufficient background in this area.
0.0.8 Text
I’ve based the class off of previous versions by Robert Greevy and “Mathematical Statistics and Data Analysis,” by Rice. I will not explicitly use this book in the class, but it is probably the most complete reference for the material. I will point to other references as they come up.
0.0.9 Class resources
Previously I’ve done everything in Brightspace, but to make it more accessible, I am going to host it through a course webpage instead.
- Brightspace - For class communication, homework submission and grading.
- Pumble - For class communication.
- Box - For sharing datasets and files.
0.0.10 Diversity and inclusion:
Creativity is critical to research in statistics. In statistics, creativity comes in the form of questions (e.g. what happens if this model is incorrect?; when I condition on a subset of the data, what things are still random?) Diversity is at the heart of creativity, because our perspectives shape how we see the world. By working together to consider other’s perspectives, we will learn more about the problems we discuss. For this reason, please interact with each other in a spirit of curiosity and empathy (not just about the class content, but as you learn about the people you will go through grad school with). I expect this class to be a welcoming environment for all students, regardless of background, skin color, gender identity, orientation, spiritual belief or any other personal feature.
0.0.11 Course outline
I might adapt course content based on the mine or the classes interests. This is generally how it has looked:
- Probability tools and
R - Law of Large Numbers and Central Limit Theorem
- Confidence intervals for a single mean
- Z intervals
- T intervals
- CIs for binomial proportion
- Hypothesis testing
- Paired means
- Two means
- Welch’s correction
- Likelihood theory
- Features of the likelihood function
- Bayesian statistics
- Binomial proportion
- Normal mean
- Contingency tables and tests for two binomial means (might switch this for effect sizes)
- Resampling and Nonparametric methods
- Overview of regression