**Instructor**: Hyunseung Kang

**Email**: hyunseungWHALE@statWHALE.wisc.edu (remove all marine mammals from the e-mail address)

**Office**: 1245B Medical Sciences Center (MSC)

**Syllabus**: Syllabus

## Updates

## Course Overview

The purpose of the course is to prepare students to start research in causal inference. Each week, we will focus on some key topics in causal inference and for more details on these topics, see the course syllabus. The course uses the R software.

At the end of the course, students will:

- Understand key concepts in causal inference (confounding, counterfactuals, missing data)
- Learn how to identify causal estimands
- Learn how to estimate/infer causal estimands
- Learn how to conduct numerical evaluations for causal estimands

## Prerequisites

The official prerequisite for the course is to be in graduate/professional standing. The effective prerequisites are:

- Working understanding of graduate-level probability theory, mathematical statistics, and linear models (i.e. at the level of Stat 609/610 and Stat 849/850). Specifically, you need to know
- conditional expectations and independence
- convergence of random variables
- properties of maximum likelihood estimators
- generalized linear models and their statistical properties
- Wald tests and likelihood ratio tests
- parametric and nonparametric two-sample tests (e.g. two-sample t-test, Wilcoxon signed rank test, permutation test)

- Working understanding of linear algebra and real analysis at the undergraduate level.
- Be able to design simulations in order to empirically validate properties of estimators (e.g. bias, variance, convergence) and statistical tests (e.g. Type I error rate, power, coverage of confidence intervals)
- Working understanding of the software R (e.g. write/debug/test some R code or install/run/debug existing R packages)

## Assignment, Quizzes, and Exams

There are no exam and quizzes for grading.

There is only one graded assignment; see this page for details. You must submit the assignment by ** Friday, May 3rd, 2024 (5:00pm Central) ** to the course Canvas website.

## Lecture Notes

- Introduction and review of prerequisite: [slides], [html].
- Basic concepts in causal inference and randomized experiments: [slides], [html].
- Identification under strong ignorability (i.e. no unmeasured confounding): [slides],[html].
- Identification of the average treatment effect (ATE), the average treatment effect on the treated (ATT)
- Identification of the causal odds ratio (COR) and the causal relative risk (CRR) for binary outcomes
- Identification of static, single-time optimal treatment regime (OTR)
- Identification under unmeasured confounding: [slides] [html].
- Instrumental variables (monotonicity and no additive interaction assumption)
- Regression discontinuity designs (next year)
- Differences-in-differences (next year)
- Negative controls, proximal learning (next year)
- Estimation of causal parameters (Z estimators): [pdf].
- Estimation of causal parameters (Influence functions and von Mises expansion): [pdf].
- A brief introduction to sensitivity analysis (Rosenbaum's Model): [html].
- Next year: synthetic controls, staggered designs