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Abstract:
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Joint models for longitudinal and survival data have become mainstream tools for analyzing time-to-event data in clinical trials. However, very few methods exist for designing clinical trials using these models. In this talk, We develop a Bayesian design methodology based on Bayesian versions of type I error and power that are defined with respect to the posterior distribution for the parameters and conditional on the relevant hypothesis being true. We demonstrate that when the design controls the Bayesian type I error rate, meaningful amounts of information can be borrowed from the prior and that the borrowable amount increases with the sample size in the new trial. In contrast, when the design is required to control type I error in the traditional frequentist sense, all prior information must be discarded. We introduce a useful connection between Bayesian analyses with the power prior and a weighted maximum likelihood analysis. This leads to an accurate approximation for the posterior probabilities required for Bayesian inference and obviates the need for Markov Chain Monte Carlo methods for Bayesian model fitting. We demonstrate our methodology with simulations and real data.
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