A control theory approach to the management of the blood clotting speed using the anticoagulant Warfarin is investigated. Controllers are developed and analysed using hospital data from patients with chronic conditions under Warfarin anticoagulation treatment. Proportional Integral (PI) and Model Predictive (MPC) controllers are used to estimate treatment decisions. These controllers are adapted in a novel manner, to enable their use with missing or irregularly sampled data. The performance of the controllers is evaluated both using a simulation of the system and by retrospectively comparing actual decisions in the data to those suggested by the control algorithms. It is shown that when the blood clotting speed is within a target range, the decisions suggested by the control algorithms are similar to those actually made (by medical staff), so would likely have led to similar desirable outcomes. When the blood clotting speed is outside the desirable range and too high or too low, the control algorithms on average suggest lower, or higher inputs respectively. These suggestions are likely to lead to improved outcomes.