Abstract:
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In medical device, good historical data are often available prior to the start of a study and can be formally incorporated into Bayesian analysis. In this paper, we investigate the use of the power priors (Ibrahim and Chen, 2000) in Bayesian hierarchical models applied to data from crossover trials. Power prior enables historical borrowing by discounting the historical likelihood to a certain power to accommodate heterogeneity between trials. However, in practice, we may be uncertain about the degree to which the historical data will agree with the current study. In such cases, probable values of the power parameter should be determined by the data. Three approaches are presented including those using (i) a hyperprior for the power parameter; (ii) a joint power prior; and (iii) an extended model that directly parameterize the similarity of the current and historical data. How key parameters affect borrowing behavior and key issues involved in each method are demonstrated. Applications of power prior historical borrowing as well as no borrowing are illustrated with real data from a crossover contact lens trial using SAS.
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