How deeply does Causal Inference for Data Science cover consistency equation?

Defines both treatment cases, illustrates them with patient data, and applies them to ATET estimation without resolving missing counterfactuals.

Consistency equation

As explained in Causal Inference for Data Science

A consistency equation states that a unit's observed outcome equals the potential outcome corresponding to the treatment the unit actually received.

The consistency equation links a unit’s observed outcome to the potential outcome matching its actual treatment. For unit i, T(i)=0 implies Y(i)=Y₀(i), while T(i)=1 implies Y(i)=Y₁(i). Potential outcomes remain partly unobserved: each patient reveals only the outcome corresponding to the treatment received. section 10.1.1

Patient recovery

Suppose Holden receives treatment, T=1, and has observed recovery Y=1. Consistency identifies that observed recovery with Holden’s treated potential outcome, Y₁=1. Avasarala does not receive treatment, T=0, so observed recovery Y=1 corresponds to Y₀=1. The unreceived alternative outcome remains unknown for each patient. section 10.1.1

Table 10.1 Hypothetical example of POs with assignment (T(i)) and observed recovery (Y(i))

Name	i	Y ₀( i)	Y ₁( i)	T( i)	Y( i)
Drummer	1	0	0	1	0
Burton	2	1	0	1	0
Holden	3	0	1	1	1
Avasarala	4	1	1	0	1

Use the hypothetical patient table to compare potential outcomes, treatment assignment, and the resulting observed outcome. section 10.1.1

The equation is useful because it replaces the observed treatment-group potential outcome with measurable data when estimating causal effects. It supports adjustment and instrumental-variable formulas, and helps identify the treated term in ATET estimation; it does not reveal the missing counterfactual by itself. section 10.1.1 section 11.4.4

How Causal Inference for Data Science covers it

Cover of Causal Inference for Data Science

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Related concepts

causal adjustmentuses · Causal adjustment estimates a causal effect by conditioning on variables that block noncausal pathways and averaging over their target-population distribution.
instrumental variableuses · An instrumental variable is a variable that affects a treatment or exposure while influencing an outcome only through that treatment or exposure, under causal identifying assumptions.

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.