Testes bayesianos em ensaios clínicos

Abstract

In this thesis, we propose two new Bayesian approaches for equivalence hypotheses testing for proportions and prove that these Bayesian hypotheses tests are equivalent. These Bayesian methodologies applied to equivalence tests combine frequentist and Bayesian tools from the perspective of decision theory, in which optimal decision rules are used to minimize the linear combination of the probabilities of type I and II errors, in addition to the use of a significance level as a function of sample size. Thus, these Bayesian methodologies overcome some limitations of the frequentist approach, predominantly used for equivalence testing. Moreover, we perform a Bayesian robustness study for the significance tests. We propose a sensitivity index by using the derivative of the constructed statistical functionals. The results of real data analysis show that this sensitivity index satisfactorily measures the local sensitivity of prior quantities with respect to the choice of the prior distribution. A simulation study was carried out to assess the rate of the type I error probability and the power of the tests under different scenarios. We also evaluate overdispersed count data by means of a misspecification analysis. We present a table to determine, in a practical way, the optimal sample size. The developed methodologies are illustrated for bioequivalence tests in the context of clinical trials.