A control theory approach to the management of blood clotting speed using the anticoagulant warfarin is investigated. Proportional Integral (PI) and Proportional-Integral-Plus (PIP) controllers are developed for models identified from patient data. These are used to estimate treatment decisions subject to stochastic disturbances, model uncertainty and missed observations, the latter representing missed clinic appointments. The focus is on the relative performance of various integral-of-error (IOE) forms, which are used to track the target International Normalised Ratio (INR) at steady state. These are adapted in novel ways to handle the missed observations. Preliminary Monte Carlo simulations suggest that forward difference, mean and trapezoidal IOE forms with modified pole assignment, could lead to more desirable outcomes than the standard case, but the differences are relatively small and more research is required into scenarios leading to set point deviations.