<Causal identification> means that $\mathbb E[Y(a_1,a_2)]$ is uniquely determined by the observed joint distribution of $(A_1,X,A_2,Y)$ under the causal assumptions. Equivalently, it admits an identifying formula containing only observed-data probabilities and conditional expectations.

The <G-computation> formula for this two-stage treatment is
$$
\boxed{
\mathbb E[Y(a_1,a_2)]
=\sum_x \mathbb E[Y\mid A_1=a_1,X=x,A_2=a_2]
\mathbb P(X=x\mid A_1=a_1)}.
$$
The first factor is the observed mean outcome after the specified treatment history and intermediate value; the second averages over the intermediate-variable distribution generated after the first treatment.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 221 / 1 / a / Solution

For treatment history $\bar A_t$, observed history $H_t$, and final <potential outcome> $Y(\bar a)$, sequential exchangeability requires
$$
Y(\bar a)\mathrel\perp A_t\mid H_t
$$
at every treatment time. Together with <consistency of potential outcomes> and <positivity in causal inference>, it identifies longitudinal effects by <G-computation>.

= Sequential ignorability
{synonym}

Sequential exchangeability

{wiki}

The g-formula identifies an interventional outcome distribution by averaging observed conditional outcome laws over the covariate distribution under suitable consistency, exchangeability, and positivity assumptions.

= G-formula
{synonym}


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 Incoming links: G-computation