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https://www.bradyneal.com/causal-inference-course#course-textbookOnce we identify some causal estimand by reducing it to a statistical estimand, we still have more work to do. We need to get a corresponding estimate. In this chapter, we'll cover a variety of estimators that we can use to do this. 7.1. PreliminariesWe denote the individual treatment effect (ITE) with τi and average treatment effe..

https://www.bradyneal.com/causal-inference-course#course-textbookIn Section 4.4, we saw that satisfying the backdoor criterion is sufficient to give us identifiability, but is the backdoor criterion also necessary? In other words, is it possible to get identifiability without being able to block all backdoor paths? As an example, consider that we have data generated according to the graph in Fig..

https://www.bradyneal.com/causal-inference-course#course-textbookRandomized experiments are noticeably different from observational studies. In randomized experiments, the experimenter has complete control over the treatment assignment mechanism (how treatment is assigned). For example, in the most simple kind of randomized experiment, the experimenter randomly assigns (e.g. via coin toss) each ..

https://www.bradyneal.com/causal-inference-course#course-textbookCausal models are essential for identification of causal quantities. We described identification as the process of moving from a causal estimand to a statistical estimand. However, to do that, we must have a causal model. 4.1. The do-operator and Interventional DistributionsThe first thing that we will introduce is a mathematical o..

https://www.bradyneal.com/causal-inference-course#course-textbook3.1. Graph TerminologyA graph is a collection of nodes ("vertices") and edges that connect the nodes. Undirected graph: the edges do not have any direction. A directed graph's edges go out of a parent node and into a child node, with the arrows signifying which direction the edges are going. Two nodes are said to be adjacent if the..

https://www.bradyneal.com/causal-inference-course#course-textbook2.1. Potential Outcomes and Individual Treatment EffectsThe potential outcome Y(t) denotes what your outcome would be, if you were to take treatment t. A potential outcome Y(t) is distinct from the observed outcome Y in that not all potential outcomes are observed. Rather all potential outcomes can potentially be observed. The one ..

https://www.bradyneal.com/causal-inference-course#course-textbook1.1. Simpson's ParadoxA key ingredient necessary to find Simpson's paradox is the non-uniformity of allocation of people to the groups. Scenario 1If the condition C is a cause of the treatment T, treatment B is more effective at reducint mortality Y. Because having severe condition causes one to be more likely to die (C → Y) and ca..