An earlier tank image is of no interest once a later, clearer image has been acquired. The frequency of image acquisition (data looks) and the image sampling design alter the probability of finding a tank-like image, but that way of looking at the problem is divorced from the real-time decision to be made based on current cumulative data. Contrast with a frequentist way of thinking: Of all the times a tested object wasn’t a tank, the probability of acquiring tank-like image characteristics at some point grows with the number of images acquired. The probability is now 0.9, and the 0.8 has become completely irrelevant. The object moves closer and some fog clears. Initially an image results in an 0.8 probability of the object being a tank. Imagine that the military has developed a pattern recognition algorithm to determine whether a distant object is a tank. This is one of the least well understood aspects of Bayesian vs. frequentist analysis, and it is due to current probabilities superseding probabilities that were computed earlier. Importantly, there are no multiplicities to control. Such probabilities are probabilities about unknowns based on conditioning on all the current data, without conditioning on unknowns. The reason that Bayesian inference is more efficient for continuous learning is that it computes probabilities looking ahead-the type of forward-in-time probabilities that are needed for decision making. probability of similarity of outcome of two treatments.probability of a clinically relevant effect.Bayesian posterior probabilities, on the other hand, can be computed at any point in the trial and provide current evidence about all possible questions, such as Classical null hypothesis testing only provides evidence against the supposition that a treatment has exactly zero effect, and it requires one to deal with complexities if not doing the analysis at a single fixed time. Bayesian sequential designs are the simplest of flexible designs, and continuous learning makes them very efficient by having lower expected sample sizes until sufficient evidence is accrued. Continuous learning from data and computation of probabilities that are directly applicable to decision making in the face of uncertainty are hallmarks of the Bayesian approach. This trial will adopt a Bayesian framework. Other background material may be found here. Endorsement of these approaches by FDA is not implied. The main resource may be found here with an overview here. These documents contain references, examples, detailed explanations and links to other resources. Dr Harrell has developed detailed supporting documents as part of his 1/4 time appointment to the FDA Center for Drug Evaluation and Research Office of Biostatistics.
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