Statistics in medicine
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This paper describes a Bayesian approach to the design and analysis of clinical trials, and compares it with the frequentist approach. Both approaches address learning under uncertainty. But they are different in a variety of ways. ⋯ For example, when choosing or modifying the design of a clinical trial, Bayesians use all available information, including that which comes from the trial itself. The ability to calculate predictive probabilities for future observations is a distinct advantage of the Bayesian approach to designing clinical trials and other decisions. An important difference between Bayesian and frequentist thinking is the role of randomization.
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In addition to the safety, it is essential to establish the causal efficacy of extant and new treatments, and well-designed clinical trials are thought by most to be the 'gold standard' to accomplish this. Contrary to most statisticians' and regulators' views, however, I will argue that the concept of causation involved in clinical trials is not all that clear. ⋯ I characterize 'epidemiological causation' as probabilistic and formulated at a population level, and dependent on certain general criteria for causation as well as study-design considerations. I then attempt to clarify the connections between these concepts of causation and Cartwright's views on complexity and causality, a 'Bayesian' framework proposed by Rubin and further elaborated by Holland, and Glymour and his colleagues' recent directed graphical causal modelling approach.