The ICH E9 addendum introduces the term intercurrent event to refer to events that happen after treatment initiation and that can either preclude observation of the outcome of interest or affect its interpretation. It proposes five strategies for handling intercurrent events to form an estimand but does not suggest statistical methods for estimation. In this article we focus on the hypothetical strategy, where the treatment effect is defined under the hypothetical scenario in which the intercurrent event is prevented. For its estimation, we consider causal inference and missing data methods. We establish that certain "causal inference estimators" are identical to certain "missing data estimators." These links may help those familiar with one set of methods but not the other. Moreover, using potential outcome notation allows us to state more clearly the assumptions on which missing data methods rely to estimate hypothetical estimands. This helps to indicate whether estimating a hypothetical estimand is reasonable, and what data should be used in the analysis. We show that hypothetical estimands can be estimated by exploiting data after intercurrent event occurrence, which is typically not used. Supplementary materials for this article are available online.