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APTS module: Causal Inference

Module leader: V Didelez and R Evans

Please see the full Module Specifications for background information relating to all of the APTS modules, including how to interpret the information below.

Aims: Causal inference deals with investigating the effect(s) of (typically hypothetical) interventions from (typically 'imperfect') data; often the data is observational, i.e. not obtained from a 'perfect' randomised experiment. The aim of the course is to introduce the fundamental principles, concepts and basic methods of causal inference, including an outlook on current challenges and recent developments.

Learning outcomes: The participants will be able to distinguish research questions that are causal, as opposed to descriptive or predictive, in nature. They will be able to formalise research questions as causal estimands, state and evaluate the required assumptions in a variety of common settings. They will further be able to use causal diagrams to identify potential sources of bias and how to mitigate these. Finally, they will be able to carry out a basic causal analysis with standard software.

Prerequisites: Familiarity with regression models, multivariate distributions and their properties. It will be helpful to revisit, prior to the course, the general notions of conditional distributions and conditional (in)dependence. Some knowledge of methods of estimation beyond maximum likelihood, such as estimating equations will be useful.

Further reading:

  • Didelez. Causal concepts and graphical models. In: Handbook of Graphical Models (eds. Maathuis, Drton, Lauritzen, Wainwright), Chapman Hall/CRC, 2018.
  • Hernán and Robins. Causal Inference: What If, Chapman Hall/CRC, 2020 - online.
  • Lauritzen. Causal inference from graphical models. In: Complex Stochastic Systems (eds. Barndorff-Nielsen, Cox, Klüppelberg), Chapman Hall/CRC, 2001.
  • Peters, Janzing and Schölkopf. Elements of Causal Inference, Cambridge, 2017.
  • Pearl. Causality: Models, Reasoning, and Inference, (3rd ed.) Cambridge, 2013.


  1. Basic concepts: causation vs association, randomisation, do-interventions, potential outcomes, causal estimands, identifiability (key assumptions), confounding and selection bias, target trial emulation.

  2. Causal diagrams: conditional independence, directed acyclic graphs (DAGs), d-separation, causal Markov condition, backdoor criterion, confounding and selection bias revisited, SWIGs.

  3. Estimating the causal effect of a point treatment: g-methods (propensity scores, inverse-probability weighting, g-formula, g-estimation), optimal adjustment, checking assumptions (positivity, negative controls), double-robustness and double-machine learning, survival outcomes.

  4. Multiple or sequential treatments and causal mediation: causal interpretation (and misconceptions) of multiple regression, time-dependent confounding, marginal structural models, notions of direct/indirect effects and their identifiability.

  5. Outlook on further topics: instrumental variables, causal discovery.

Assessment: TBA