The Veterans Health Administration, the largest integrated health care system in the country, has long employed many of the approaches Medicare is pushing on all hospitals to reduce unnecessary readmissions. But new data show VA hospital patients are just as likely to end up back in a hospital bed as are patients at private hospitals. The new statistics underscore how hard it may be for hospitals to stop patients from rebounding back through their doors, a major goal of Medicare as it seeks to curtail the nation’s ballooning health costs. VA hospital patients aged 65 or older suffering from heart failure, heart attacks or pneumonia returned to a hospital within a month at the same rate as did Medicare patients initially cared for at private hospitals, according to an analysis of the data. The data were published by Medicare last month on its Hospital Compare Web site.