Randomization and causation

Professor: Mats J. Stensrud
TAs: Elise Dumas

Motivation

This course covers formal frameworks for causal inference. We focus on experimental designs, definitions of causal models, interpretation of causal parameters and estimation of causal effects. We put emphasis on how these methods can be used to answer practically relevant questions.

Content

• Experimental design
  • Randomisation
  • Matched pairs, block designs, (fractional) factorial designs and latin squares
• Defining a causal model
  • • Causal axioms
    • Falsifiability
    • Structural equations
    • Causal directed acyclic graphs
    • Single world intervention graphs
• Interpretation of causal parameters 
  • • Individual and average level effects
    • Mediation and path specific effects
    • Instrumental variables
• Statistical inference: Estimands, estimators and estimates
  
  • • Relation to classical statistical models
    • Doubly and multiply robust estimators

Teaching methods

Lectures, where I will use a (digital) blackboard. The sessions will not be recorded. 

The TA will respond to questions on Ed Discussion (see the link below). Please use Ed Discussion for all questions about the course. 

Assessment methods

Final exam (80% of the total grade). 
One midterm exam (20% of the total grade). The midterm will be on April 14, 2025, during the lecture.

Teaching resources

• Hernan, M.A. and Robins, J.M., 2020. Causal inference: What if?
• Pearl, J., 2009. Causality. Cambridge university press.

Lecture notes

• The digital blackboard 
• Will be updated continuously and will be made available after each session. Let me know if you detect typos. The slides are available under each week. 

I will introduce the course and give you a first taste of causal inference. Don't worry if things aren't entirely clear yet. We will formalize and solidify the concepts. Don't hesitate to ask questions. 

PS: There is no exercise session this week, as we have not covered any material yet. 

We proved identification results for average causal effects. We also studied effect heterogeneity and interaction. 

I will talk about causal graphs and relate independencies in graphs to counterfactual variables. Many beautiful and important results have recently been published on causal graphs. 

PS: In case you want to know more about soundness and completeness of d-separation (which will take too much time to prove in class): Verma and Pearl described soundness in the following paper, https://arxiv.org/pdf/1304.2379.pdf. Completeness was first shown by  Christopher Meek (https://arxiv.org/pdf/1302.4973.pdf). I will see if there are some sources that are easier to read (and more clearly present the proofs, which are essentially based on the graphoid axioms and laws of probability). 

I will show and illustrate some features of NPSEM-IE and DAGs. Then I will introduce SWIGs. Next time we will see how SWIGs can be used for interesting causal inference tasks, which will be fun! 

We will continue studying SWIGs. We will go through several examples and illustrate why SWIGs are useful in many settings.

We will finish the work and dynamic SWIGs and then consider estimation.

This week we will continue with estimation, using both classical standardization methods and propensity methods. 

We will study a so-called doubly robust estimator, and we will develop some results for marginal structural models for time-varying treatment regimes. 

We study inverse probability weighting and marginal structural models. 

We will study instrumental variables.