Course 2025-2026 a.y.

• Review of measures of association. Contingency tables, risk difference, risk ratio, odds ratio, Simpson’s paradox.
• Basic ideas of causal inference as a missing data problem. The potential outcomes framework. Counterfactuals and causal effects. Average treatment effects.
• Randomized experiments: Fisher’s exact test and Neyman’s approach to repeated sampling.
• Observational studies. Unconfoundedness and propensity scores.
• Regression discontinuity designs.
• Causal survival analysis.
• Unmeasured confounding and instrumental variables methods.
• Bayesian causal inference.
• Applications in health.
   

• Provide an overview of the potential outcomes approach for causal inference.
• Understand the basic assumptions underlying causal analysis.
• Master statistical methods for learning causal relationships.

• Identify causal inference problems in health applications.
• Analyze causal inference problems and identify the most suitable research design for addressing them, both with experimental and observational data.
• Apply causal inference methods to real-world data, either experimental or observational, with the aid of software tools.

• Lectures

Face to face lectures on campus

For determining the final assessment, students must choose between the following two options

1) The general exam, at the end of the course.

2) The combination of
2.1) A group project presentation or a group paper presentation, accounting for 40% of the final grade. Such presentations will take place during the course.
2.2) The general exam, accounting for 60% of the final grade, at the end of the course.

As for 2.1), each group is identified by the instructors and must express their preference over presenting a paper versus a project.

Project: a group will be assigned a dataset for which a causal analysis must be conducted using the tools that have been discussed during the course. The causal analysis and the results must be presented, with slides, and students must point out connections with the material presented during the course.

Paper: a group will be assigned a research paper on causality and will have to deliver a presentation discussing it, with slides. The presentation should summarize the main findings of the paper and emphasize the connections with the topics discussed during the course.

General exam: it consists of a written test, with questions on both the methodological and the applied parts of the course, and aims at testing students’ understanding of the statistical foundations and the practical uses of modern approaches to causal inference problems. 

• Ding, P. (2024). A first course in causal inference. CRC Press. A preliminary draft of the textbook is available at https://arxiv.org/pdf/2305.18793
• Additional references will be provided during the course.