Abstract

Throughout the world, researchers conduct randomized controlled trials and observational studies to test a treatment's efficacy. Here we are dealing specifically with two-arm comparisons, where subjects are assigned to the treatment or control group. However, the outcome of the treatment might not demonstrate efficacy in a population that meets the eligibility criteria. In such cases, it is desirable to efficiently identify populations with characteristics that make the treatment effective in so-called subgroups. Estimating the treatment effect can be used to identify them. Unfortunately, it is impossible to observe the outcome both in the treatment group and in the control group for a given subject. Therefore, it is essential to estimate the treatment effect for each subject using just one treatment dataset. Currently, there are many methods for estimating treatment effects, varying from randomized controlled trials to observational studies. In this presentation, we focus on estimating treatment effects using a linear regression model with Lasso for straightforward subgroup interpretation. In a linear regression model, the main effect and interaction terms describe the outcome for estimating the treatment effect. When using the usual Lasso, the interaction term of an explanatory variable for which the main effect is estimated to be zero may be estimated to be nonzero. However, clinical trials often test interactions between drugs known a priori to be effective for a given disease and explanatory variables. Therefore, if the primary effect term is estimated to be zero, the interaction term should also be zero. Tibshirani and Friedman (2020) proposed a Pliable lasso that introduces a hierarchical constraint such that the interaction term can be nonzero only if the main effect is nonzero. The Pliable lasso is a method for estimating the effect of a treatment on a single outcome. However, in reality, randomized controlled trials often have multiple outcomes of interest, including primary and secondary endpoints. Simultaneously, observational studies are conducted to discover new clinical hypotheses, so it is natural to consider multiple endpoints. For example, the Pliable lasso is used with multiple outcomes. The correlation structure between outcomes cannot be considered in that situation, which could lead to an inaccurate estimation of the treatment's effects and the failure to recognize the correct subgroup. Therefore, we propose an extension of the Pliable lasso that can be applied to multiple outcomes. The Pliable lasso is specifically extended to consider the correlation structure among multiple outcomes using the Reduced rank regression framework and identifies subgroups for multiple outcomes by visualizing the relationship between explanatory variables and outcomes using path diagrams.