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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.