Thirty-nine percent of patients who are given angiograms to check for heart disease turn out not to have a significant problem, according to a study published in Thursday’s New England Journal of Medicine. The researchers said the findings suggest doctors must do better in determining which patients should be subjected to the cost and risks of an angiogram. More than a million people get an angiogram, in which a thin tube is inserted in the arm or groin and threaded up to the heart to check for blocked arteries that could lead to a heart attack. Dye is injected through the tube to make blockages show up on X-rays. The study is based on the records of nearly 2 million angiograms performed at 663 hospitals between 2004 and April 2008.