Complex sentence: For instance, patients undergoing long-term anticoagulation therapy with warfarin have to be cautious and increase their dosage of warfarin, and have their clotting time checked frequently because failure to do so could lead to undertreating with anticoagulation, resulting in serious consequences of thromboembolism.
Split into simpler sentences: For instance, patients undergoing long-term anticoagulation therapy with warfarin have to be especially cautious and increase their dosage of warfarin accordingly. Failure to do so could lead to undertreating with anticoagulation, resulting in serious consequences of thromboembolism.