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 2:35–3:45pm; 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)
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: MW 1-2pm, or by appointment.
Zoom link provided on Canvas.

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