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Dose-response curves
Hezoučký, Martin ; Hlávka, Zdeněk (advisor) ; Maciak, Matúš (referee)
Title: Dose-response curves Author: Martin Hezoučký Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Zdeněk Hlávka, Ph.D., Department of Probability and Mathematical Statistics Abstract: In this thesis, we deal with the process of research and development of new medical substances with a focus on statistical methods used to determine appropriate doses. For this purpose, we examine the dose-response relationship. First, we describe a typical procedure for the development of a new drug. Second, we focus in detail on the MCP-Mod method. Third, we propose a new method based on the theory of gradual change models. This approach tests whether the administration of the drug has a significant effect. If so, the dose with desired effect is estimated using an appropriate model. Specifically, we provide an esti- mate using linear, quadratic and Emax gradual change models. We also describe a construction of a confidence interval for the point of change and also for the dose with the desired effect. The advantage of the proposed method over the MCP-Mod is the determination of the confidence intervals. Finally, we apply the above mentioned methods to data from the U.S. Tox21 research program and compare the results based on several tested substances and clearly demonstrate the...
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Dose-response curves
Hezoučký, Martin ; Hlávka, Zdeněk (advisor) ; Maciak, Matúš (referee)
Title: Dose-response curves Author: Martin Hezoučký Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Zdeněk Hlávka, Ph.D., Department of Probability and Mathematical Statistics Abstract: In this thesis, we deal with the process of research and development of new medical substances with a focus on statistical methods used to determine appropriate doses. For this purpose, we examine the dose-response relationship. First, we describe a typical procedure for the development of a new drug. Second, we focus in detail on the MCP-Mod method. Third, we propose a new method based on the theory of gradual change models. This approach tests whether the administration of the drug has a significant effect. If so, the dose with desired effect is estimated using an appropriate model. Specifically, we provide an esti- mate using linear, quadratic and Emax gradual change models. We also describe a construction of a confidence interval for the point of change and also for the dose with the desired effect. The advantage of the proposed method over the MCP-Mod is the determination of the confidence intervals. Finally, we apply the above mentioned methods to data from the U.S. Tox21 research program and compare the results based on several tested substances and clearly demonstrate the...
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Berry-Esseen inequality
Hezoučký, Martin ; Pawlas, Zbyněk (advisor) ; Maslowski, Bohdan (referee)
In this submitted bachelor thesis we deal with the convergence in dis- tribution rate estimates of the standardized mean of independent identically dis- tributed random variables to standard normal distribution. In the introductory part we present applied probability distributions and state necessary mathemati- cal theorems - primarily the central limit theorem and Berry-Esseen's theorem. In the application part, we deal with specific probability distributions and deter- mine for them all parameters affecting their convergence rate. In particular, we focus on estimates of the constant C from Berry-Esseen's inequality for these se- lected distributions. Subsequently we compare the final estimates of the constant C for these probability distributions and deal with its coherence with the theo- retical estimates of this constant. 1
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