| Abstract [eng] |
A. Mainelis.Two-way Enriched Clinical Trial Design in Bayesian Framework: master thesis/ supervisor Assoc. Prof. Dr. V. Skorniakov; Vilnius university, faculty of Mathematics and Informatics, department of Statistical Analysis. The objective of this master thesis is to apply Bayesian methodology to the two-way enriched design (TED) which helps to cope with the high rate of the placebo response. The main part is dedicated to the model parameters estimation using the maximum likelihood (ML) and Bayes approach. For the latter, the informative priors like constrained uniform, beta with appropriate parameters distributions and the objective priors like uniform distributions, Jeffreys, reference were tested. The parameters were estimated on the simulated data. The ML estimates had the lowest bias in almost all the cases, but Bayesian estimates had lower RMSE and Kullback-Leibler divergence in the majority of the configurations. Models with the informative priors showed the best results. In the rest part of this thesis Bayes credible intervals for the hypothesis testing in TED are proposed. The type I error and the power of the new testing procedure were evaluated using the Markov Chain Monte Carlo simulations with the various parameters configurations. The power for testing was higher than in the original approach in almost all the cases. However, type I error rate was controlled well only in the models with the uniform distributions as priors. Using the proposed method in TED, the sample size and the cost of the researches could be reduced. This work could be extend for the continuous outcome in Bayesian framework. Also, the alternative testing procedure might be developed. |
