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1
Introduction
In clinical research, during the planning stage of a clinical study, the following questions are of particular interest to the investigators: (i) How many subjects are needed to have a desired power for detecting a clinically meaningful difference (e.g., an 80% chance of correctly detecting a clinically meaningful difference)? (ii) What is the trade off between cost-effectiveness and power if only a small number of subjects are available for the study due to limited budget and/or certain medical considerations. To address these questions, a statistical evaluation for sample size calculation is often performed based on certain statistical inference (e.g., power or confidence interval) of the primary study endpoint with certain assurance. In clinical research, sample size calculation plays an important role for assuring validity, accuracy, reliability, and integrity of the intended clinical study.
For a given study, sample size calculation is usually performed based on some statistical criteria controlling type I error (e.g., a desired confidence level) and/or type II error (i.e., a desired power). For example, we may choose sample size in such a way that there is a desired precision at a fixed confidence level (i.e., fixed type I error). This approach is referred to as precision analysis for sample size calculation. The method of precision analysis is simple and easy to perform and yet it may have a small chance of correctly detecting a true difference. As an alternative, the method of prestudy power analysis is usually conducted to estimate sample size. The concept of the prestudy power analysis is to select the required sample size for achieving the desired power for detecting a clinically or scientifically meaningful difference at a fixed type I error rate. In clinical research, the prestudy power analysis is probably the most commonly used method for sample size calculation. In this book, we will focus on sample size calculation based on power analysis for various situations in clinical research.
In clinical research, to provide an accurate and reliable sample size calculation, an appropriate statistical test for the hypotheses of interest is necessarily derived under the study design. The hypotheses should be established to reflect the study objectives under the study design. In practice, it is not uncommon to observe discrepancies among study objectives (hypotheses), study design, statistical analysis (test statistic), and sample size calculation. These discrepancies can certainly distort the validity and integrity of the intended clinical trial.
In Section 1.1, regulatory requirement regarding the role of sample size calculation in clinical research is discussed. In Section 1.2, we provide some basic considerations for sample size calculation. These basic considerations include study objectives, design, hypotheses, primary study endpoint, and clinically meaningful difference. The concepts of type I and type II errors and procedures for sample size calculation based on precision analysis, power analysis, probability assessment, and reproducibility probability are given in Section 1.3. The aim and structure of this book is given in Section 1.4.2.
1.1Regulatory Requirement
As indicated in Chow and Liu (1998, 2003, 2013), the process of drug research and development is a lengthy and costly process. This lengthy and costly process is necessary not only to demonstrate the efficacy and safety of the drug product under investigation, but also to ensure that the study drug product possesses good drug characteristics such as identity, strength, quality, purity, and stability after it is approved by the regulatory authority. This lengthy process includes drug discovery, formulation, animal study, laboratory development, clinical development, and regulatory submission. As a result, clinical development plays an important role in the process of drug research and development because all of the tests are conducted on humans. For approval of a drug product under investigation, the United States Food and Drug Adminis...
