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about.qmd
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---
title: "Syllabus"
---
### Overview
This course surveys modern statistical methods for analyzing **censored** time-to-event data in clinical, epidemiological, sociological, and engineering studies. We provide intuitive explanations of statistical theory, such as counting-process martingale, to address real-world problems and build problem-solving skills. The course combines methodological exposition with extensive case studies, primarily from health sciences research (sample R/SAS code will be provided). The focus is on the **application** of data analysis and study design.
### Course Structure
The course consists of three parts. The first part covers methods for univariate event times, e.g., Kaplan–Meier curve, log-rank test, and Cox proportional hazards model. The second part extends to complex outcomes such as recurrent events, multivariate events, (semi-)competing risks, joint survival and longitudinal data analysis, multistate data, and composite endpoints. The third part explores cutting-edge topics, including causal inference and machine learning for censored data.
### Learning Outcomes
Students will:
- Understand the features of censored data and their impact on statistical inference.
- Select appropriate non- and semi-parametric methods for various data types.
- Evaluate and verify assumptions for estimation and inference.
- Apply statistical procedures to solve real-world problems using R (or SAS).
- Clearly interpret and present analytical results to address substantive questions.
### Prerequisites
Students should have foundational knowledge in random variables, expectation, variance, and maximum likelihood estimation, as well as introductory courses in hypothesis testing (e.g., *t*-test, ANOVA) and (generalized) linear regression models. Prior experience with R or SAS is helpful but not required.
### Time and Location
**MW 2:30–3:45pm; Clinical Sciences Center (CSC) - Room G5/119**
- **Note:** Classes on **1/27** and **4/28** will be held in **HSLC 1220.**
### Instructors
#### Main Instructor
**Lu Mao, PhD**\ ([https://lmaowisc.github.io](https://lmaowisc.github.io){target="_blank"})\
WARF 207A, 610 Walnut St, Madison, WI 53726\
Email: lmao\@biostat.wisc.edu\
Phone: 608-263-5674\
Office Hours: T&Th 3–4pm, or by appointment.\
Zoom link provided on Canvas.
#### Teaching Assistant
**Yunhong Wu**\
Email: wu292\@wisc.edu\
Office Hours: To be decided, or by appointment.
### Readings
- \[**Required**\] *Applied Survival Analysis: From Univariate to Complex Time-to-Event Outcomes* (Posted on Canvas by chapter)
- \[For Methodological Insight\] Kalbfleisch, J. D. & Prentice, R. L. (2002). *The Statistical Analysis of Failure Time Data* (2nd Ed). John Wiley & Sons.
- \[For Applied Focus\] Klein, J. P. & Moeschberger, M. L. (2003). *Survival Analysis: Techniques for Censored and Truncated Data* (2nd Ed). Springer.
- \[For Theoretical Depth\] Fleming, T. R. & Harrington, D. P. (1991). *Counting Processes and Survival Analysis*. John Wiley & Sons.
### Course Schedule
#### Kickoff
| Date | Topic | Notes |
|------|---------|----------|
| 1/22 | Lecture | Overview |
| | Reading | Syllabus |
#### Part I: Univariate Events
| Date | Topic | Notes |
|--------------|---------------------------------------------|--------------|
| 1/27 | Introduction | Chapter 1 |
| 1/29 | Mathematical Foundations | Chapter 2 |
| 2/3 | Nonparametric Estimation of the Survival Curve | Chapter 3 |
| 2/5 | Comparing Survival Rates Between Groups | Chapter 3 |
| 2/10 | Cox Proportional Hazards Model – Assumptions and Inference | Chapter 4 |
| 2/12 | Cox Proportional Hazards Model – Residual Analysis | Chapter 4 |
| 2/17 | Cox Proportional Hazards Model – Time-Varying Covariates | Chapter 4 |
| 2/19 | Other Non- and Semi-parametric Methods | Chapter 5 |
| 2/24 | Study Design and Sample Size Calculation | Chapter 6 |
| 2/26 | Left Truncation | Chapter 7 |
| 3/3 | Interval Censoring | Chapter 7 |
#### Part II: Complex Outcomes
| Date | Topic | Notes |
|--------------|---------------------------------------------|--------------|
| 3/5 | Multivariate Events – Conditional (Frailty) Models | Chapter 8 |
| 3/10 | Multivariate Event Times – Marginal Models | Chapter 8 |
| 3/12 | Recurrent Events | Chapter 9 |
| 3/17 | Competing and Semi-competing Risks | Chapter 10 |
| 3/31 | Joint Analysis of Longitudinal and Survival Data | Chapter 11 |
| 4/2 | Multistate Models – Introduction | Chapter 12 |
| 4/7 | Multistate Models – Cox-Type Markov and Semi-Markov Models | Chapter 12 |
| 4/9 | Composite Endpoints – Nonparametric Estimation | Chapter 13 |
| 4/14 | Composite Endpoints – Semiparametric Regression | Chapter 13 |
#### Part III: Special Topics
| Date | Topic | Notes |
|--------------|---------------------------------------------|--------------|
| 4/19 | Causal Inference with Censored Data – IPTW and Standardization | Chapter 14 |
| 4/21 | Causal Inference with Censored Data – Marginal Structural Models | Chapter 14 |
| 4/23 | Machine Learning with Censored Data – Variable Selection | Chapter 15 |
| 4/28 | Machine Learning with Censored Data – Nonlinear Regression | Chapter 15 |
| 4/30 | Guest Lecture or recap | |
### Homework and Exams
- Homework: Biweekly.
- In-class: quizzes
- Mid-term project.
- Final data analysis project.
### Grading
- **20%** Attendance and in-class quizzes\
- **35%** Homework\
- **20%** Mid-term\
- **25%** Final project