The Sample Size Calculation in Clinical Trials and Comparisons with Classical Approaches
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linical trials are well-planned studies. One of the earlier steps in clinical trials is the determination of sample size. The question "how many subjects should be used?" must be answered carefully by considering many important aspects of the study. Some of the clinical trials might be too expensive. Besides, in some of them, finding subjects may be difficult to include clinical trials. For such these reasons, it is not efficient including either too few or too many subjects in clinical trials. Therefore, sample size calculation is an important issue in clinical trials due to ethical, economic and scientific reasons. There are several factors that affect the sample size such as study design, trial objectives or clinical important difference. In this thesis, we give an overview of sample size calculation in clinical trials. Parallel group and cross-over study designs are taken into account. We also considered equality, superiority, non-inferiority and equivalence trials for two samples. First, we gave proofs of sample size calculations with both known and population variance. Then, we show numeric examples to clarify sample size calculation. Additionally, we share how these calculations are carried out RStudio. We also create simulation scenarios under different distributions, trial objectives, sample size with the clinical important difference and specified effect sizes to compare observed power. We show that the observed power is highest in non-inferiority trials compared to superiority and equality trials based on same clinical important difference, Type I error, study design and sample size. The observed power is higher in cross-over design compared to parallel group design with same clinical important difference, Type I error, trial objective and sample size. The responses are created under different distributions, however; there is no considerable effect of different distributions on observed power.