Ql CHAPTER 31 Statistical approaches to make decisions in clinical experiments Albert Vexler and Xiwei Chen Department of Biosratistics. Sc/tool of Public Htalclt and Healllt ProfessiOltS, Stace UttivtrSity of New York at Buffalo, Buffalo, NY. USA THEMATIC SUMMARY BOX At the end of this chapter, students should be able to: • Correctly formulate statisti cal hypotheses with respect to the aims of epidemiological and/or biomedical st ud ies • Const ruct and provide statistical decision-making test rules corresponding to practical experiments • Use parametric and nonparametric likelihood testing techniques in appli ed researches • Understand basic properties of likelihood ratio type tests in parametric and nonparamet- ric manners • Use basic test procedures and their components in practical statistical decision-making mechanisms • Employ statisti cal software at a beg inning level Introduction, preliminaries, and basic components of statistical decision-making mechanisms Often, experiments in biomedicine and other health-related sciences involve mathe- matically formalized tests, employing appropriate and efficient statistical procedures to analyze data. Mathematical strategies to make decisions via formal rules play important roles in medical and epidemiological discovery, in policy formulation, and in clinical practice. In this context, in order to make conclusions about populations on the basis of samples from those populations, clinical trials commonly require the application of the mathematical statistical discipli ne. The aim of the scientific methods in decision theory is to simultaneously max- imize quantified gains and minimize losses in reaching a conclusion. For example, statements of clinical experiments can request to maximize factors (gains) such as Oxidative Stress and Antioxidant Protection: The Sdence of Free Radical Biology & Disease, First Edition. Edited by Donald Armstrong and Robert D. Stratton. © 2016 John Wiley & Sons, Inc. Published 2016 by John Wtley & Sons, Inc. 507