Causal Inference for Combining RCTs and Observational Studies: Methods Comparison and Medical Application Bénédicte Colnet, INRIA Saclay; Imke Mayer, Centre d'Analyse et de Mathématiques Sociales, EHESS; Guanhua Chen, Department of Biostatistics and Medical Informatics, University of Winsconsin-Madison; Awa Dieng, Google Research; Ruohong Li, Indiana University School of Medicine; Gaël Varoquaux, INRIA Saclay; Jean-Philippe Vert, Google Research; Julie Josse, INRIA Sophia-Antipolis; Shu Yang, North Carolina State University