<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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-221/1/a/solution