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Course Syllabus for Mathematics of Causal Inference

Essential Data

The course code for Mathematics of Causal Inference is 5BD005. The course name is Mathematics of causal inference, and it is worth 7.5 credits. The form of education is higher education, study regulation of 2007. The main field of study is Biostatistics and Data Science, and the level is AV - Second cycle. The grading scale is Fail (U) or pass (G). The department responsible for the course is the Department of Medical Epidemiology and Biostatistics.

Specific Entry Requirements

To be eligible for the course, students must have at least the grade G (Pass) for the courses "Theory of statistical inference" and "Probability Theory".

Outcomes

The course aims to give the student an introduction to the mathematical foundations of modern causal inference. Emphasis is placed on mathematical concepts, derivations, and proofs. Upon completion of the course, the student should be able to:

• Explain and mathematically derive key causal inference target parameters, such as marginal and conditional causal effects, controlled direct effects, and natural direct effects, and discuss their interpretation and relevance in different contexts.
• Describe, with mathematical rigour, common sources of bias (e.g., exposure-outcome confounding, mediator-outcome confounding, selection bias, and truncation by death) and their implications for causal effect estimation.
• Implement modern causal inference methods, including instrumental variables, propensity scores, doubly robust estimation, and E-values, and explain, with mathematical rigour, how these methods can be used to mitigate biases in the estimation of causal target parameters.
• Critically evaluate the assumptions, strengths, and limitations of different causal inference methods in applied research.
• Justify and defend methodological choices for causal effect estimation in diverse research settings, considering both theoretical and practical constraints.

Content

The course covers mathematical concepts, derivations, and proofs underlying modern causal inference.

Teaching Methods

The forms of teaching and learning are seminars, self-studies, and group learning. The course emphasizes active learning.

Examination

The grading decision will be based on the examiner's assessment of the student's performance during the oral presentations in seminars, active participation in group discussions, and individual discussions with the examiner. All seminars are compulsory, and the examiner assesses if and, in that case, how absence from compulsory components can be compensated.

Other Directives

The course language is English.

Literature and Other Teaching Aids

Study material and reference articles will be provided during the course. Recommended literature includes:

• Pearl, J. (2009). Causality. Cambridge university press.
• Hernán MA, Robins JM (2023). Causal Inference: What If. Boca Raton: Chapman & Hall/CRC.