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Assumption 3.3 ((Strict) Causal Edges Assumption) In a directed graph, every parent is a direct cause of all its children

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An estimand is the quantity that we want to estimate.

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Assumptions of causal inference: 1. Unconfoundedness (Assumption 2.2) 2. Positivity (Assumption 2.3) 3. No interference (Assumption 2.4) 4. Consistency (Assumption 2.5)

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The Positivity-Unconfoundedness Tradeoff Although conditioning on more covariates could lead to a higher chance of satisfying unconfoundedness, it can lead to a higher chance of violating positivity.

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e would be, if you were to take treatment π‘ . A potential outcome π(π‘) is distinct from the observed outcome π in that not all potential outcomes are observed. Rather all potential outcomes can <span>potentially be observed. The one that is actually observed depends on the value that the treatment π takes on <span>

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We refer to the flow of association along directed paths as causal association

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More generally, the potential outcome π(π‘) denotes what your outcome would be, if you were to take treatment π‘

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Let's start by considering two extreme examples. In the first causal graph here you see that A and Y have no common causes. And therefore, any association between them will be causation. This is the setting that we expect to find in a randomized experiment.

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Today we will focus on confounding in a setting with no selection bias, with no measurement error, and with such a large population that we do not need to worry about chance variability

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usal graph here you see that A and Y have no common causes. And therefore, any association between them will be causation. This is the setting that we expect to find in a randomized experiment. <span>In the second graph here, you see that A and Y have a common cause, L. But there is no causal effect of A on Y. In this setting, all the association between A and Y is due to confounding. <span>

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What is the backdoor path criterion? This is a graphical rule that tells us whether we can identify the causal effect of interest if we know the causal DAG. And the rule is the following: we can identify the causal effect

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Two sources of bias: - common cause (confounding) - conditioning on common effect (selection bias)

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We have seen that confounding is a systematic bias when we are conducting causal inference research.

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When there is an association between A and Y, even if A has a null causal effect, a zero causal effect on Y, then we say that there is bias under the null.

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When there is an association between A and Y, even if A has a null causal effect, a zero causal effect on Y, then we say that there is bias under the null.

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Other (wrong definitions of confounder): - change in estimate definition - conventional definition

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Systematic bias is an association between the treatment A and the outcome Y that does not arise from the causal effect of A on Y.