Causal thinking

MATH-352

Media

This file is part of the content downloaded from Causal thinking.

This course will give a unified presentation of modern methods for causal inference. We focus on concepts, and we will present examples and ideas from various scientific disciplines, including medicine, computer science, engineering, economics and epidemiology.

Content

Association vs. causation
Definitions of causal effects
- Causal models
- Counterfactuals and potential outcomes
- Individual level causal effects vs. average causal effects
- Population causal effects
Study design
- Randomisation and experiments
- Observational studies
Causal graphs
- Causal Directed Acyclic Graphs
- Single World Intervention Graphs
Identification of causal effects
- Identifiability assumptions
- SWIGs
Causal mechanisms
- Mediation and path specific effects
- Instrumental variables
Applications
- Medical interventions, including pharmaceuticals
- Experiments in technology industry and engineering
- Experiments in life sciences
- Causal effects and mechanisms in the social sciences.
Estimation of causal effects
- Estimation using classical statistical models
- Estimation using machine learning

Teaching methods

Lectures, where I will use a (digital) whiteboard (will be made available here).

The TA will respond to questions on Ed Discussion (see the link below), usually within 3 working days (not counting weekends). Please use Ed Discussion for all questions about the course. We do not respond to private emails about the homeworks. Questions need to be posted on edDiscussions.

Assessment methods

Final exam (80% of the total grade).
One midterm exam in November (20% of the total grade).

Textbook

What if by Hernan and Robins

I will not record the lectures

We will start 10h15 today (no exercise session before the lecture).

I will introduce the course and give you a first taste of causal inference. I will go through some examples. Don't hesitate to ask questions.

Take a look at the slides. Some of the material is covered in Chapter 1 of Causal Inference What If (pages 3-12), which uses the same notation.

As a reminder, my handwritten notes will always be available after the lecture (see link above, "the digital whiteboard").

Definitions of causal effects. Estimands. Randomized experiments.

Continuation of the heart transplant example. See Chapter 1 and 2 (until chapter 2.3) of the textbook by Hernan and Robins.

No lecture because Monday is a holiday.

Observational studies. Effect modification and Interaction and connections to precision ("personalized") medicine.

Chapters 3.1, 4.1, 4.3, 5.1, 5.2, 5.3 of the textbook by Hernan and Robins.

Target trials. Structural equations. Causal graphs (DAGs).

Chapters 3.6, 6.1 of the textbook by Hernan and Robins.

We continue with causal graphs. D-separation and the backdoor criterion will be covered.

Chapters 6.3, 6.4, 7.3 of the textbook by Hernan and Robins.

No teaching -- Autumn break

Single World Intervention Graphs (SWIGs).

My lecture notes on SWIG includes more details than what I cover in class. This is intentional, as you might use this as reference material if you want to dig deeper into certain topics. However, the material covered in class and the exercises are the material that is directly relevant to the exam.

If you want more (informal) text on DAGs and SWIGs, please read chapters 6 and 7.5 in the textbook by Hernan and Robins.

We will continue with Single World Intervention Graphs. We will also discuss dynamic Single World Intervention Graphs.

We have attached some further readings on SWIGs below, if you are interested. Furthermore, the following Chapter 7.5 "Single-world intervention graphs" in Hernan and Robins provides an informal overview.

I will go through principles of statistical inference. In particular, I will discuss finite population and superpopulation frameworks. I will also discuss hypothesis testing and some estimation of causal effects.

Some of the material I will discuss can be found in Chapter 10 in the book by Hernan and Robins.

The midterm will take place this week.

We have included a final exam from a previous year so that you have an idea of the format, which will be the same as the midterm. Please be aware that this final exam covers more topics than what we have and will have seen at this point.

We have also included a cheat sheet that will be included with the midterm. We will add the cover page of the midterm on Friday before the exam.

We cannot guarantee answers to your questions on the Ed forum before the midterm if they are posted past Friday at 16:00.

The midterm will occur during class hours, from 10.15 to 11.45, with an added 30 minutes for those with extra time. The exercise session before the midterm is cancelled.

We continue with estimation. The points I will consider are (mostly) described in Chapters 11-12 in the book by Hernan and Robins.

Exercise sheet 9 will be shorter as we will also go over the midterm's solutions next week.

We continue with estimation. I will briefly mention a doubly robust strategy, and I will talk about estimation when we are interested in effects of time-varying treatments. The things I will discuss are mostly described in Chapters 12-13 in the book by Hernan and Robins, although I give my own twist.

We will consider estimation of time-varying treatment regimes. I will focus on marginal structural models, which are discussed in chapter 12 in the book by Hernan and Robins.

When we are done with marginal structural models, we will start with the final topic of the course which is causal inference in the presence of unmeasured confounding.

We will give a problem sheet that has the structure of a "mock exam". You will also have the chance to raise questions in an additional office hour in mid January.

We include two graded homeworks from previous years. These homeworks were meant to be completed over a one week period and hence take longer to solve.

Have a nice winter break!