Heartburn drugs are already under investigation for possible links to dementia, kidney and heart problems. And now, according to a new report, an analysis of nearly 250,000 medical records in the country Denmark has found a link between the drugs and the risk of having a stroke. According to their report at the American Heart Association’s annual meeting this week, the researchers say that the risk of stroke was 21 percent higher in patients taking a proton pump inhibitor, a drug that relieves heartburn.