  In this study, we compared two groups, in which subjects were assigned to
either the treatment or the control group. In such trials, if the efficacy of
the treatment cannot be demonstrated in a population that meets the eligibility
criteria, identifying the subgroups for which the treatment is effective is
desirable. Such subgroups can be identified by estimating heterogeneous
treatment effects (HTE). In recent years, methods for estimating HTE have
increasingly relied on complex models. Although these models improve the
estimation accuracy, they often sacrifice interpretability. Despite significant
advancements in the methods for continuous or univariate binary outcomes,
methods for multiple binary outcomes are less prevalent, and existing
interpretable methods, such as the W-method and A-learner, while capable of
estimating HTE for a single binary outcome, still fail to capture the
correlation structure when applied to multiple binary outcomes. We thus propose
two methods for estimating HTE for multiple binary outcomes: one based on the
W-method and the other based on the A-learner. We also demonstrate that the
conventional A-learner introduces bias in the estimation of the treatment
effect. The proposed method employs a framework based on reduced-rank
regression to capture the correlation structure among multiple binary outcomes.
We correct for the bias inherent in the A-learner estimates and investigate the
impact of this bias through numerical simulations. Finally, we demonstrate the
effectiveness of the proposed method using a real data application.
