Methods and Applications of Statistics in Clinical Trials, Volume 2: Planning, Analysis, and Inferential Methods

Chapter 39

Sample Size for Comparing Means

Hansheng Wang and Shein-Chung Chow

39.1 Introduction

Sample size calculation plays an important role in clinical research. In clinical research, a sufficient number of patients is necessary to ensure the validity and the success of an intended trial. From a statistical point of view, if a clinically meaningful difference between a study treatment and a control truly exists, such a difference can always be detected with an arbitrary power as long as the sample size is large enough. However, from the sponsor’s point of view, it is not cost-effective to have an arbitrary sample size because of limited resources for a given time frame. As a result, the objective of sample size calculation in clinical research is to obtain the minimum sample size needed for achieving a desired power for detecting a clinically meaningful difference at a given level of significance. For good clinical practice, it is suggested that sample size calculation/justification should be included in the study protocol before conducting a clinical trial [1].

In practice, the objective of a clinical trial can be classified into three categories: testing treatment effect, establishing equivalence/noninferiority, and demonstrating superiority. More specifically, a clinical trial could be conducted to evaluate the treatment effect of a study drug, it could be conducted to establish therapeutic equivalence/noninferiority of the study drug as compared with an active control agent ...