By Ransdell Pierson NEW YORK (Reuters) Jun 14 - For millions of heart patients, a pair of new blood thinners have been heralded as the first replacements in 60 years for warfarin, whose hardships and risks have deterred many from using the stroke-prevention medicine. But growing complaints of risks and deaths tied to the new crop of drugs have made some top U.S. cardiologists hesitant to prescribe them. Some are proposing a more rigorous monitoring regimen for when they are used. Most concerns revolve around Pradaxa (dabigatran), a twice daily pill from Boehringer Ingelheim that was approved by the U.S. Food and Drug Administration in October 2010 to prevent strokes in patients with atrial fibrillation. It was the first new oral treatment for that use since warfarin was introduced in the 1950s. "The good news is you now have an alternative to warfarin," said Dr. Alan Jacobson, director of anti-coagulation services at the Veterans Administration (VA) healthcare syst...