  We consider a randomized controlled trial between two groups. The objective
is to identify a population with characteristics such that the test therapy is
more effective than the control therapy. Such a population is called a
subgroup. This identification can be made by estimating the treatment effect
and identifying interactions between treatments and covariates. To date, many
methods have been proposed to identify subgroups for a single outcome. There
are also multiple outcomes, but they are difficult to interpret and cannot be
applied to outcomes other than continuous values. In this paper, we propose a
multivariate regression method that introduces latent variables to estimate the
treatment effect on multiple outcomes simultaneously. The proposed method
introduces latent variables and adds Lasso sparsity constraints to the
estimated loadings to facilitate the interpretation of the relationship between
outcomes and covariates. The framework of the generalized linear model makes it
applicable to various types of outcomes. Interpretation of subgroups is made by
visualizing treatment effects and latent variables. This allows us to identify
subgroups with characteristics that make the test therapy more effective for
multiple outcomes. Simulation and real data examples demonstrate the
effectiveness of the proposed method.
