Using Bayes’ Theorem to Answer a Practical Heart Valve Question
Gary L. Grunkemeier PhD

The thromboembolism (TE) risk of a heart valve patient who has survived for perhaps 15 years since implant without an event is unknown. As patients are heterogeneous with regard to TE risk, they must have a lower than average risk. With a mixture of risks in a population, the population hazard will be a decreasing function of time. By fitting a certain parametric function to the observed TE-free curve, the mixing distribution can be estimated. Then, given an observation for a particular patient, e.g. zero events in 15 years, Bayes’ theorem can be used to update the mixing distribution for such patients. The average risk after 15 years is ~35-40% of the risk at implant for both the aortic and mitral positions, though there is a wide range and some patients still have higher risks.