Using Bayes' theorem to answer a practical XXXX .

@entity1 @entity715 @entity340 @entity1031
BACKGROUND AND AIM OF THE STUDY: The risk of @entity1031 ( @entity1031 ) risk in a @entity340 @entity1 who has lived perhaps for 15 years since implant without @entity1031 or @entity715 is unknown. As @entity1 are heterogeneous with regard to embolic risk, these @entity1 must have a lower than average risk; whether this risk reduction could be quantified was the aim of the present study. METHODS: If all @entity1 had the same risk, the @entity1031 -free curve would be exponential, with a constant hazard (equal to the 'linearized' rate). 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 @entity1031 -free curve, the mixing distribution can be estimated. Subsequently, given an observation for a particular @entity1 , e.g. zero emboli in 15 years, Bayes' theorem can be used to update the mixing distribution for these @entity1 . RESULTS: Using observed @entity1031 -free curves for Starr-Edwards valves, the mixing distribution for @entity1031 -free periods from one to 25 years was estimated. Because the risk distributions were skewed, the mean value was higher than the median. The mean (median) risk (% per year) fell from 4.5 (1.8) at implant to 1.7 (0.7) at 15 years for the aortic position, and from 7.0 (3.4) to 2.4 (1.2) for the mitral position. Thus, the average risk after 15 years was approximately 35-40% of the risk at implant for both the aortic and mitral positions, using either the mean or median risk. CONCLUSION: The mean risk for @entity1 after 15 @entity1031 -free years is approximately one-third of the risk of all @entity1 at implant. However, there is a wide range, with some @entity1 still having higher risks. Bayes' theorem is useful for deriving such answers. Linearized rates have limited value for describing @entity1031 risk in a heterogeneous population.
