We developed a causal inference test for large-scale observational studies with binay outcomes which is robust to the choice of matching methods. We validate the efficiency of the proposed algorithms by testing the causal relation between Hospital Readmission Reduction Program (HRRP) and readmission to different hospital (non-index readmission) on the State of California Patient Discharge Database from 2010 to 2014. Our result shows that HRRP has a causal relation with the increase in non-index readmission and the proposed algorithms proved to be highly scalable in testing causal relations from large-scale observational studies.