625.651.8VL - Mathematical Models in Healthcare
Applied and Computational Mathematics
Summer 2026
Description
A firm mathematical foundation for work in biostatistics is provided by a detailed consideration of four mathematical frameworks that can be applied throughout medicine. The class will focus on these framework ideas, which build on earlier coursework in statistics and probability, and their applications. The mathematical frameworks are Markov models, Gaussian processes, logistic regression, and Bayesian networks. The clinical settings to be explored will be associated with treatment, prognosis, and survival within the settings of asthma, diabetes, cancer, and epidemics. While the course is primarily mathematical, students will be expected to work within at least one programming environment (R or Python will be easiest, but Julia, MATLAB, and others will also be supported).
Instructor
Course Structure
Please note that since we are a Virtual Live (VL) class the Modules will populate as we go into each week's lecture time.
Course Topics
- Markov Models
- Gaussian Processes
- Logistic Regression
- Bayesian Networks
These four mathematical approaches to problems in healthcare will be covered in the context of both class-time, break-out room problems, and within your class projects. The goal is to learn at least one of these methods in detail and to feel comfortable with the other three. These methods go beyond their applications within healthcare, so you should find all of these methods to be generally helpful regardless of whether you are primarily interested in healthcare or have your main interests outside of healthcare.
Course Goals
Course Learning Outcomes (CLOs)
- Describe the format of an EHR record and how the time-stamped measures can be used for each of the four types of mathematical models
- Understand the challenges associated with sparse and missing data and what modeling techniques can be used to address those issues
- Evaluate the pros and cons of different models and why you might prefer one over another. For example, under what conditions would you use a network model versus a univariate description of an outcome variable.
Textbooks
Markov Models:
Hidden Markov Models for Time Series, An Introduction using R, Zucchini, MacDonald, and Langrock
Gaussian Processes:
Surrogates: Gaussian Process Modeling, Design, and Optimization for the Applied Sciences, Gramacy, CRC Press
Logistic Regression:
Regression Methods in Biostatistics, Vittinghoff, Glidden, Shiboski, and McCulloch, Springer
Bayesian Networks:
Risk Assessment and Decision Analysis with Bayesian Networks, Fenton and Neil, CRC Press
Student Coursework Requirements
- Weekly problem sets (25% of final grade)
- Breakout room problems (25% of final grade)
- Term project with interim deliverables throughout semester (50%) - Full introduction in module 1.
- Project concept and Choices
- Module 2 - Submit initial ideas (5%)
- Module 7 - Pseudo code and outline (5%)
- Module 8 – Bibliography (10%)
- Module 10 - Connections & Methods (20%)
- Module 12 – Final Project Submission (60%)
Grading Policy
EP uses a +/- grading system (see “Grading System”, Graduate Programs catalog, p. 10).
| Score Range | Letter Grade |
|---|---|
| 100-97 | = A+ |
| 96-93 | = A |
| 92-90 | = A− |
| 89-87 | = B+ |
| 86-83 | = B |
| 82-80 | = B− |
| 79-77 | = C+ |
| 76-73 | = C |
| 72-70 | = C− |
| 69-67 | = D+ |
| 66-63 | = D |
| <63 | = F |
Academic Policies
Deadlines for Adding, Dropping, and Withdrawing from Courses
Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar. Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.
Academic Misconduct Policy
Students with Disabilities - Accommodations and Accessibility
Student Conduct Code
Classroom Climate
JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).
Course Auditing
When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team (EP-Registration@exchange.johnshopkins.edu) in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.