  In most medical research, the average treatment effect is used to evaluate a
treatment's performance. However, precision medicine requires knowledge of
individual treatment effects: What is the difference between a unit's
measurement under treatment and control conditions? In most treatment effect
studies, such answers are not possible because the outcomes under both
experimental conditions are not jointly observed. This makes the problem of
causal inference a missing data problem. We propose to solve this problem by
imputing the individual potential outcomes under a specified partial
correlation (SPC), thereby allowing for heterogeneous treatment effects. We
demonstrate in simulation that our proposed methodology yields valid inferences
for the marginal distribution of potential outcomes. We highlight that the
posterior distribution of individual treatment effects varies with different
specified partial correlations. This property can be used to study the
sensitivity of optimal treatment outcomes under different correlation
specifications. In a practical example on HIV-1 treatment data, we demonstrate
that the proposed methodology generalises to real-world data. Imputing under
the SPC, therefore, opens up a wealth of possibilities for studying
heterogeneous treatment effects on incomplete data and the further adaptation
of individual treatment effects.
