Intervened graph

As explained in Causal Inference for Data Science

An intervened graph is a causal graph modified to represent an intervention by removing arrows into the intervened variable and fixing its value.

An intervened graph represents what would happen after deliberately setting a variable to a value. To model do(T = A), remove every arrow pointing into treatment T and fix T to A. The resulting graph defines the intervention distribution P|do(T = A), rather than the observed distribution P|T = A. section 2.2.4

This distinction separates a decision from an observation. P|T = A describes patients who happened to receive treatment A; P|do(T = A) describes the hypothetical result of giving treatment A to everyone. The graph therefore turns a causal question into a formal model. section 2.2.4

Choosing a kidney-stone treatment

Suppose confounder C affects both treatment T and outcome O. Forcing T to t removes C → T while retaining the pathways from T to O, producing the graph for P(O|do(T = t)). In a randomized trial, no confounder points into T, so the observed and intervened graphs coincide: P(O|do(T = t)) = P(O|T = t). section 2.5.1 section 2.2.4

Figure 2.6 Data-generation process producing the intervened probability distribution P|do(T = A), which models what would happen if we gave treatment A to every patient

Use the intervention diagram to visualize how assigning treatment A to every patient changes the data-generating process and produces P|do(T = A). section 2.2.4

A conditional intervention targets a subgroup, such as patients with confounder value Z = z, and expresses its effect as P(O|do(T = t), Z = z). This shortcut is unsafe when the subgroup is defined by a post-treatment mediator, where counterfactual reasoning is required. section 2.5.8

How Causal Inference for Data Science covers it

How deep it goes

Defines graph surgery and intervention probabilities, contrasts conditioning, and defers post-treatment subgroup problems to counterfactuals.

Examples

Uses hospital treatment decisions, kidney-stone subgroups, RCTs, and diagrams of observed versus intervened data-generating processes.

What it assumes

Assumes treatment, outcome, confounder, causal graph, and probability notation while clarifying intervention versus conditioning.

What you can do after

Evaluate treatment effects by distinguishing observed treatment probabilities from intervention probabilities and identifying when randomization makes them coincide.

How it connects

Connects causal inference with conditioning, confounding, randomized controlled trials, conditional effects, mediators, and counterfactuals.

liveBookmanning.com

Read Causal Inference for Data Science on liveBook Get the book at manning.com

Related concepts

• interventionproduced by · An intervention is a deliberate, externally imposed change or control applied to a variable or system to alter or assess its behavior or outcomes.
• probability distributionproduces · A probability distribution is a mathematical specification assigning probabilities to the possible values or outcomes of a random variable, with total probability one.
• directed acyclic graphconfigures · A directed acyclic graph is a graph with directed edges and no directed cycles.

This explainer was generated by Manning's knowledge graph from the text of Causal Inference for Data Science. The section links point to the parts of the book it draws on.