MATH-655 / 4 credits

Teacher: Stensrud Mats Julius

Language: English

Remark: Fall semester


Every year


This course covers recent methodology for causal inference in settings with time-varying exposures (longitudinal data) and causally connected units (interference). We will consider theory for identification and estimation of effects, illustrated by real-life examples.


This course will cover advanced methods for identification and estimation of causal effects. We will consider time-varying exposures in the presence of time-dependent covariates that are simultaneously confounders and intermediate variables (mediators). Such longitudinal settings are ubiquitous in practice, because exposures and outcomes are often functions of time. Furthermore, we will study settings where there are causal connections between units (interference), which arise in many contemporary data analyses, for examples in studies of social networks and analyses of infectious diseases.


To motivate the methodology, we will analyze examples from different scientific disciplines, including medicine, computer science and economics.


Tentative plan
1. Identification of causal effects in iid settings
1.1. Conventional Identifiability assumptions
1.2. DAGs and SWIGs
1.3. Time-varying confounding
1.4. Identifiability in the presence of unmeasured confounding
1.5. Mechanisms
2. Estimation of causal effects
2.1. Non-parametric and semi-parametric inference
2.2. Efficiency bounds
2.3. Convergence rates
2.4. Regular and non-regular estimators
2.5. Influence functions
2.6. Estimation using machine learning
3. Interference
3.1. Definitions of interference
3.2. Estimands in interference settings
3.3. Definitions of target populations
3.4. Partial interference
3.5. Identification in interference settings
4. Applications
4.1. Medical interventions, including pharmaceuticals
4.2. Infectious diseases
4.3. Social networks


Causality; Causal inference; Longitudinal Studies; Design of experiments; Observational studies; Causal Graphs

Learning Prerequisites

Required courses

The students are expected to know the basics of causal theory, statistical theory and probability theory.

Recommended courses

Thus, they should have taken intro courses in  statistics probability and causal inference.

Learning Outcomes

By the end of the course, the student must be able to:

  • Describe the fundamental theory of causal models
  • Critique assess causal assumptions and axioms
  • Describe when and how causal effects can be identified and estimated from non-experimental data.
  • Demonstrate how to derive semi-parametric estimators and prove efficiency guarantees.
  • Estimate causal parameters from observational data



Relevant articles and book chapters will be presented during the course.


Some broad resources are:
• Hernan, M.A. and Robins, J.M., 2020. Causal inference: What if?
• Imbens, G.W. and Rubin, D.B., 2015. Causal inference in statistics, social, and biomedical sciences. Cambridge University Press
• Pearl, J., 2009. Causality. Cambridge university press

Ressources en bibliothèque

Moodle Link

In the programs

  • Exam form: During the semester (session free)
  • Subject examined: Advanced methods for causal inference
  • Lecture: 28 Hour(s)
  • Practical work: 56 Hour(s)
  • Type: optional

Reference week

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