# Causal Inference and Propensity Score Methods

In this course students gain an overview on the statistical techniques and research designs used by epidemiologists to estimate treatment effects from patient data and learn how to apply these techniques.

We begin by introducing the Neyman-Rubin causal model (RCM), also called the potential outcomes framework, which postulates that each patient has as many potential outcomes as there are treatment options. Within this framework it is possible to define certain types of treatment effects that we often want to estimate in epidemiological studies, such as average causal effects. It is then explained how completely randomized experiments (randomized controlled trials – RCTs) can be used to estimate these causal effects. Students gain insight into how in an RCT design with a treatment and a control group, only one potential outcome per patient is observed, while the other potential outcome is missing. We will then see that due to an ingenious property of RCTs, called exchangeability, simple mean differences between treatment and control groups are equal to average causal effects. Students gain awareness that this property is the central reason for the pivotal importance of RCTs for estimating causal effects.

Subsequently, we will consider estimation of treatment effects in settings when treatment assignment cannot be randomized by the experimenter. This setting is referred to as an observational design and emerges in epidemiology usually in the form of cross-sectional retrospective as well as prospective studies. The key difference compared to RCTs is that exchangeability is not known to hold in general. However, sometimes the reasons for treatment assignment have been observed (in the data) in the form of so-called confounding variables. When this is true so-called conditional exchangeability holds. The causal inference literature then offers an immense spectrum of statistical techniques for validly estimating treatment effects even outside of RCTs. We go on by studying and applying a core set of these estimation techniques.

We start by covariate-based regression adjustment which students have encountered in earlier statistics classes. We focus on the assumptions and circumstances under which this technique has good performance for estimating causal effects (e.g. linearity and covariate balance). Then we consider examples where linear regression miserably fails to correctly estimate causal treatment effects. Students gain awareness how dangerous it can be to blindly use regression adjustment for treatment effect estimation. As alternative to regression adjustment we then consider alternative estimation techniques with a main focus on the important class of propensity score adjustment techniques. Here we devote significant attention to propensity score weighting, stratification, and matching techniques for estimating treatment effects. These techniques share the advantage that the relationship between confounders and outcome variables does not need to be known or modeled correctly. Instead, the relationship with treatment assignment is modeled and small errors in model specification are alleviated by matching or stratification. All propensity score techniques are thoroughly practiced in order to enable students to apply them on own research problems. We also look at the so-called covariate overlap and covariate balancing assumptions and how to assess them. After considering propensity score techniques we briefly move on to so-called double robust estimation of treatment effects. These estimators combine propensity score weighting with regression adjustment and in many settings can give researchers the best of both worlds.

It is the goal of this course to enable students to use all techniques but also be aware of the underlying assumptions that allow their use or forbid it. In addition, we summarize and discuss the implications for planning and designing epidemiological research. It is often not known that observational studies require a great amount of preparation. An important framework for doing so is the ‘Target Trial Framework’ which is discussed and practiced to enable students to judge the quality of observational studies and design their own.