  Estimating treatment effects from observational data provides insights about
causality guiding many real-world applications such as different clinical study
designs, which are the formulations of trials, experiments, and observational
studies in medical, clinical, and other types of research. In this paper, we
describe causal inference for application in a novel clinical design called
basket trial that tests how well a new drug works in patients who have
different types of cancer that all have the same mutation. We propose a
multi-task adversarial learning (MTAL) method, which incorporates feature
selection multi-task representation learning and adversarial learning to
estimate potential outcomes across different tumor types for patients sharing
the same genetic mutation but having different tumor types. In our paper, the
basket trial is employed as an intuitive example to present this new causal
inference setting. This new causal inference setting includes, but is not
limited to basket trials. This setting has the same challenges as the
traditional causal inference problem, i.e., missing counterfactual outcomes
under different subgroups and treatment selection bias due to confounders. We
present the practical advantages of our MTAL method for the analysis of
synthetic basket trial data and evaluate the proposed estimator on two
benchmarks, IHDP and News. The results demonstrate the superiority of our MTAL
method over the competing state-of-the-art methods.
