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

Writefor the observed history just before $A_t$. A sufficient condition is sequential exchangeabilityfor every treatment regime, together with consistency of potential outcomes and positivity in causal inference. Repeated conditioning then gives the longitudinal G-formulaGraphically, it is enough that each $A_t$ be D-separated from the final counterfactual under the specified regime after conditioning on its observed past. The two independences used in part b are precisely the $T=2$ instance.