The invention provides a method of treating a tumor in a human patient comprising (i) identifying a patient as having a LAG-3 positive tumor and (ii) administering to the patient a PD-1 pathway inhibitor, a combination of a PD1 pathway inhibitor and an immune checkpoint inhibitor, a combination of a LAG-3 inhibitor and a PD-1 pathway inhibitor, or an anti-CTLA4 antibody. In some embodiments, the method further comprises identifying the patient as having a LAG-3 positive PD-L1 positive tumor. In some embodiments, the LAG-3 inhibitor is an anti-LAG-3 antibody and the PD-1 pathway inhibitor is an anti-PD-1 antibody. The methods of the invention can improve response rates to treatment with a PD-1 pathway inhibitor, a combination of a PD1 pathway inhibitor and an immune checkpoint inhibitor, or a combination of a LAG-3 inhibitor and a PD-1 pathway inhibitor.